Bank Earnings Management and Tail Risk during the Financial Crisis

Transcription

1 LEE J. COHEN MARCIA MILLON CORNETT ALAN J. MARCUS HASSAN TEHRANIAN Bank Earnings Management and Tail Risk during the Financial Crisis We show that a pattern of earnings management in bank financial statements has little bearing on downside risk during quiet periods, but seems to have a big impact during a financial crisis. Banks demonstrating more aggressive earnings management prior to 2007 exhibit substantially higher stock market risk once the financial crisis begins as measured by the incidence of large weekly stock price crashes as well as by the pattern of full-year returns. Stock price crashes also predict future deterioration in operating performance. Bank regulators may therefore interpret them as early warning signs of impending problems. JEL codes: G01, G11, G21, G28, M40 Keywords: financial institutions, earnings management, crashes, financial crisis. BANK INVESTORS HAVE LONG been concerned with tail risk, that is, extreme declines in a bank s stock price. The financial crisis of only heightened this concern. While regulators are more concerned with operating performance than stock prices per se, they too must be concerned with dramatic stock price declines to the extent that such declines signal deterioration in future performance (as we show below). Moreover, contingent capital regulation with market value triggers also can make stock prices relevant to regulators. The authors are grateful to Jim Booth, Ozgur Demirtas, Atul Gupta, Jim Musumeci, Jun Qian, Sugata Roychowdhury, Ronnie Sadka, Phil Strahan, and seminar participants at Boston College for their helpful suggestions. LEE J. COHEN is Assistant Professor of Finance, Finance Department, University of Georgia ( leecohen@uga.edu). MARCIA MILLONCORNETTis Professor of Finance, Finance Department, Bentley University ( mcornett@bentley.edu). ALAN J. MARCUS is Mario J. Gabelli Professor of Finance, Finance Department, Boston College ( alan.marcus@bc.edu). HASSAN TEHRANIAN is the Griffith Family Millennium Chair in Finance, Finance Department, Boston College ( hassan.tehranian@bc.edu). Received January 25, 2012; and accepted in revised form November 6, Journal of Money, Credit and Banking, Vol. 46, No. 1 (February 2014) C 2014 The Ohio State University

2 172 : MONEY, CREDIT AND BANKING While tail risk is determined in large part by bank financial policies such as the composition of on- and off-balance-sheet asset and liability portfolios, the ability to assess that risk also depends on bank reporting and accounting policies. For example, banks have discretion in setting the level of several key income statement accounts such as provisions for loan losses, and they can use that discretion to modulate the transparency, or opacity, of their financial reports. While earnings management may not directly cause tail events, it nevertheless may affect the best estimate of tail exposure conditional on observable bank attributes. For example, Jin and Myers (2006) and several others have shown for industrial firms that reductions in transparency are associated with increased tail risk. This paper asks whether the association between earnings management, which may be used to obscure true performance, and tail risk also characterizes banks, and, in particular, whether earnings management predicted bank performance during the financial crisis. Earnings management can increase the risk of extreme stock market returns if it limits the availability of information about the firm. In Jin and Myers (2006), firm managers use their discretion to impede the flow of public information about firm performance. Managers normally have an incentive to postpone the release of bad news, but in some circumstances either that incentive or the ability to hide information collapses, leading to a sudden release of accumulated negative information and a firm-specific stock price crash. In a more general setting, even if earnings management is not strategically exploited by managers, it still might result in fatter-tailed return distributions if it interrupts the steady flow of information to outside investors. Discrete information events will be reflected in substantial stock price movements. This should be true of financial as well as industrial firms. Much of the earnings management literature for industrial firms has focused on the manipulation of accruals: a pattern of departures from a simple statistical model of normal accruals is taken as evidence of earnings management (Healy 1985, Dechow, Sloan, and Sweeny 1995, Cohen, Dey, and Lys 2005). Hutton, Marcus, and Tehranian (2009) propose a measure of earnings management based on abnormal accruals and find that it is in fact associated with tail risk, suggesting that it does cause information to reach the market in discrete episodes rather than diffusing steadily and continuously. In light of widespread concern over tail risk in financial institutions as well as the emerging literature linking financial statement opacity to crash risk for industrial firms, it is interesting to know whether a measure of earnings management, appropriately defined for banks, would similarly predict increased probability of tail risk, and in turn whether tail events in stock prices can provide timely warnings of risk in operating performance. Of course, accruals for banks reflect different considerations than those that drive accruals for industrial firms. Earnings management in banks typically is measured by the proclivity to make discretionary loan loss provisions or by discretionary realizations of security gains or losses. For example, Cornett, McNutt, and Tehranian (2009) estimate a measure of bank earnings management using these variables and find that it exhibits the reasonable properties of being positively related to CEO pay-for-performance sensitivity and

3 LEE J. COHEN ET AL. : 173 inversely related to board independence. Adopting a similar approach, we show in this paper that, like industrial firms, banks also display a positive relation between apparent earnings management and tail risk. However, in contrast to industrial firms, bank tail risk typically is not evident in normal periods, and therefore is hard to evaluate even from long sample periods. Nevertheless, earnings management seems to have a substantial association with tail risk in crisis periods. This pattern poses a difficult challenge for regulators, who are concerned most of all about large losses. Our results suggest that earnings management might usefully be considered a reliable proxy for exposure to large losses during periods of financial stress. The remainder of the paper is organized as follows. In Section 1, we briefly review the literature on tail risk and earnings management. As part of this review, we discuss how measures of earnings management for industrial firms must be modified for banks. Section 2 discusses our sample and data sources. Section 3 presents empirical results. We begin with an analysis and justification of our measure of bank earnings management, and proceed to demonstrate that this measure and downside risk appear to be positively related. Finally, Section 4 concludes the paper, where we consider the policy implications for banks and their regulators. 1. RELATED LITERATURE 1.1 Earnings Management and Crash Risk Jin and Myers (2006) present a model in which lack of full transparency concerning firm performance enables managers to capture a portion of the firm s cash flows. To protect their positions, managers may manage earnings by hiding temporary losses to avoid disclosing negative performance. However, if performance is bad enough, managers may be unwilling or unable to conceal any more losses. At this point, all of the previously unobserved negative performance information becomes public at once, resulting in a firm-specific stock price crash. 1 Jin and Myers measure transparency using characteristics of the broad capital market in which the firm is situated and find that cross-sectionally (i.e., across countries), less transparent markets exhibit more frequent crashes. Hutton, Marcus, and Tehranian (2009) further test the Jin and Myers model by developing a firm-specific measure of earnings management and show that it predicts higher crash risk at the firm-specific level as well. Consistent with these results, Kothari, Shu, and Wysocki (2009) provide evidence, based on voluntary management earnings forecasts, that managers withhold bad news when possible. A common measure of earnings management in industrial firms is based on discretionary accruals from the modified Jones (1991) model (Dechow, Sloan, and Sweeney 1. In the Jin and Myers model, insiders can actually divert cash flow to themselves. This would be difficult in the banking context, but even here, managers can increase their compensation by artificially meeting earnings targets. Of special interest is the possibility that a history of nondecreasing earnings that induces investors to view the bank as low risk may increase the stock price and the value of equity-based compensation. This risks a sudden dramatic change (and a stock price crash) if the bank is later forced to report a decrease in earnings, as in Jin and Myers.

4 174 : MONEY, CREDIT AND BANKING 1995). Specifically, normal accruals are estimated from a simple statistical model based on firm assets, property, plant, and equipment, and change in sales. Abnormal or discretionary accruals are the residuals between actual accruals and the predicted accruals from the modified Jones model. Firms with consistently large discretionary accruals are deemed more likely to be manipulating earnings, or at the very least, have less transparent financial statements. Healy (1985) concludes that managers use discretionary accruals to manipulate bonus income. Sloan (1996) shows that the market seems not to fully recognize the information content of accruals management, and Dechow, Sloan, and Sweeney (1996) argue that patterns of large discretionary accruals can be used to detect earnings management. Cohen, Dey, and Lys (2005) find that abnormal accruals tend to be larger when management compensation is more closely tied to stock value. Finally, as noted above, Hutton, Marcus, and Tehranian (2009) find that abnormally large discretionary accruals are associated with crash risk (which they define as 3-sigma declines in stock price). Clearly, measures of abnormal accruals from the Jones (1991) model need to be modified for banks or other financial institutions that are not engaged in salesbased businesses. Instead, the focus for banks typically tends to be on loan loss provisions or the realizations of gains or losses on securities, both of which allow considerable management discretion. Leeway in these variables may be used to smooth earnings (Beatty, Ke, and Petroni 2002) or to shore up regulatory capital (Beaver and Engel 1996, Ahmed, Takeda, and Thomas 1999). Notice that these goals conflict with transparency by making it more difficult for outside analysts to discern the true financial condition of the firm. Such practices presumably impede information flow, and it is at least conceivable that they also make information more lumpy, particularly as the limits of accounting discretion are reached. In the next subsection, we consider earnings management in banks more closely. 1.2 Earnings Management in Banks Loan loss provisions are an expense item on the income statement, reflecting management s current assessment of the likely level of future losses from defaults on outstanding loans. The recording of loan loss provisions reduces net income. Commercial bank regulators view accumulated loan loss provisions, the loan loss allowance account on the balance sheet, as a type of capital that can be used to absorb losses. A higher loan loss allowance balance allows the bank to absorb greater unexpected losses without failing. Symmetrically, if the loan loss allowance is less than expected losses, the bank s capital ratio will overstate its ability to sustain unexpected losses. In addition to loan loss provisions, banks also have discretion in the realization of security gains and losses (Beatty, Chamberlain, and Magliolo 1995, Beatty Ke, and Petroni 2002). Unlike loan loss provisions, security gains and losses are relatively unregulated and unaudited discretionary choices. It is unlikely that auditors, regulators, or shareholders will subsequently take issue with a manager s decision to sell an investment security that happens to increase or decrease earnings.

5 LEE J. COHEN ET AL. : 175 Thus, realized security gains and losses represent a second way that management has been able to smooth or otherwise manage earnings. More recently, however, evolving accounting rules, particularly SFAS 157 (which took effect in November 2007), have increased scrutiny of earnings management achieved through the recording of gains or losses in the securities portfolio. Fair value accounting requires assets and liabilities to be listed on a firm s balance sheet at current values. Thus, bank earnings can be affected by security sales only to the extent that values have changed over the very short term. As discussed below, our sample period runs from 1997 through Thus, the ability to manage earnings by strategically realizing securities gains or losses decreases during the period of our analysis. 2 Consistent with these considerations, previous studies have found that banks use both loan loss provisions and securities gains and losses to manage earnings and capital levels. Scholes, Wilson, and Wolfson (1990) find that capital positions play a role in banks willingness to realize gains on municipal bonds. Collins, Shackelford, Wahlen (1995), Beaver and Engel (1996), and Ahmed, Takeda, and Thomas (1999) find that discretionary accruals are negatively related to capital, although Beatty, Chamberlain, and Magliolo (1995) reach the opposite conclusion. Wahlen (1994) shows that managers increase discretionary loan loss provisions when they expect future cash flows to increase. Finally, Beatty, Ke, and Petroni (2002) find that public banks are more likely than private ones to use loan loss provisions and realized securities gains and losses to eliminate small earnings decreases. By and large, both loan loss provisions and the realization of securities gains and losses appear to be opportunistically used to manage earnings. Indeed, earnings management may be used to discreetly smooth earnings over time or to eventually take a big bath, that is, report one drastic earnings decline after hiding a series of smaller declines in previous years (Arya, Glover, and Sunder 1998, Demski 1998), a pattern consistent with infrequent but large stock market declines. 2. DATA The sample examined in this study includes all publicly traded banks headquartered in the United States and operating during the 1997 through 2009 period. We use bank characteristics measured in the decade prior to the financial crisis to predict tail risk in both the precrisis period, , and the crisis period, All accounting data are obtained from the Y-9C consolidated Bank Holding Company (BHC) database, which aggregates bank affiliates and subsidiaries to the bank holding company level for U.S. domestic banks, found on the Chicago Federal Reserve s 2. In addition, in March 2009, ASC320 required financial institutions to recognize other than temporary impairment (OTTI) on their available-for-sale (AFS) and held-to-maturity (HTM) portfolios. If the loss is considered temporary, the adjustment is reported in other comprehensive income and may be subsequently recovered if the value of the investment returns. However, if management considers the loss other than temporary, the loss is charged to operations and subsequent recoveries of fair value are not recorded in earnings until the investment is sold. Banks treatment of OTTI could be viewed as a way of obscuring their performance.

6 176 : MONEY, CREDIT AND BANKING TABLE 1 NUMBER OF COMMERCIAL BANKS IN THE SAMPLE Year BHCs Total 4,112 NOTE: This table lists the distribution of the sample bank holding companies (BHCs) by year. All accounting data are obtained from FFIEC Call Reports databases found on the Chicago Federal Reserve s website ( website, Bank stock return data are collected from the Center for Research in Security Prices (CRSP) database. Table 1 lists the number of publicly traded banks with available consolidated BHC data by year in our sample. Our analysis includes a total of 4,112 bank-years. 2.1 Discretionary Loan Loss Provisions and Security Sales Variation in bank earnings is driven predominately by the performance of the loan portfolio. Loans over 90 days past due and still accruing interest as well as loans no longer accruing interest are observable measures of the current loans at risk of default. While a portion of the loan loss provisions set aside for these obviously bad loans will be standard and nondiscretionary, there is considerable room for judgment in the eventual losses that will be realized on these as well as healthier loans. Banks therefore may manage earnings through allowable discretion in the recording of loan loss provisions. In principle, each bank manager s basis for judgment with respect to these provisions is subject to periodic review by regulators. 3 However, in practice, large banks in particular appear to have considerable discretion: Gunther and Moore (2003) find that while there are many instances of regulator mandated revisions in loan loss provisions, only six in their study involve banks with over $500 million in total assets and only four involve banks that are publicly traded. In addition, as noted above, banks also have had leeway to manage earnings through the discretionary 3. Managerial judgment must be based on a reviewable record as noted in the Chicago Federal Reserve s Micro Data Reference Manual s data dictionary in its description of Item BHCK4230: Provision for Loan and Lease Losses. The item should... include the amount needed to make the allowance for loan and lease losses... adequate to absorb expected... losses, based upon management s evaluation of the loans and leases that the reporting bank has the intent and ability to hold for the foreseeable future or until maturity or payoff.

7 LEE J. COHEN ET AL. : 177 realization of security gains and losses, particularly prior to 2007 and the enactment of SFAS 157. The challenge is to devise a measure of discretionary loan loss provisions and discretionary realization of securities gains and losses and combine them into a measure of earnings management. We employ the Beatty, Ke, and Petroni (2002) model of normal loan loss provisions using OLS regressions that allow for both year and regional (specifically, eight regional districts defined by the Comptroller of the Currency) fixed effects. We estimate the model in the period ending in 2006, the last full year before the onset of the financial crisis. This ending date ensures that disruptions to normal bank behavior patterns elicited by the crisis will not affect our estimates of normal reserving behavior. Their regression model is: 4 LOSS it = α tr + β 1 LNASSET it + β 2 NPL it + β 3 LLR it + β 4 LOANR it + β 5 LOANC it + β 6 LOAND it + β 7 LOANA it + β 8 LOANI it + β 9 LOANF it + ε it, (1) where i = bank holding company identifier; t = year (1994 to 2006); r = U.S. Office of the Comptroller of the Currency defined district number; α tr = fixed effect for region and year; LOSS = loan loss provisions as a fraction of total loans; LNASSET = the natural log of total assets; NPL = nonperforming loans (includes loans past due 90 days or more and still accruing interest and loans in nonaccrual status) as a percentage of total loans; LLR = loan loss allowance as a fraction of total loans; LOANR = real estate loans as a fraction of total loans; LOANC = commercial and industrial loans as a fraction of total loans; LOAND = loans to depository institutions as a fraction of total loans; LOANA = agriculture loans as a fraction of total loans; LOANI = consumer loans as a fraction of total loans; LOANF = loans to foreign governments as a fraction of total loans; ε = error term. The fitted value in equation (1) represents normal loan losses based on the composition of the loan portfolio, and therefore, the residual of the regression is taken 4. Cornett, McNutt, and Tehranian (2009) also employ the Beatty, Ke, and Petroni (2002) model. However, they use the level of nonperforming loans on the right-hand side, whereas Beatty, Ke, and Petroni use the change in nonperforming loans. We experimented with both specifications, and found that it made no difference to our results. We present the results using levels, as it allows our sample to begin a year earlier.

8 178 : MONEY, CREDIT AND BANKING as the abnormal or discretionary component of loan loss provisions. 5 However, because equation (1) models loan loss provisions as a fraction of total loans, while our measure of earnings management (defined below) is standardized by total assets, we transform the residual from equation (1) and define our measure of discretionary loan loss provisions (DISC_LLP it )as DISC LLP it = ε it LOANS it ASSETS it, (2) where LOANS it = total loans and ASSETS it = total assets of bank i in year t. To find discretionary realizations of gains and losses on securities, we again follow Beatty, Ke, and Petroni (2002). We estimate the following OLS regression over the precrisis period with time fixed effects. Their model of normal realized security gains and losses (GAINS it )is GAINS it = α t + β 1 LNASSET it + β 2 UGAINS it + ε it, (3) where i = bank holding company identifier; t = year (1994 to 2006); GAINS = realized gains and losses on securities as a fraction of beginning-ofyear total assets (includes realized gains and losses from availablefor-sale securities and held-to-maturity securities); LNASSET = the natural log of beginning-of-year total assets; UGAINS = unrealized security gains and losses (includes only unrealized gains and losses from available-for-sale securities) as a fraction of total assets at the beginning of the year; ε = error term. The residual from equation (3) is taken as the discretionary component of realized security gains and losses (DISC_GAINS it ). Panel A of Table A1 in the Appendix summarizes the variables used to find discretionary and nondiscretionary loan loss provisions and realized securities gains, Panel B reports descriptive statistics for all variables in equations (1) through (3), and Panel C presents the results of the regressions in equations (1) and (3). Note that higher levels of loan loss provisions decrease earnings, while higher levels of realized securities gains and losses increase earnings. Accordingly, we define bank i s discretionary earnings in year t, DISC_EARN it, as the combined impact of discretionary loan loss provisions and discretionary realization of securities 5. This approach is analogous to the common use of the modified Jones model to derive normal accruals for industrial firms and the use of residuals from that model as a measure of discretionary accruals. Our procedure differs for the crash years, however. As noted above, we apply the coefficients estimated through 2006 to bank data in to estimate discretionary loan loss provisions during those years. Therefore, disruptions to bank activities during the crash will not distort our estimates of normal bank behavior.

9 LEE J. COHEN ET AL. : 179 TABLE 2 SUMMARY STATISTICS FOR BANKS,PRECRISIS YEARS: Panel A. Descriptive statistics on discretionary earnings variables Mean Median Std dev 1st%ile 99th%ile Observations DISC_EARN (%) ,267 DISC_LLP (%) ,267 DISC_GAINS (%) ,267 Return on assets (%) ,267 Panel B. Descriptive statistics on earnings management variables EARN_MGT (%) ,267 LLP_MGT (%) ,267 GAINS_MGT (%) ,267 Panel C. Descriptive statistics on bank stock market performance Worst-week return (%) ,267 Residual standard deviation (%) ,267 NOTE: This table provides summary statistics for all variables used in the analysis. DISC_EARN = discretionary earnings as a percent of total assets = DISC_GAINS DISC_LLP, DISC_LLP = discretionary loan loss provisions as a percent of total assets, DISC_GAINS = discretionary realized security gains and losses as a percentage of total assets. Return on assets = net income in year t/total assets at end of year t. EARN_MGT = DISC_EARN t 1 + DISC_EARN t 2 + DISC_EARN t 3 LOAN_MGT = DISC_LLP t 1 + DISC_LLP t 2 + DISC_LLP t 3 GAINS_MGT = DISC_GAINS t 1 + DISC_GAINS t 2 + DISC_GAINS t 3 Panel C statistics on bank performance are summary statistics of annual data for the sample of banks pooled across years. Worst-week return is lowest bank-specific return over the course of each fiscal year. Residual standard deviation is the standard error of regression residuals from the estimation of an index model regression, equation (8), of bank returns against the return on the CRSP value-weighted market index and the Fama French bank industry index. Each regression is estimated for each bank using weekly observations for the year. gains or losses: DISC EARN it = DISC GAINS it DISC LLP it. (4) High levels of DISC_EARN amount to underreporting of loan loss provisions and/or higher realizations of securities gains, which, ceteris paribus, increase income. Negative values for DISC_EARN would indicate that loan loss provisions are overreported and/or fewer security gains are realized, both of which decrease reported operating income. Panel A of Table 2 reports descriptive statistics for each variable in equation (4), estimated over the precrisis period, The average level of both discretionary loan loss provisions and realized securities gains (both as a percent of assets) are measured as departures from normal behavior (i.e., as regression residuals), and therefore by construction, are virtually zero. 7 However, there is meaningful variation in these 6. The exclusion of from these summary statistics explains why there are 4,112 banks in Table 1, but only 3,267 observations in Table 2. Also, while the behavioral equations (1) and (3) are estimated over the period, the final sample period does not begin until 1997 because some of the variables used in the following regression analysis entail 3-year lagged values (see below). 7. The average value is not precisely zero because, while we estimate equations (1) and (3) over the period, the final sample begins in 1997 as the earnings management variables are defined as 3-year moving sums of lagged values.

10 180 : MONEY, CREDIT AND BANKING 2.0% 1.8% 1.6% 1.4% 1.2% 1.0% 0.8% 0.6% 0.4% 0.2% 0.0% FIG. 1. Standard Deviation of Discretionary Earnings. NOTE: Cross-sectional standard deviation of discretionary earnings, DISC_EARN, across the sample of banks in each year. Discretionary earnings equal discretionary realization of securities gains or losses minus discretionary loan loss provisions, each expressed as a percentage of total assets. numbers. Discretionary loan loss provisions, DISC_LLP, in the precrisis period range from a 1st percentile value of 0.481% to a 99th percentile value of 0.867% of assets, with a standard deviation (across banks and time) of 0.257% of assets. The corresponding range for realized securities gains is from 0.656% to 0.764% of assets, with a standard deviation of 0.281% of assets. The standard deviation of discretionary earnings, DISC_EARN, is 0.370% of assets, indicating that a nontrivial portion of the variation in reported bank performance (the standard deviation of bank ROA is 0.614%) is due to management s discretionary accounting and security sales choices. Figure 1 plots the standard deviation across banks of DISC_EARN in each year. Notice the dramatic increase in the cross-sectional standard deviation of discretionary earnings in the period. This may indicate that normal bank behavior as expressed in equation (4) significantly changes during the crisis. We therefore will focus primarily on patterns computed prior to The next section offers further evidence on accounting discretion. 2.2 Earnings Management Table 3 examines the time-series properties of discretionary earnings, DISC_EARN, as well as its two components, discretionary loan loss provisions, DISC_LLP, and discretionary realizations of gains or losses on securities, DISC_GAINS. We regress each of these variables on their own past values in the previous 3 years. We estimate the relation over the precrisis period, , because Figure 1 suggests that the extreme events of the crisis years might disrupt the patterns that characterized each bank in the previous decade.

11 LEE J. COHEN ET AL. : 181 TABLE 3 TIME-SERIES BEHAVIOR OF COMPONENTS OF DISCRETIONARY BANK EARNINGS Dependent variable Explanatory variable Coefficient t-statistic Panel A. Discretionary earnings DISC_EARN DISC_EARN( 1) DISC_EARN( 2) DISC_EARN( 3) Observations 3,267 Fixed effects Y Panel B. Discretionary loan loss provisions DISC_LLP DISC_LLP( 1) DISC_LLP( 2) DISC_LLP( 3) Observations 3,267 Fixed effects Y Panel C. Discretionary securities gains/losses DISC_GAINS DISC_GAINS ( 1) DISC_GAINS ( 2) DISC_GAINS ( 3) Observations 3,267 Fixed effects Y NOTE: Each component of earnings management is regressed on its own lagged values. Observations are annual over the period Discretionary items are estimated as residuals from equations that predict loan loss provisions and realized securities gains and losses based on bank characteristics (see Beatty, Ke, and Petroni 2002). The models of normal loan loss provisions and realized securities gains and losses are contained in the Appendix. These regressions are estimated with bank and year fixed effects. Panel A of Table 3 shows that in the short term (i.e., at a 1-year lag), discretionary earnings exhibit positive serial correlation, with a positive and statistically significant coefficient (0.105) on the 1-year lagged value. However, at longer lags of 2 or 3 years, this relation reverses. The coefficients at these lags ( and 0.150, respectively) are negative, highly significant, and of considerably greater combined magnitude than the coefficient on the 1-year lag. When we decompose discretionary earnings into its two components, we find precisely the same patterns (Panels B and C). Both discretionary loan loss provisions as well as discretionary realizations of securities gains or losses show the same positive serial correlation at 1-year horizons, but negative and larger combined serial correlations at the 2- and 3-year horizons. This pattern suggests that discretionary contributions to earnings due either to abnormal loan loss provisions or to security sales show a reliable tendency to reverse in later years. If managers consistently employ unbiased estimates of future loan losses to determine the proper level of current reserves, we would find no time-series dependence in the discretionary loan loss series. The significant time-series patterns that actually characterize the data suggest that loan loss provisions are subject to strategic considerations. Managers may use their discretion in choosing loan losses to paint some desired picture of the firm. But over time, as accumulated loan loss provisions must be reconciled to actual loss experience, those discretionary choices must be reversed.

12 182 : MONEY, CREDIT AND BANKING Similarly, the reversal patterns in realized gains or losses on security sales suggest that managers selectively choose securities to sell based in part on the contribution to current earnings, leaving them with a preponderance of offsetting gains or losses on future sales. The pattern revealed in Table 3 is highly reminiscent of the literature on discretionary accruals that has been used to examine earnings management in industrial firms. There too we observe some short-term momentum in discretionary accruals followed by reversals. For example, Dechow, Sloan, and Sweeney (1996) examine the pattern of discretionary accruals for known earnings manipulators, specifically, firms subject to enforcement actions by the SEC. Discretionary accruals gradually increase as the alleged year of earnings manipulation approaches and then exhibit a sharp decline. The initial increase in discretionary accruals is consistent with manipulation to increase reported earnings: the decline, with the reversal of prior accrual overstatements. Our results on discretionary choices for banks similarly demonstrate a pattern of reversals that undoes prior distortion of reported earnings. Therefore, we define earnings management, EARN_MGT, as the 3-year moving sum of the absolute value of DISC_EARN. Although managers may prefer accounting choices that increase earnings, following Hutton, Marcus, and Tehranian (2009), who look at earnings management and crash risk in industrial firms, we use absolute values of discretionary earnings rather than signed values. Both positive and negative abnormal earnings may indicate a tendency to manage earnings: discretionary accounting choices that artificially enhance reported earnings in one period eventually must be reversed. Like them as well, we use the 3-year moving sum (instead of a 1-year value) to capture the multiyear effects of discretionary choices because the moving sum is more likely to reflect sustained, underlying bank policy. EARN MGT = DISC EARN t 1 + DISC EARN t 2 + DISC EARN t 3. (5) We also break earnings management into its components, loan loss provisions and realized securities gains and losses, to see whether one or the other of these sources of discretionary behavior has greater association with tail risk. Therefore, we also evaluate the following 3-year moving sums: Loan loss management: LLP MGT = DISC LLP t 1 + DISC LLP t 2 + DISC LLP t 3. (6) Securities gains/losses management: GAINS MGT = DISC GAINS t 1 + DISC GAINS t 2 + DISC GAINS t 3. (7) Panel B of Table 2 presents descriptive statistics for these variables in the precrisis years. The mean value of EARN_MGT (computed over the preceding 3 years, t 3 to t 1) is 0.601% of assets. The mean value of LLP_MGT is 0.430% of assets, and

13 LEE J. COHEN ET AL. : 183 the mean of GAINS_MGT is 0.380%. 8 During the period, mean return on assets is 1.090%. Therefore, these values are appreciable fractions of typical ROA. 2.3 Tail Risk We are ultimately concerned with tail risk, specifically, the impact of crosssectional variation in earnings management on the incidence of extreme negative returns. Therefore, we need to net out that portion of returns attributable to common market factors and industry effects. Bank-specific returns are defined as the residuals from an expanded index model with both market and bank-industry factors. We estimate equation (8) each bank-year using weekly data, and allow for nonsynchronous trading by including two lead and lag terms for the market and industry indexes (Dimson 1979) 9 r j,t = α j + β 1, j r m,t 2 + β 2, j r i,t 2 + β 3, j r m,t 1 + β 4, j r i,t 1 + β 5, j r m,t + β 6, j r i,t + β 7, j r m,t+1 + β 8, j r i,t+1 + β 9, j r m,t+2 + β 10, j r i,t+2 + ε j,t, (8) where r j,t is the stock market return of bank j in week t, r m,t is the CRSP valueweighted market index, and r i,t is the Fama French value-weighted bank industry index. The residual of equation (8), ε j,t, is the bank-specific return in each week. Our bank-specific crashes therefore represent extreme price movements over and above those due to market-wide and industry-wide events. Summary statistics for worst-week bank-specific returns and residual risk in the precrisis years appear in Panel C of Table 2. The average residual standard deviation of bank-specific stock returns in this period is 3.098%. Figure 2 shows that this value is fairly consistent over the precrisis period. Under the assumption that bank-specific returns are normally distributed, the expected value of the worst-week bank-specific return in a sample of 52 weekly observations would be 2.26 standard deviations below the mean; with a mean of zero and standard deviation of 3.098% for the precrisis period, this would imply an expected worst-week return of % = 7.00%. In fact, the sample-average worst-week return in the precrisis period is 7.138%, suggesting that, at least prior to the crisis, fat-tailed distributions are not an issue. However, Figure 2 demonstrates that residual standard deviations rise sharply with the onset of the crisis. As bank-specific returns already control for market and industry performance, this pattern indicates that banks are differentially affected by the crisis, leading to greater within-industry dispersion of returns. Part of the increase in cross-sectional dispersion, of course, is due to the sharp increase in the incidence of banks that suffer a crash during the financial crisis. 8. These values do not add up because the absolute value of a sum is not the sum of absolute values. 9. Results using only one lead and lag of weekly returns were nearly identical.

14 184 : MONEY, CREDIT AND BANKING 8% Residual standard deviation of weekly return 7% 6% 5% 4% 3% 2% 1% 0% FIG. 2. Standard Deviation of Bank-Specific Weekly Rates of Return. NOTE: Standard error of regression residuals from estimation of index model regression, equation (8), of bank returns against the return on the CRSP value-weighted market index and the Fama French bank-industry index. Each regression is estimated for each bank using weekly observations for the year. The residual standard deviations are averaged across banks in each year. TABLE 4 INCIDENCE AND AVERAGE MAGNITUDE OF WEEKLY CRASHES Year Percentage crashes Mean crash (measured in standard deviations) Median crash (measured in standard deviations) % % % % % % % % % % % % % NOTE: The percentage of crashes equals the fraction of banks with at least 1 week in the year with bank-specific returns less than 3.09 standard errors below the mean. The mean (median) crash is the average (median) across banks of the weekly stock return during crash weeks, expressed as a multiple of the bank-specific standard deviation. Table 4 presents annual measures of crash propensity. We measure residual standard deviation for each bank in each year. 10 If returns in the coming year are normally 10. Once we reach the crisis years, however, bank-specific crashes will have large impacts on the estimate of cross-sectional dispersion in that year. To avoid the resulting overestimate in residual standard

15 LEE J. COHEN ET AL. : 185 distributed, only 0.1% of banks in any week would be expected to exhibit bankspecific returns less than 3.09 standard deviations below their mean value, and in any year, only 1 ( ) 52 = or 5.07% of banks would experience a week with returns below this level. In fact, crash incidence exceeds this value. Table 4 shows for each year the actual percentage of banks with firm-specific returns in at least 1 week falling below this cutoff. The percentage in the precrisis years is generally between 5% and 10%, but it balloons to 74.2% in The negative returns corresponding to these crashes are quite large; in the precrisis period, the median bank-specific loss in a crash week is roughly 3.39 times the weekly residual standard error from equation (8), or about 10.5%, while in the period the median loss in a crash week is 4.49 times the standard error. 3. EMPIRICAL RESULTS 3.1 Crash Risk Table 5 presents an analysis of the association between crash risk and earnings management. The table reports probit (panel) regressions for the likelihood of a bankspecific crash in any year. The dependent variable (indicating a crash) is assigned a value of 1 if in any week in that year the bank-specific return is less than 3.09 times the bank-specific standard deviation. The right-hand-side variables of interest are EARN_MGT or, in alternative specifications, its two components, LLP_MGT or GAINS_MGT. These are winsorized at their 1st and 99th percentile values. We also interact these explanatory variables with a financial crisis dummy to allow them to have different effects during the crisis period. The additional controls are total bank assets, bank capital ratio, 11 and the Amihud (2002) measure of stock illiquidity. Amihud s measure equals the ratio of the absolute value of daily stock returns divided by daily dollar trading volume, averaged over the year. Less liquid stocks may be more prone to tail events, as they are less able to absorb sudden shifts in demand. The regressions are estimated with year fixed effects. 12 Column (1) of Table 5 employs EARN_MGT as the right-hand-side variable, while column (2) breaks out earnings management into its two component terms. In columns (1) and (2), the coefficients on these terms are fixed over the entire sample period. In these columns, earnings management as a whole and more particularly discretionary loan loss provisions are marginally significant. However, in columns (3) and (4), we introduce crisis-period interaction terms that allow earnings management deviation, we set residual standard deviation for equal to the firm s average value in the precrisis years. 11. The capital ratio for each bank is defined as (Tier 1 capital allowable under the risk-based capital guidelines) / (average total assets net of deductions), as reported on the bank s consolidated Y-9C Report. In turn, total bank assets equal all foreign and domestic assets reported on each bank s consolidated Y-9C Report. 12. Including bank fixed effects would result in biased coefficient estimates (Stata 2009, p. 410), so we exclude them in Table 5. Nevertheless, in unreported regressions, we experimented with bank fixed effects and found that they had almost no impact on our estimates.

16 186 : MONEY, CREDIT AND BANKING TABLE 5 CRASH INCIDENCE AS A FUNCTION OF BANK EARNINGS MANAGEMENT (1) (2) (3) (4) EARN_MGT * (t-statistic) (1.935) (0.415) (Economic magnitude) EARN_MGT * CRISIS ** (2.219) LLP_MGT ** (2.052) ( 0.148) GAINS_MGT ( 0.067) (0.252) LLP_MGT * CRISIS *** (3.627) GAINS_MGT * CRISIS ( 0.234) Total assets (t 1) (0.243) (0.328) (0.193) (0.304) Capital ratio (t 1) ( 1.175) ( 0.882) ( 1.387) ( 0.410) Amihud measure (t 1) ( 0.973) ( 1.028) ( 0.763) ( 0.728) Firm fixed effects N N N N Year fixed effects Y Y Y Y N 4,112 4,112 4,112 4,112 Pseudo R NOTE: Probit regressions, with dependent variable equal to 1 if the lowest bank-specific return in the year is worse than 3.09 standard deviations below zero. Sample period = Bank specific returns are calculated as residuals from estimation of an index model regression, equation (8), of weekly bank returns against the return on the CRSP value-weighted market index and the Fama French bank industry index. Earnings management variables are winsorized at 1st and 99th percentile values. Regressions are estimated with year fixed effects. Economic magnitude equals the predicted change in the probability of a crash week occurring during the year given a change in the right-hand-side variable from the 10th percentile in the sample distribution to the 90th percentile. *significant at 10% level; **significant at 5% level; ***significant at 1% level. to have different effects in the pre- and postcrisis periods. In this specification, there is no apparent relationship between earnings management and crash likelihood in the precrisis years (the coefficients on EARN_MGT or its components are all statistically insignificant at the 5% level in columns (3) and (4)), but the interaction terms between the crisis dummy and both earnings management and loan-loss provisions are statistically significant. For example, the EARN_MGT * CRISIS interaction term in column (3) has a t-statistic of and a coefficient of Most of the power of total EARN_MGT clearly comes from management of loan loss provisions rather than from securities gains or loss management. The LLP_MGT * CRISIS interaction term in column (4) has a t-statistic of with a positive coefficient, In contrast, securities gains or losses management apparently has little relation to crash propensity. Even in the crisis, it is statistically insignificant, with the GAINS_MGT * CRISIS

17 LEE J. COHEN ET AL. : 187 term receiving a t-statistic of only This may be due to the fact that (as discussed above), during the latter part of our sample period, SFAS 157 significantly limited the ability of banks to use security portfolio gains and losses as a tool to manage earnings. The economic impacts in Table 5 equal the increase in crash probability during the year corresponding to an increase in each variable from the 10th percentile of the sample distribution to the 90th percentile. This is analogous to a shift of the righthand-side variable from the middle of the first quintile of its distribution to the middle of the fifth quintile, and thus is comparable to a common (5) (1) difference. The impact of EARN_MGT during the crisis is economically large, 8.88%, and the impact of LLP_MGT is even higher, 16.43%. The latter value is between one-fifth and onequarter of the unconditional probability of a crash in the crisis years (see Table 4). By way of comparison, Hutton, Marcus, and Tehranian (2009) find that a comparable increase in earnings management in their sample of industrial firms increases crash likelihood by around one-sixth of the unconditional probability of a crash. Crash sensitivities for this sample of banks are thus a bit stronger than the corresponding values for industrial firms. The control variables, total assets, capital, and liquidity, all are statistically insignificant in explaining crash likelihood. In sum, it appears from Table 5 that banks engaging in greater earnings management are more likely to experience crashes during the crisis, even though such crash risk does not make itself evident in the precrisis years. Table 6 presents similar regressions, but instead of a 0 1 crash indicator on the left-hand side, we use a 0 1 jump indicator, where a jump is defined as an increase in stock price of a least 3.09 standard deviations. This allows us to test whether bank earnings management is related to skewness (specifically, negative crashes) or kurtosis (fat tails on both sides of the return distribution). Table 6 is notable for what it does not show. With only one exception, neither earnings management nor either of its components is significant in any of the specifications. We conclude from these results that while crash risk is reliably higher for banks that manage earnings more aggressively, jump potential is not. To test this more formally, we compute chi-square tests for the equality of the regression coefficients on EARN_MGT in predicting crash versus jump probabilities. 13 The chi-square statistic for such equality is 25.3, which allows us to reject the hypothesis of equality at a 0.00% level. A similar test for the (joint) equality of the coefficients on the components of earnings management, LLP_MGT and GAINS_MGT, yields a chi-square of 14.7 and a p-value of 0.07%. 13. This test requires that the coefficients for jumps versus crashes be nested in a single regression framework, which allows us to impose a constraint that the coefficients are equal. Therefore, we compute these chi-square statistics using a multinomial probit regression allowing for three states: crashes, jumps, or neither event.

18 188 : MONEY, CREDIT AND BANKING TABLE 6 JUMP INCIDENCE AS A FUNCTION OF BANK EARNINGS MANAGEMENT (1) (2) (3) (4) EARN_MGT (t-statistic) (0.899) (0.318) (Economic magnitude) EARN_MGT * CRISIS (1.287) LLP_MGT ** (2.127) (1.391) GAINS_MGT ( 1.320) ( 1.352) LLP_MGT * CRISIS (1.375) GAINS_MGT * CRISIS (0.961) Total assets (t 1) *** *** *** *** ( 3.891) ( 3.913) ( 3.931) ( 4.206) Capital ratio (t 1) (0.029) (0.196) ( 0.115) (0.141) Amihud measure (t 1) (0.665) (0.500) (0.766) (0.653) Firm fixed effects N N N N Year fixed effects Y Y Y Y N 4,112 4,112 4,112 4,112 Pseudo R NOTE: Probit regressions, with dependent variable equal to 1 if the lowest bank-specific return in the year is more than 3.09 standard deviations above zero. Sample period = Bank-specific returns are calculated as residuals from estimation of an index model regression, equation (8), of weekly bank returns against the return on the CRSP value-weighted market index and the Fama French bank industry index. Earnings management variables are winsorized at 1st and 99th percentile values. Regressions are estimated with year fixed effects. Economic magnitude equals the predicted change in the probability of a jump week occurring during the year given a change in the right-hand-side variable from the 10th percentile in the sample distribution to the 90th percentile. *significant at 10% level; **significant at 5% level; ***significant at 1% level. 3.2 Stock Price Crashes versus Operational Risk As we acknowledge above, regulators may be less concerned with stock price risk per se than with the underlying operating performance of a bank. Moreover, stock price movements may reflect variables such as short-term fluctuations in risk premia that do not reflect on operational performance. On the other hand, large stock price drops may in fact signal a market expectation of deteriorating performance, and this would concern regulators. We address these issues by examining full-year stock price performance, implied volatilities, and changes in bank return on assets. First, we consider the relation between earnings management and annual returns (rather than weekly crashes) during the crisis. Stock returns over a full year may be more reflective of persistent underlying conditions than weekly returns, even if they are extreme. We calculate each bank s annual firm-specific return by compounding its