Bank Earnings Management and Tail Risk during the Financial Crisis

Transcription

1 Bank Earnings Management and Tail Risk during the Financial Crisis Lee Cohen Boston College Marcia Millon Cornett Bentley University Alan J. Marcus Boston College Hassan Tehranian Boston College November 2011 Abstract We show that a pattern of earnings management in banks has little bearing on downside risk during quiet periods, but seems to have a big impact during a financial crisis. More aggressive earnings managers prior to 2007 exhibit substantially higher crash risk once the financial crisis begins. Moreover, the association of earnings management with the magnitude of worst-week returns is economically large, with an impact roughly double the pre-crisis standard deviation of bank-specific returns. Consistent with the literature on earnings management and crash risk in industrial firms, these results support the hypothesis that banks which more aggressively manage earnings can hide relevant information for some time, but in a period of severe distress in which accounting choices can no longer obscure performance, information comes out in larger amounts, resulting in substantially worse stock market performance. JEL classification: G01, G11, G21, G28, M40 Keywords: financial institutions, earnings management, crashes, transparency The authors are grateful to Jim Booth, Mark Bradshaw, Ozgur Demirtas, Amy Hutton, Atul Gupta, Jim Musumeci, Jun Qian, Sugata Roychowdhury, Ronnie Sadka, Phil Strahan, and seminar participants at Boston College for their helpful suggestions.

2 Bank Earnings Management and Tail Risk during the Financial Crisis 1. Introduction Bank regulators and investors have long been concerned with tail risk, i.e., extreme declines in a bank s stock price. The financial crisis of only heightened this concern. While tail risk is determined in large part by bank financial policies such as the composition of the 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 the provision for loan losses, and they can use that discretion to modulate the transparency, or opacity, of their financial reports. While accounting opacity 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 that greater accounting opacity of industrial firms is associated with greater tail risk. This paper asks whether the association between opacity and tail risk also characterizes banks, and, if so, how this relation may have exacerbated stock price movements during the financial crisis. Opacity 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 opacity is not strategically exploited by managers, it still might result in fatter-tailed return

3 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. Accounting opacity is often measured by proxies for earnings management. 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, Sweeny, 1995; Cohen, Dey and Lys, 2008). 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 such opacity does cause information to reach the market in discrete events 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. 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 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 earnings management and tail risk. However, that risk typically is not evident 2

4 in normal periods, and therefore is hard to evaluate even from long sample periods. Nevertheless, opacity seems to have a large impact on 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 accounting opacity 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 2, we briefly review the literature on tail risk and accounting opacity. As part of this review, we discuss how measures of earnings management for industrial firms must be modified for banks. Section 3 discusses our sample and data sources. Section 4 presents empirical results. We begin with an analysis and justification of our measure of bank earnings management, and proceed to demonstrate that such management and tail risk appear to be positively related. Finally, Section 5 concludes the paper, where we consider the policy implications for banks and their regulators. 2. Related literature 2.1 Earnings management and crash risk Jin and Myers (2006) present a model in which lack of full transparency concerning firm performance enables managers to hide 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 absorb 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. 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 3

5 markets exhibit more frequent crashes. Hutton, Marcus, and Tehranian (2009) further test the Jin and Myers model by developing a firm-specific measure of opacity and show that opacity 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 disclosures of 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, 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. 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 (2008) 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 earnings management based on the Jones (1991) model need to be modified for banks or other financial institutions that are not engaged in sales-based businesses. Instead, the focus for earnings management in banks typically tends to be on loan loss provisions or the realizations of gains or losses on securities, both of which allow 4

6 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. 2.2 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. Consistent with their goal of maintaining the safety and soundness of banks, commercial bank regulators encourage a loan loss allowance balance greater than expected losses, implying that bank managers should overestimate loan losses (beyond their expected values) during good times to build a safety cushion to carry them through bad times. However, inflating loan loss provisions in this manner reduces reported net income and thus, measured bank performance. When managers compensation is based on reported profitability, they will 5

7 be understandably reluctant to adhere to regulators preference that they build their loan loss allowances. This tension inevitably influences a bank s treatment of its loan loss provisions. In addition to loan loss provisions, banks also appear to manage earnings through the realization of security gains and losses (Beatty et al., 1995; Beatty et al., 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. Thus, realized security gains and losses represent a second way that management can smooth or otherwise manage earnings. 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 et al. (1990) find that capital positions play a role in banks willingness to realize gains on municipal bonds. Collins et al. (1995), Beaver and Engel (1996), and Ahmed et al. (1999) find that discretionary accruals are negatively related to capital, although Beatty et al. (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 et al. (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 as well as 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, i.e., report one drastic earnings decline after hiding a series of smaller declines in previous years (Demski, 1998; Arya et al., 1998), a pattern consistent with infrequent but large stock market declines. 6

8 3. 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 in the decade prior to the financial crisis to predict tail risk in both the pre-crisis period, , as well as the crisis period, All accounting data are obtained from FFIEC Call Reports databases found on the Chicago Federal Reserve s Website, Data are collected at the holding company level. That is, based on the highest holding company number of the bank, we collect and combine data for all banks with the same highest holding company number. Thus, we treat the bank holding companies as if they have only one bank, by combining their subsidiaries into one (consolidated) statement. Bank stock return data are collected from the Center for Research in Security Prices (CRSP) data base. Table 1 lists the number of publicly traded banks with available Call Report data by year. Our analysis includes a total of 4,478 bank-years 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 non-discretionary, 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 7

9 basis for judgment with respect to these provisions is subject to periodic review by regulators. 1 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 may manage earnings through the discretionary realization of security gains and losses. 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 et al. (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. The regression model is: 2 LOSS it = α tr + β 1 LNASSET it + β 2 NPL it + β 3 LLR it + β 4 LOANR it + β 5 LOANC it + (1) β 6 LOAND it + β 7 LOANA it + β 8 LOANI it + β 9 LOANF it + ε it, where: 1 Managerial judgment must be based on a reviewable record as noted in the Chicago Federal Reserve s Call Report dictionary in its description of Item 4230: Provision for Loan and Lease Losses. The objective of the item is said to bring the balance in Allowance for Loan and Lease Losses (3123) to an adequate level 2 Cornett et al. (2009) also employ the Beatty model. However, they use the level of nonperforming loans on the right-hand side, whereas Beatty (2002) uses 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. Results using the other specification are available upon request. 8

10 i = bank holding company identifier; t = year (1994 to 2006); r LOSS = U.S. Office of the Comptroller of the Currency defined district number = 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 LOANR LOANC LOAND LOANA LOANI LOANF ε = loan loss allowance as a fraction of total loans; = real estate loans as a fraction of total loans; = commercial and industrial loans as a fraction of total loans; = loans to depository institutions as a fraction of total loans; = agriculture loans as a fraction of total loans; = consumer loans as a fraction of total loans; = loans to foreign governments as a fraction of total loans; = 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 as the discretionary component of loan loss provisions. 3 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) 3 This approach is highly 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

11 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 et al. (2002). We estimate the following OLS regression over the pre-crisis 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-of-year total assets (includes realized gains and losses from available-for-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 Appendix A 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 gains or losses: 10

12 DISC_EARN it = DISC_GAINS it DISC_LLP it (4) High levels of DISC_EARN amount to under-reporting of loan loss provisions and higher realizations of securities gains, which, ceteris paribus, increase income. Negative values for DISC_EARN would indicate that loan loss provisions are over-reported and 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 pre-crisis 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. 5 However, there is meaningful variation in these numbers. Discretionary loan loss provisions, DISC_LLP, in the pre-crisis period range from a first percentile value of 0.254% to a 99 th percentile value of 0.457% of assets, with a standard deviation (across banks and time) of 0.138% of assets. The corresponding range for realized securities gains is from 0.216% to 0.272% of assets, with a standard deviation of 0.081% of assets. The standard deviation of discretionary earnings, DISC_EARN, is 0.157% of assets, indicating that a nontrivial portion of the variation in reported bank performance (the standard deviation of bank ROA is 0.617%) is due to management s discretionary accounting and security sales choices, and is consistent with the notion that banks do indeed manage earnings. 4 The exclusion of from these summary statistics explains why there are 4,478 banks in Table 1, but only 3,526 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). 5 The average value is not precisely zero because, while we estimate equations (1) and (3) over the period, the final sample begins in 2007 as the earnings management variables are defined as three-year moving sums of lagged values. 11

13 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 earnings management patterns computed prior to The next section offers further evidence on earnings management. 3.2 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 three years. We estimate the relation over the precrisis period, , because Figure 1 suggests that the extreme events of the crisis years disrupt the patterns that characterized each bank in the previous decade. Panel A of Table 3 shows that in the short-term (i.e., at a one-year lag), discretionary earnings exhibit positive serial correlation, with a positive and statistically significant coefficient (0.0631) on the one-year lagged value. However, at longer lags of 2 or 3 years, this relation reverses. The coefficients at these lags ( and , respectively) are negative, highly significant, and of considerably greater combined magnitude than the coefficient on the one-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 12

14 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 employed 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. 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. 13

15 Therefore, we define earnings management, EARN_MGT, as the three-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 three-year moving sum (instead of a one-year value) to capture the multi-year effects of earnings management because the moving sum is more likely to reflect a sustained, underlying policy of the bank to manage earnings. 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_RSG t-3 (7) Panel B of Table 2 presents descriptive statistics for the earnings management variables in the pre-crisis years. The mean value of EARN_MGT (computed over the preceding three years, t 3 to t 1) is 0.272% of assets. The mean value of LLP_MGT is 14

16 0.232% of assets, and the mean of GAINS_MGT is 0.113%. 6 During the period, mean return on assets is 0.568%. Therefore, these values are an appreciable fraction of typical ROA. 3.3 Tail risk We are ultimately concerned with tail risk, specifically, the impact of cross-sectional 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). 7 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 jt (8) where r j,t is the stock market return of bank j in week t, r m,t is the CRSP value-weighted market index, and r it is the Fama-French value-weighted bank industry index. The residual of equation (8), ε jt, 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 bankspecific stock returns in this period is 3.12%. Figure 2 shows that this value is fairly consistent 6 These values do not add up because the absolute value of a sum is not the sum of absolute values. 7 Results using only one lead and lag of weekly returns were nearly identical. 15

17 over the pre-crisis period. Under the assumption that bank-specific returns are normally distributed, one would predict that 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 3.12% for the pre-crisis period, this would imply a typical worst week return of % = 7.05%. In fact, the sample-average worst-week return in the pre-crisis period is 7.20%, suggesting that, 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. Table 4 presents annual measures of crash propensity. We measure residual standard deviation for each bank in each year. 8 If returns in the coming year were normally distributed, only 0.1% of banks in any week would be expected to exhibit bank-specific 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 one week below this cutoff. The percentage in the pre-crisis years is generally between 5% 8 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 deviation, we set residual standard deviation for equal to the firm s average value in the pre-crisis years. 16

18 and 10%, but it balloons to 74.2% in The negative returns corresponding to these crashes are quite large; in the pre-crisis period, the median bank-specific loss in a crash week is roughly 3.40 times the weekly residual standard error from equation (8), or about 10.6%, while in the period the median loss in a crash week is 4.80 times the standard error. 4. Empirical results Figure 3 presents a first, nonparametric, look at the relation between tail risk and earnings management. In each year, we sort banks by EARN_MGT from least to most, and divide the sample into 5 quintiles. We then compute the worst-week bank-specific return for each bank as a multiple of its residual standard deviation and calculate the average value of that multiple for each quintile. Panel A shows the average multiple across quintiles for two periods: pre-crisis ( ) and crisis ( ). It is clear that in the pre-crisis period, there is little apparent crash risk. We observe again that the average worst week return is only about 2.3 times the standard error of bank returns, just about the value one would predict from a normally distributed variable. Moreover, there is essentially no relation between earnings management and crash propensity: the pre-crisis profile across the quintiles is essentially flat. However, in the crisis years, the pattern changes abruptly. First, worst-week returns are far greater multiples of sigma, considerably beyond what might reasonably be observed under the normal distribution. This perhaps, is not surprising given the turmoil of those years. Far more surprising is the now steeply downward profile of the crisis-period worstweek returns: more aggressive earnings managers have much more severe crash risk than 17

19 banks with histories of less aggressive accounting choices. 9 This association is the key message of the figure. The association during the crisis period is highly significant as indicated by the t-statistics for the difference between losses in the fifth and first quintiles. Panels B and C of Figure repeat the analysis for each component of earnings management independently. The general message of these panels is the same as in Panel A. There is no pre-crisis association between either component of earnings management and crash risk, but a strong association in the crisis years. However, the relation is far stronger for loan loss management than it is for management of securities gains or losses. Table 5 presents a more formal 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 1 st and 99 th 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, 10 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 9 EARN_MGT is constructed using coefficients estimated over the sample period ending in Nevertheless, earnings management variables continue to evolve after 2006 based on loan losses and realized securities gains during the crisis years. 10 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 Call Report. In turn, total bank assets equal all foreign and domestic assets reported on each bank's Call Report. 18

20 more prone to tail events, as they are less able to absorb sudden shifts in demand. The regressions are estimated with year fixed effects. 11 Column (1) of Table 5 employs total earnings management 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. However, in columns (3) and (4), we introduce crisis interaction terms that allow earnings management to have different effects in the pre- and post-crisis periods, as suggested by the results in Figure 3. The key result is that, consistent with Figure 3, there is no apparent relationship between earnings management and crash likelihood in the pre-crisis years (the coefficients on earnings management or its components are all statistically insignificant at the 5% level in every column), but the earnings management-crisis period interaction terms are highly significant. For example, the EARN_MGT*CRISIS interaction term in column (3) is statistically significant (t = 3.390) with a positive coefficient (79.254). Similarly, the column (4) coefficient on LLP_MGT*CRISIS is also statistically significant (t = 3.648), again with a positive coefficient (117.76). However, securities gains or losses management has little relation to crash propensity. Even in the crisis, it is statistically insignificant, with the GAINS_MGT*CRISIS term receiving a t-statistic of only.294. The economic impacts in Table 5 equal the increase in crash probability during the year corresponding to an increase in each variable from the tenth percentile of the sample distribution to the 90 th percentile. This is analogous to a shift from the middle of the first quintile in Figure 3 to the middle of the fifth quintile, and thus is comparable to a (5) (1) 11 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. 19

21 difference. The economic impact of earnings management during the crisis is large. For example, the impact of EARN_MGT during the crisis is 15.07% and the economic impact of LLP_MGT is even higher, 18.48%. These marginal impacts are 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 more aggressive earnings managers are more likely to experience crashes during the crisis, even though such crash risk does not make itself evident in the pre-crisis years. Table 6 presents similar regressions, but instead of a probit equation with a 0-1 crash indicator on the left-hand side, we use OLS, and employ as the dependent variable the worstweek bank-specific return of each bank in each year, R min, defined as the bank s minimum residual from equation (8). 12 This allows us to focus on the magnitudes of down-side risk. 12 Because minimum returns are bounded from below by 1, this dependent variable presents potential biases from truncation issues. To ensure that this issue does not affect our results, we re-estimate each regression using a standard logistic transformation of the left-hand side variable. Specifically, we use the transformed variable, R * min, as the dependent variable, where R * min = ln 20 1 R min R min R * min can take on any real value, from when R min = 1 to + when R min = 0. (Because R min is defined as the minimum weekly bank-specific return during the year, there are no instances in which it is positive.) These results are fully consistent with those in Table 6 in terms of both significance and economic impact.

22 As in Table 5, the explanatory variables of primary interest in these regressions are earnings management as well as its two components, loan loss provision management and security gains or losses management. The regressions are estimated with year fixed effects as well as bank fixed effects. Column (1) in Table 6 is the simplest specification, treating the entire period as uniform and omitting any specific crisis-year effects. Worst-week returns tend to be lower when earnings management is higher (the negative coefficient of on EARN_MGT signifies negative returns of higher absolute value), and this result is highly statistically significant, with a t-statistic of The economic impact in this table is the predicted change in the minimum weekly bank-specific return given a change in the righthand side variable from the tenth percentile in the sample distribution to the 90 th percentile. This is again comparable to a (5) (1) quintile difference. The economic impact of EARN_MGT is fairly modest, an additional loss of 1.19% in the worst-week annual return. Recall that the standard deviation of the residual return across the banks in the sample averages 3.12% in the period, so this impact corresponds to an incremental weekly loss of less than one-half of a standard deviation. Total bank assets receive a statistically significant positive coefficient (0.022, with a t-statistic of 3.832), indicating less severe worst-week returns. This is somewhat at odds with the lack of a relationship with likelihood of a crash found in Table 5, but the economic impact of asset size is minimal. Higher capital ratios predict less severe worst-week returns, but Amihud s illiquidity measure is effectively independent of downside risk. In this specification, we include residual standard deviation as an additional control, because greater cross-sectional variation (higher residual standard deviation) will mechanically result in 21

23 higher-magnitude bank-specific returns. Not surprisingly, sigma is a potent predictor of worst-week return, with a coefficient of 0.785, a t-statistic of 8.443, and an economic impact of 2.56%. Column (2) of Table 6 presents a similar specification, but with earnings management broken out into its two components, LLP_MGT and GAIN_MGT. As in Figure 3 and Table 5, most of the impact of earnings management is in fact attributable to discretionary loan loss provisions, LLP_MGT; its t-statistic is 6.125, and its economic significance is actually a bit higher than that of total earnings management. In contrast, as in Table 5, the coefficient on realized security gains or losses is far from statistically significant (t-statistic = 0.334), and its economic significance level is also near zero ( 0.06%). Coefficients on the other control variables are virtually identical to their values in Column (1). In sum, the Column (1) and (2) results indicate that earnings management, or more precisely, discretionary choices concerning loan loss provisions, are associated with downside risk, more specifically, to an increase in the maximum weekly loss the bank suffers in any year. However, while the increase in that loss is statistically significant, the average economic magnitude, while not trivial, is not overwhelming. Columns (3) and (4) expand the regression specification in the first two columns to allow for differential effects during the crisis years of As in Table 5, we introduce a dummy variable with a value of 1 in those three crisis years and interact the dummy with our measures of earnings management. Column (3) presents regression estimates using EARN_MGT as an explanatory variable, while Column (4) breaks earnings management into its two components. 22

24 The effect of earnings management is substantially higher during the crisis years. The coefficient on the earnings management-financial crisis interaction term is (tstatistic = 5.518), with an economic impact of 3.38%. Adding the economic impacts of the direct effect of EARN_MGT and its crisis interaction term gives the total impact of EARN_MGT in the crisis years: 0.37% 3.38% = 3.75%. Consistent with the literature on earnings management and crash risk in industrial firms, these results support the hypothesis that banks which more aggressively manage earnings can hide relevant information from the market for some time. But when they enter a period of severe distress in which accounting choices can no longer obscure performance, information comes out in larger amounts. This results in substantially worse stock market performance. Downside risk of aggressive earnings managers is thereby increased. Coefficients on the other control variables in the column (3) regression are, again, highly similar to their values in columns (1) and (2). In column (4), we split earnings management into its component parts, and we find results consistent with both the quintile sorts of Figure 3 as well as the estimates of the column (2) regression. The direct effect of earnings management is again primarily attributable to discretionary loan loss provisions. While the coefficient on LLP_MGT is statistically significant (t-statistic = 2.250), the coefficient GAINS_MGT is again statistically insignificant and economically trivial. However, neither variable appears to have substantial economic impact in the pre-crisis period. The biggest economic impact is captured by the interaction between discretionary loan loss provisions and the banking crisis dummy, LLP_MGT * CRISIS (coefficient = 23

25 7.612, t-statistic = 6.035). That interaction term increases the economic impact of LLP_MGT from 0.45% to 0.45% 3.91% = 4.36%. Finally, management of the realization of securities gains and losses also is statistically significant during the crisis period, though not nearly as important as loan loss management. The coefficient on the GAINS_MGT * CRISIS interaction term is 3.609, with a t-statistic of and economic impact of 0.81%. While this is only one-fifth the economic impact imputed to loan loss management during the crisis, this is still a meaningful incremental impact on worst-week returns. In sum, tail risk in banks with a history of earnings management is considerably greater than in their more transparent counterparts, at least in periods of economic stress. 4.1 Robustness tests Truncation issues. As we note in footnote 12, the use of worst-week returns raises some questions of bias due to truncated dependent variables. We suggest there that a standard logistic transformation of returns allows the left-hand side variable to range from to +. The transformation has little impact on regression results. The same variables matter and they exhibit similar rankings in terms of both statistical significance and economic impact. (See Appendix B.) Holding period. We use worst-week returns to measure downside risk. It is possible that another holding period would present different results, for example if worst-weeks are followed either by corrections or by further losses. We investigate this possibility using 4- week returns rather than one-week returns. However, this specification results in similar results. Not surprisingly, worst-month losses are bigger than worst-week losses, averaging 24

26 13.5 percent, which is about 1.6 times the average worst-week return. But the impact of earnings management remains the same, as does the relative importance of loan loss provisions relative to realized gains or losses on security sales Conclusion While earnings management has little apparent predictive significance for downside risk during the pre-crisis period, it is highly predictive of both crash risk and worst-week returns during the crisis period. By either measure, downside risk for banks that display a pattern of earnings management in the pre-crisis period is substantially greater during the crisis years. The impact of earnings management on worst-week returns is economically large, with a magnitude that approaches two standard deviations of the pre-crisis standard deviation of bank-specific returns. Management of loan loss provisions appears to be far more important than discretionary choices in realization of gains or losses on security holdings. The challenging policy implication of these results for regulators, investors, and risk managers is that tail risk does not seem to be evident in pre-crisis data we do not observe the tail risk associated with earnings management until the crisis. This, of course, limits the use of past rate of return data to assess risk of extreme returns. Nevertheless, these results indicate that a history of earnings management, whatever its motivation, seems to reliably predict worst-case outcomes during a crisis. Therefore, even if that tail risk has not been manifest during normal periods, one might reasonably look at earnings management as predictive of tail exposure. 13 To save space, results for these robustness checks are not reported. They are available upon request. 25

27 While we do not have any direct evidence on the mechanism underlying the relation between earnings management and downside risk, it seems reasonable to speculate that banks which more aggressively manage earnings have more to hide. They may easily deny the market relevant information during quiet periods. However, when a crisis strikes and stresses become more evident, the negative information revealed about earnings managers may lead to more substantial revision of market perception about the prospects of those banks with consequent impact on their stock prices. 26