The Mispricing of Loan Loss Provisions

The Mispricing of Loan Loss Provisions Lee-Seok Hwang College of Business Administration Seoul National University Lshwang@snu.ac.kr Young Jun Kim ** College of Business Administration Hankuk University of Foreign Studies kyjys21@gmail.com College of Business, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-916, Korea. Tel: 822-880-5075 and E-mail: Lshwang@snu.ac.kr ** Corresponding author, College of Business, Hankuk University of Foreign Studies, 270 Imun-dong Dangdaemun-gu, Seoul 130-791, Korea. Tel: 822-880-5075 and E-mail: kyjys21@gmail.com

The Mispricing of Loan Loss Provisions ABSTRACT This study documents evidence on the mispricing of banks' loan loss provisions (LLP) in the equity market. First, we find that equity investors do not correctly price information in LLP: the level of LLP (change in LLP) is strongly (weakly) negatively related to one-year ahead future returns. When LLP is decomposed into non-discretionary LLP (NLLP) and discretionary accruals (DLLP), the level of and change in NLLP appears to be the main driver of return predictability. Second, we show that analysts do not fully impound information in LLP into their one year-ahead earnings forecasts: the level of and change in LLP are negatively related to analyst forecast optimism. Decomposition of LLP suggests that such bias is mainly due to NLLP. In sum, our findings suggest that equity market participants do not fully appreciate the loan-related risk information in LLP. JEL classification: C23, G14, M41 Key Words: Analysts forecasts; Loan loss provisions: Mispricing

1. Introduction Loans account for the largest component of bank assets and loan loss provision (LLP) is the largest single accrual in banks (Beatty and Liao 2013). LLP is a measure of future credit losses. As the largest item among bank accruals, LLP affects banks reported earnings significantly and, accordingly, banks valuation. However, LLP contains both estimation errors and managerial discretion (as will be discussed later). This feature makes it difficult to value the risk in banks loans and, eventually, bank stocks. Thus, the correct assessment of banks LLP is critical to bank valuation. Most prior studies focus on the relation between LLP information and contemporaneous stock returns (Beaver and Engel 1996; Ahmed et al. 1999) and document that LLP is associated with contemporaneous stock returns. However, that does not necessarily imply that equity market participants fully understand the information in LLP. There is ample evidence in the accounting literature that the market does not fully price accounting information (Bradshaw et al. 2001; Sloan 1996; Soliman 2008). However, there are few studies examining whether market participants fully incorporate the information in LLP. This study examines whether equity investors and analysts properly incorporate loan loss provisions (LLP) information into their decisions. There are several reasons why investors may find it difficult to understand LLP. First, LLP is based on a managerial estimation of future loan default. It inevitably contains estimation errors. Second, LLP is subject to managerial discretion, for example, as a means of earnings smoothing, which obscures bank transparency (Bushman and Williams 2011). Third, there is large variation in recognition of LLP across time and among banks (Beatty and Liao 2011). Accordingly, even bank regulators acknowledge that it is difficult for information users to estimate banks loan losses. Thus, Basel II requires banks to disclose the credit risk 2

model used to estimate credit loan losses in order to enhance understandability of information users. Taken together, it is not easy for market participants to assess the risk in bank loans. The accounting literature documents that market participants, in particular equity investors and analysts, do not fully impound accounting information into their decisions. For instance, equity investors and analysts do not fully understand the implication of accruals (Sloan 1996; Bradshaw et al. 2001). They also do not completely use the information in asset turnover (Soliman 2008). As mentioned above, because LLP is difficult to decipher, it is likely that both types of market participants do not properly understand implications of loanrelated risk information in LLP. Thus, it is an interesting empirical question whether equity investors and analysts fully incorporate information in LLP into their decisions. We measure LLP information in the two different dimensions: the level of LLP and the change in LLP. The accounting literature shows that a level of and change in accounting variables have different implication for investors. For instance, accruals anomaly studies focus on earnings level while post-earnings announcement drift (PEAD) studies focuses on change in earnings. Next, similar to accruals studies, we decompose each LLP measurement into a non-discretionary component and a discretionary component. Prior studies show that non-discretionary accruals and discretionary accruals have different information for future stock returns (Xie 2001). Thus, we examine which dimension (level vs. change) and which component (discretionary vs. non-discretionary) of LLP is mainly accountable for mispricing of LLP. Using data on US banks during 1994 to 2010, this study examines whether market participants correctly price banks' loan loss provisions (LLP) in the equity market. Our findings are summarized as follows. First, we find that equity investors do not correctly price 3

information in LLP: the level of LLP (change in LLP) is strongly (weakly) negatively related to one-year ahead future returns. When LLP is decomposed into non-discretionary LLP (NLLP) and discretionary LLP (DLLP), both the level of and change in NLLP appears to be the main driver of return predictability. The stock return predictability of LLP information is robust to controlling for firm characteristics and Fama-French risk factors (1993). However, there is still the possibility that the risk factor model is mis-specified and the abnormal returns earned by LLP information documented is merely compensation for risk. Thus, we examine whether trading strategies based on loan loss provisions outperform consistently. We find that the annual trading strategies based on the level of and change in NLLP generate more profits than losses in most years of during the study period. This finding rules out a risk-based explanation and reinforces a mispricing explanation. Second, we show that analysts do not fully impound information in LLP into their one year-ahead earnings forecasts: the level of and change in LLP are negatively related to analyst forecast optimism. Decomposition of LLP suggests that such bias is mainly due to NLLP. In other words, analysts tend to issue more optimistic earnings forecasts for banks with high level of and greater increase in NLLP. In sum, our findings suggest that equity market participants do not fully appreciate the loan-related risk information in LLP. Our study makes several contributions to the accounting and finance literature. First, our study contributes to the LLP valuation literature by providing evidence that LLP and components of LLP are mispriced. This paper is the first to examine whether equity investors incorporate LLP information into their decision. In addition, in contrast to prior studies on mispricing focusing on level of or change in accounting information, we investigate both LLP level of and change in LLP information. Second, our study also contributes to the analyst forecast literature. There are only a few studies focusing on bank analysts. To our knowledge, 4

our study is the first to examine whether bank analysts fully incorporate information in LLP into their decisions. Our study provides valuable implications for various market participants such as equity investors, analysts, regulators, and standard-setters. First, our findings suggest that equity investors and analysts do not fully utilize information in LLP. Thus, they should cautiously analyze loan-related risk information contained in LLP and incorporate them into their decisions. Second, regulators should improve the current loan loss disclosure system so as to enhance market participants understandability of LLP. The complicated current loan loss disclosure system may be contributing to the mispricing of LLP. Third, standard-setters should develop a loan loss provisioning model which objectively measures the expected loan loss under consideration. FASB and IASB are now revising the current incurred loss model, which is known to be a more objective provisioning model, into the new expected loan loss provisioning standards which allows for more discretion of bank managers. The new model should be designed to avoid the opportunistic use of LLP. The remainder of the paper is organized as follows. Section II includes the literature review and hypotheses development. Section III presents the empirical models for hypothesis testing. Section IV describes the data sources and descriptive statistics. Section V reports the empirical results. Section VI concludes. II. Literature review and hypothesis development Loan loss provisions When a bank originates loans, the bank estimates loan losses and increases loan loss allowances (a contra-asset account) through LLP (an expense account or contra revenue account). Thus, LLP is a measure of future credit losses and is known to be more timely and 5

more judgmental than other loan loss accounts. The effect of accounting treatment of LLP on banks capital has changed with the regulatory regime. During the pre-basel period (prior to 1992), loan loss allowances (LLA) were included in Tier 1 capital and thus loan loss provisions (LLP) increased Tier 1 capital. 1 On the other hand, in the post-basel period, loan loss allowances (LLA) were not included in Tier 1 capital and thus loan loss provisions (LLP) did not increase Tier 1 capital but rather decreased capital. Loan loss provision (LLP) is the largest and the most important single accrual item on a bank balance sheet (Beatty and Liao 2013). Given the importance of LLP in banks, numerous prior studies exclusively examine the banks use of LLP. First, many studies provide evidence that bank managers opportunistically exercise discretion over LLP. For example, Kanagaretnam et al. (2003) and Liu and Ryan (2006) find that banks smooth earnings through LLP. Kim and Kross (1998) find that banks manage capital using LLP in the pre-basel period. Using international data, Bushman and Williams (2012) provide evidence that allowing more discretion in LLP may lead to deterioration in transparency. Second, there is large variation in recognition of LLP across banks and across time. Betty and Liao (2011) find that banks with more timely recognition of LLP are less likely to reduce lending in recessions. Bhat et al. (2012) show that banks use different types of credit risk modeling to estimate loan loss provisions and banks' LLP varies with the type of credit risk modeling they use. Specifically, banks relying on forward-looking credit risk modeling make more timely recognition of loan losses during the period when economic conditions change. On the other hand, banks using backward-looking credit risk modeling recognize loan losses more timely 1 The Basel Capital Accord (BASEL) is a risk-based capital framework. Banking regulators require banks to maintain minimum capital requirement. If a bank does not meet this requirement, banking regulators take the prompt corrective actions. 6

during when the economic conditions are stable. Our study is closely related to market valuation of LLP. Early studies pay special attention to short-window market reaction to increase in LLP by using an event study methodology and they find positive market reaction to large banks March-May 1987 announcements of increase in LLP for less-developed-country (LDC) debt (Grammatikos and Saunders 1990; Musumeci and Sinkey 1990; Elliott et al. 1991; Griffin and Wallach 1991). These studies interpret increase in LLP as a signal to the stock market of banking s willingness to deal with non-performing loans. Beaver et al. (1989) is the first long-window association study to document a positive relation between market value and loan loss reserves (LLR) in their 1979 1983 sample period. Similar to studies on short-window market reaction, they interpret this positive relation between market value and LLP as managers' signal to the market that they are able to withstand increase in LLR. In his 1979 1983 sample period, Wahlen (1994) confirms the conjecture of Beaver et al. (1989) by showing a positive relation between stock returns and unexpected LLP after controlling for unexpected non-performing loans and unexpected charge-offs. By decomposing LLP into NLLP and DLLP in a 1977-1991 sample, Beaver and Engel (1996) show that NLLP are negatively associated with market value of equity and DLLP are positively associated with market value of equity, supporting the idea of Wahlen (1994) that DLLP has positive pricing implications. By using a relatively recent sample from 1987 1995, which includes a part of post-basel data, they find that both NLLP and DLLP are negatively associated with market value of equity and contemporaneous stock returns. Surprisingly, in spite of relatively large number of value relevance studies on LLP, to our knowledge, few studies have yet examined the mispricing perspectives on LLP. Numerous accounting studies investigate whether markets price accounting information by examining the relation between accounting information and contemporaneous 7

returns. However, the evidence that the market prices accounting information does not necessarily imply that the market rationally prices accounting information of interest. For instance, Subramanyam (1996) finds that the market prices abnormal accruals. However, Xie (2001) shows that the market does not fully incorporate information in abnormal accruals into prices. In similar vein, Soliman (2008) finds that change in asset turnover is positively related to contemporaneous stock returns. He also shows that the change in asset turnover predicts one-year ahead stock returns, which implies that equity investors do not fully incorporate the information in changes in asset turnover into prices. In this regard, our study follows the similar lines of these studies. Prior studies show that equity investors negatively price LLP and NLLP and that they do not price DLLP. It does not imply that equity investors fully understand information in LLP, NLLP, and DLLP. The reason is that loan loss provisions seem to be as difficult to decipher as other accounting information. First, LLP is managerial estimation of future loan defaults. It inevitably contains estimation errors. Second, LLP is subject to managerial discretion, for example, as a means of earnings smoothing, which obscures bank transparency. Third, banks recognize loan losses based on their own policy and the state of the economy. Accordingly, even bank regulators acknowledge that it is difficult for information users to estimate banks loan losses. Thus, Basel II requires banks to disclosure more detailed information on loan losses to the market. Taken together, there is high possibility that the equity investors do not correctly price LLP and they are likely to under- or over-react to information in LLP. Studies on accrual anomaly document that investors differently price nondiscretionary accruals and discretionary accruals. For instance, Sloan (1996) shows that stocks with lower (higher) accruals have higher (lower) one-year ahead abnormal stock returns. More importantly, Xie (2001) documents that most of abnormal stock returns to stocks with high accruals arise from discretionary accruals, which suggests that equity 8

investors do not understand implications of discretionary accruals. Similar reasoning can be applied to loan loss provisions, which is the largest accrual component in a bank balance sheet. Beaver and Engel (1996) show that the contemporaneous stock returns are differently associated with NLLP and DLLP. As equity investors in industrial firms misprice a component of total accruals, equity investors in banks are likely to misprice a component of LLP, either NLLP or DLLP or both. Based on our above arguments, we propose the following hypothesis. Hypothesis 1-A: Equity investors do not fully understand the implications of LLP. Hypothesis 1-B: Equity investors do not distinguish the different implications of NLLP and DLLP. Some prior studies provide evidence that sell-side analysts efficiently process accounting information because they have more knowledge and devote more time to investigate stocks (Banker and Chen 2006; Frankel, Kothari, and Weber 2006; Weiss 2010). However, other prior studies also provide evidence that analysts also do not fully incorporate information on documented market mispricing into their decisions. These studies use evidence for market mispricing to disentangle it from risk. For example, Bradshaw et al. (2001) find that analysts earnings forecasts do not reflect predictable decrease in future earnings for firms with high accruals. Bradshaw et al. (2006) also document that analysts forecasts are positively associated with their measure of external financing. They interpret mispricing evidence as an explanation for the negative relation between external financing and stock returns. Soliman (2008) shows that analysts as well as equity investors do not incorporate the predictive information in changes in asset turnover into their earnings forecasts. While Lev and Nissim (2004) show that TI/BI(the ratio of estimated taxable 9

income to book income) predict one-year ahead stock returns, Weber (2009) also documents that analysts do not fully utilize these information into their earnings forecast decisions. LLP is as difficult as or even more difficult than other accounting items because LLP intrinsically include managers subjective forecasts of future loan defaults in addition to being influenced by other discretionary uses of LLP such as earnings smoothing and capital management. It is difficult for analysts to value the loans banks hold. Therefore, it is an empirical question of whether analysts fully incorporate the information in LLP into their forecast decisions. Hypothesis 2-A: Sell-side analysts do not fully understand the implication of LLP. Hypothesis 2-B: Sell-side analysts do not distinguish the different implications of NLLP and DLLP. III. Sample selection and research design Sample The sample period starts from 1994 through 2010. We use post-basel data to analyze our research question. As mentioned before, most prior studies use pre-basel data. Accounting data are taken from Compustat Bank. We choose all commercial banks (SIC code: 6020) to maintain consistency of the business environment. Stock return data is from CRSP. Non-performing assets (NPA) are available since 1993 in Compustat Bank. Analysts forecast data are obtained from IBES. Macroeconomic data, such as GDP growth rate ( GDP) and unemployment rate (UNEMP), are from the Federal Reserve Bank of St. Louis (http://research.stlouisfed.org/). We impose a minimal requirement on data to avoid survivorship bias. We delete bank-year observations missing any variable. Except for oneyear ahead stock returns and macroeconomic data, we winsorize all variables, at the top and 10

bottom 1 percent each year to mitigate the influence of extreme observations. Following Bradshaw et al. (2006), we winsorize one-year ahead forecast error (FE) at ± 1. These sample selection criteria lead to 5,441 bank-year observations between 1994 and 2010. 2 We deflate all variables by lagged total assets except for one-year ahead stock returns and macroeconomic data. Table 1 provides descriptive statistics for the main variables. LLP has mean and median values of 0.004 and 0.003, respectively, which suggests that the distribution of LLP is symmetric. NLLP has mean and median values similar to that of LLP which suggests that the distribution of the level of NLLP is similar to that of LLP. DLLP has a mean of zero, by construction. The change variables, such as LLP and NLLP, have different distribution characteristics from level variables, such as LLP and NLLP. Specifically, LLP has mean and median of 0.001 and 0.000, respectively, which are different from those of LLP. Similarly, the level of earnings (EBTP) has different distribution characteristics from a change of earnings ( EBTP). [TABLE 1 ABOUT HERE] Research Design To test for our hypotheses, we need to use three types of research design. First, we use a model for non-discretionary LLP (NLLP) and discretionary LLP (DLLP). Second, we use asset pricing tests to test whether equity investors fully incorporate loan loss provisions into their decisions (Hypotheses 1). Finally, we use an analyst earnings forecasts model to test whether equity investors fully impound loan loss provisions into their decisions (Hypotheses 2). We explain three types of research design in turn. 2 To use change variables such as LLP, one year data (year 1994) is lost. In addition, one-year ahead forecast error (FE) is constructed using the sample of observations for which analyst forecast data are available. 11

Estimation of (Non)-Discretionary LLP Following prior studies, we estimate the following pooled time-series and crosssectional regression model (1) and we denote the predicted values as non-discretionary LLP (NLLP t ) and the residuals as discretionary LLP (DLLP t ). 3 This decomposition is analogous to that of accruals into non-discretionary and discretionary accruals (Jones 1991; Dechow and Dichev 2002). LLP t = α 0 + α 1 NPA t+1 +α 2 NPA t +α 3 LOAN t + α 4 NCO t +α 5 Size+α 6 GDP t + α 7 UNEMP t + u t (1),where LLP t NPA t+1 LOAN t NCO t Size GDP t UNEMP t Loan loss provision (COMPUSTAT pll ) scaled by lagged total assets (COMPUSTAT at ) Change in non-performing assets (COMPUSTAT npa ) scaled by lagged total assets (COMPUSTAT at ) Change in total loans (COMPUSTAT lntal ) scaled by lagged total assets (COMPUSTAT at ) Net charge off (COMPUSTAT nco ) scaled by lagged total assets (COMPUSTAT at ) The natural log of total assets (COMPUSTAT at ) Change in GDP over the year Change in unemployment rates over the year Following Beaver and Engel (1996), we include the next (current) period change in the non-performing assets (NPA), current period loan growth ( Loan t ), and net charge-off (NCO) as a determinant of NLLP. Since Beaver and Engel (1996), subsequent studies have added other variables as determinants of NLLP. Following these studies, we use lagged total assets (Size t-1 ) because banks tend to be regulated based on bank size (Beck and 3 Most LLP studies use this pooled time-series and cross-sectional regression model (Beatty and Liao 2013). Following studies on accruals, we also run cross-sectional regressions by year and find qualitatively similar results. 12

Narayanmoorth, 2013; Bushman and Williams, 2012). We also include the change in GDP over the year ( GDP t ) and the change in unemployment rates over the year ( UNEMP t ) to control for macroeconomic effects on LLP (Bushman and Williams, 2012; Beatty and Liao, 2011). Variables of interest We focus on both the level of LLP (LLP) and change in LLP ( LLP). The literature shows that the level and change of accounting information have different implications for equity investors. For example, studies on the accrual anomaly (Sloan 1996) show that investors fixate on earnings levels do not distinguish the different implications of the level of accruals and the level of cash flows. Studies on PEAD (Bernard and Thomas 1989) document that information in the change in earnings is not reflected into stock prices. Moreover, Collins and Hribar (2000) find that the two anomalies are distinct from each other. This evidence indicates that the level and the change in accounting items have different predictive information. Because it is an empirical question how market participants use information in the level of and change in LLP, we include the level of LLP (LLP) or change in LLP ( LLP) or both in our analysis. 4 We call each specification the level analysis, the change analysis, and the level-change analysis, respectively. Equity investors We conduct three tests to test whether equity investors correctly price LLP information. First, we sort banks into quintiles based on LLP ( LLP) and construct a hedge portfolio by taking a long position in the highest LLP ( LLP) quintile and a short position in 4 Similar to our study, Soliman (2008) include both level and change in profit margin and asset turnover in the model to show how market participants use information in profit margin and asset turnover. 13

the lowest LLP ( LLP) quintile. Then we examine the one-year ahead returns of the hedge portfolio. Second, we run the following cross-sectional regression using equation (2) to see whether abnormal returns to LLP exist even after controlling for firm characteristics known to predict future stock returns such as market value of equity (MV) and book-to-market ratio (BM). The hedge portfolio approach has the advantage of not assuming a linear relationship between returns and LLP whereas the regression approach has the advantage of controlling for other firm characteristics. Note that LLP variables and LLP variables are the re-scaled quintile rank ranging from 0 to 1. 5 The coefficients on re-scaled quintile LLP variables and LLP variables, β 1 and β 2 in eq (2) can be interpreted as returns to a zero-investment LLP and LLP portfolio, respectively. R i R f = β 0 + β 1 LLP quin (NLLP quin or DLLP quin ) + β 2 LLP quin ( NLLP quin or DLLP quin )+ β 3 Beta+ β 4 log(mv)+ β 5 BM + ε i (2) where, R i R f LLP quin the raw monthly stock return for firm i the return on the one-month T-bill. rescaled quintile ranks (ranging from 0 to 1) for the LLP; the quintile portfolio is constructed every calendar year. LLP is loan loss provision scaled by lagged total assets. NLLP fitted value from equation (1) DLLP residual from equation (1) LLP change in loan loss provision over the year scaled by lagged total assets Beta the slope coefficient from the regression of a firm s monthly raw returns on the monthly value-weighted market return over a rolling five-year window ending in the current fiscal year. MV the natural log of market value of equity at the end of the current fiscal year 5 This re-scaled rank approach was suggested by Bernard and Thomas (1990). Since then, numerous mispricing studies employ this approach (Mashruwala 2006; Pincus 2007). 14

BM the natural log of the ratio of book value of equity to market value of equity at the end of the current fiscal year. Third, we estimate the monthly Fama-French three factor time-series regression using equation (3) on each loan loss provision quintile to discern whether abnormal returns to LLP is robust to controlling for risk factors. The intercept (α) represents monthly abnormal returns to each loan loss provision quintile. where, R pt R ft = α+ β 1 (R mt - R ft )+ β 2 SMB t + β 3 HML t + ε pt (3) R pt R M -R f SMB HML the equal-weighted return on quintile portfolio p (1 through 5) for month t the monthly excess return on the CRSP value-weighted market return the excess monthly return of small firms over big firms the excess monthly return of high BM firms over low BM firms Analyst forecasts To discern the mispricing explanation from the risk-based explanation, we examine whether sell-side analysts fully incorporate information in LLP into their earnings forecasts. To do so, we run the following regression using equation (4). The dependent variable is oneyear ahead forecast error (FE). The independent variables of our interest are RLLP t and RLLP t. Similar to equation (2), we re-scale the quintile ranks ranging from 0 to 1 to facilitate the interpretation of the regression results (Bradshaw et al. 2006). We also include level of earnings (EBTP) and their change ( EBTP t ) to assess whether LLP provides incremental information over earnings information. FE i,t = δ 0 + δ 1 EBTP t + δ 2 EBTP t + δ 3 LLP quin (NLLP quin or DLLP quin ) + δ 4 LLP quin ( NLLP quin 15

or DLLP quin ) + ε i,t (4) where, FE 1-year-ahead forecast error, computed as the realized annual earnings per share for the upcoming year minus the corresponding monthly consensus forecast of this amount, all scaled by stock price as of the end of the forecast month EBTP income before taxes and provisions scaled by lagged total assets EBTP change in income before taxes and provisions scaled by lagged total assets over the year LLP quin rescaled quintile ranks (ranging from 0 to 1) for the LLP; the quintile portfolio is constructed every calendar year. LLP is loan loss provision scaled by lagged total assets. NLLP quin fitted value from equation (1) DLLP quin residual from equation (1) LLP quin change in loan loss provision over the year scaled by lagged total assets IV. Empirical results Table 2 presents the estimation results of equation (1), which is used to decompose LLP into the discretionary and non-discretionary components. We obtain similar result with prior studies. Specifically, net charge-off (NCO) has a strongly negative association with LLP, which is consistent with Beaver and Engel (1996). The regression coefficient on current period change in non-performing assets ( NPA t ) (0.12) is much greater than that on subsequent change in non-performing assets ( NPA t+1 ) (0.01). GDP growth during the period ( GDP t ) is negatively related to LLP indicating that loan loss provisioning is pro-cyclical (Laeven and Majnoni 2003). Adjusted R 2 is 0.872 which assures that our model explains much of the variation in LLP. Stock return test 16

Table 3 reports mean annual returns to various loan loss provision quintile portfolios and their hedge returns. The first column shows that the higher the LLP, the lower the future returns. The hedge portfolio based on the level of LLP yields a positive annual return of 6.04% and is statistically significant at the 1% level. By using the estimation results in Table 2, we decompose LLP into NLLP and DLLP. The second column shows abnormal returns to the NLLP hedge portfolio is 9.74%, much higher than that using LLP. The third column shows that DLLP hedge portfolio return is -5.38%, a negative return, indicating that higher DLLP may be viewed as good news. Thus, abnormal returns to LLP are driven by NLLP but partly offset by DLLP. We also examine the abnormal returns to change in LLP. The fourth column shows that, similarly to the level of LLP, higher change in LLP ( LLP) is related to lower future returns. An annual hedge portfolio return on LLP is 4.03% but only marginally different from zero (t = 1.69). We also decompose LLP into NLLP and DLLP. The fifth column shows that abnormal return to the NLLP hedge portfolio is 7.47%, which is even larger than LLP level hedge portfolio returns. The sixth column shows that abnormal return to the DLLP hedge portfolio is negative but not statistically significant. Similar to the level variable, most of the abnormal return comes from NLLP. Overall, our findings indicates that equity investors seems to have difficulty in interpreting information in non-discretionary loan loss provision (NLLP) whether it is measured in the level or change. Table 4 presents the cross-sectional regression to capture the incremental effect of LLP information on future annual stock return after controlling for other firm characteristics known to predict future stock returns. Panel A reports the estimation result based on pooled cross-sectional regression with year fixed effects. Columns (1) and (2) are the results for incremental stock return predictability of the level of LLP. Column (1) shows that the regression coefficient on LLP is negatively significant at the 1% level. This result is consistent with the hedge portfolio returns that show higher future returns for banks with 17

lower levels of LLP. We also examine the source of LLP predictability by decomposing LLP into level of NLLP and level of DLLP. Column (2) reports that the level of NLLP has a significantly incremental negative effect on stock returns while the level of DLLP has a significantly incremental positive effect on stock returns. The effect of the level of NLLP on stock returns is much larger than that of the level of DLLP which implies that abnormal returns due to the level of LLP is mainly driven by the level of NLLP. These results are consistent with the hedge portfolio return results in Table 3. [TABLE 4 ABOUT HERE] Next, we focus on the change variables. Columns (3) and (4) provide the result for incremental stock return predictability of the change in LLP and the changes in LLP components, respectively. Column (3) shows that the coefficient on the change in LLP ( LLP) is negative and significant. In column (4), NLLP is negatively related to future stock returns while DLLP has no incremental effect. This is consistent with the results in Table 3. Similar to the results using the level of LLP, the source of predictability due to change in LLP ( LLP) comes from the change in NLLP ( NLLP). So far, we separately examine the effect of the level of LLP and the change in LLP in columns (1) through (4). In columns (5) and (6), both the level of LLP and change in LLP ( LLP) are considered simultaneously. In column (5) LLP is negative and marginally significant while LLP is insignificant. In column (6), both NLLP and NLLP predict future stock returns and moreover, the predictability of NLLP is as twice as larger than that of NLLP. Another interesting feature is that DLLP also negatively predicts stock returns. However, DLLP has the least predictive power among the three variables that are come out significant (NLLP, NLLP, and DLLP). We also provide Fama-MacBeth cross-sectional regression results in Panel B. Most of test results in Panel B is similar to Panel A. Specifically, the common finding in Panel A and 18

Panel B is that NLLP is negative and significant in both level and level-change analyses and NLLP is significant only in the change analysis. The only difference in Panel B compared to Panel A is that NLLP and DLLP lose return predictability in the level-change analysis. However, the t-value of NLLP is only marginally below significance level. Because the small number of years (17 or 16) statistical power of Fama-MacBeth regressions is presumably low. Thus, we consider Panel A as our main result. The results in Tables 3 and 4 are not definite evidence that the return predictability in LLP is not due to other risk factors or bank characteristics. To discern the risk-based explanation from the mispricing explanation, we conduct a time-series regression test using equation (4). Table 5 presents the coefficient estimates of the Fama French three-factor model with monthly returns for each loan loss provision quintile. The intercepts (α), which represent abnormal returns, are positive for the level of LLP and NLLP but not for DLLP. Also, abnormal returns to the level of NLLP is larger than that for the level of LLP, which is consistent with the portfolio sort returns reported in Table 3. We also examine the change variables. The fourth column shows that abnormal return to the LLP hedge portfolio is positive. In the fifth column, abnormal return to the LLP hedge portfolio is higher than that of the NLLP hedge portfolio, which is opposite of the results in Table 3. Lastly, the change in discretionary LLP ( DLLP) is not significant, consistent with Table 3. Taken together, abnormal returns to hedge portfolios based on the level of and change in both LLP and NLLP are robust to controlling for risk factors. It indicates that investors do not correctly price the level of and change in both LLP and NLLP, but not DLLP. Overall, these results support the mispricing explanation. Because the return predictability of LLP could be driven by a few years, we also check the stability of the results over time. Table 6 and Figure 1 present the performance of hedge portfolios based on LLP information across years. Table 6 shows that the most stable 19

trading strategy is one based on NLLP level and it yields positive returns in 14 out of 17 years, which is statistically significant (p=0.004). The next most stable trading strategy are those based on NLLP and DLLP. Abnormal returns to both strategies are positive in 11 out of 16 years, which is marginally significant (p=0.067). The abnormal returns to the level of LLP is also marginally significant. Figure 1 also shows that the magnitude of profit/loss of trading strategies based on LLP information are larger in the late 2000s during the recent financial crisis. Overall, the results in Table 6 are consistent with those in Tables 3, 4, and5, which indicate that the stock return predictability of LLP is driven by mispricing rather than mismeasurement of risk. [FIGURE 1 ABOUT HERE] [TABLE 6 ABOUT HERE] In sum, the results are consistent across i) the univariate sort test (Table 3), ii) crosssectional regression test (Table 4), iii) time series regression test (Table 5), and iv) the stability of the predictability of LLP information (Table 6). These results provide supporting evidence that equity investors misprice LLP information. Analyst forecast error tests We also examine whether sell-side analysts, sophisticated financial intermediaries, fully incorporate LLP information into their decision. Specifically, we test the association between forecast errors and LLP information. Table 7 presents the mean and median of oneyear ahead earnings forecast error (FE) across quintiles formed based on various loan loss provisions. 6 We also report the difference in the means and medians between the lowest quintile portfolio and the highest quintile portfolio. For each LLP variable, we conduct t-tests 6 Because the distribution analyst forecast errors are not symmetric and have a thick left tail, we provide both mean and median of the one-year ahead earnings forecast error in Panel A and Panel B, respectively. 20

comparing the mean FE between the highest and lowest quintile portfolio in Panel A, and Wilcoxon signed-rank tests comparing the median FE between the highest and lowest quintile portfolio in Panel B. Panel A of Table 7 reports the mean one-year ahead earnings forecast error across various LLP quintiles. 7 The result in Panel A shows that one-year ahead earnings forecast errors (FE) are significantly more negative for the highest LLP portfolio (LLP, NLLP, LLP, and NLLP) relative to the lowest LLP portfolio, which implies that the degree of overoptimism in analysts earnings forecasts is negatively related to LLP information. The test results using median FE in Panel B are similar to those using mean FE in Panel A. Based on the results in Table 7, analysts do not seem to employ all the information in LLP. However, note that the portfolio test in Table 7 is a univariate test. We conduct cross-sectional regression test in Table 8 to complement the univariate test in Table 7. [TABLE 7 ABOUT HERE] Table 8 presents the results of cross-sectional regressions of analyst one-year ahead earnings forecast error on loan loss provision and its components. We provide pooled regressions results in Panel A and Fama-MacBeth regressions in Panel B. Panel A presents the results of pooled regressions of FE on loan loss provision and their components. The overall results in Panel A show that analysts do not understand information in LLP and their components. Specifically, column (1) shows the regression with the level of LLP. The coefficient on LLP is negative which indicates that the degree of over-optimism is increasing in the level of LLP. Column (2) presents the regression where the level of LLP is decomposed into NLLP and DLLP. Both the coefficients on NLLP and DLLP are negatively significant and the coefficient on NLLP level is much larger than that of the level of DLLP, implying that 7 We construct quintile portfolios by using observation with only analyst forecast data available. 21

over-optimism due to the level of LLP is mainly attributable to the level of NLLP. This is similar to what is shown for equity investors. Column (3) presents the results on LLP. The coefficient on LLP is negative and significant. It indicates that the degree of over-optimism is also increasing in the change in LLP ( LLP). As in the case of the level analysis, column (4) shows that the coefficient on the level of NLLP is much larger for than that on the level of DLLP. Moreover, over-optimism of LLP is driven by NLLP. [TABLE 8 ABOUT HERE] Columns (4) and (5) provide the results considering the level and change of LLP information together. Column (5) presents the regression results on LLP and LLP. The coefficients on LLP and LLP in column (5) are negative and significant. Furthermore, the magnitude of the two coefficients are similar, implying that analysts have similar difficulty in understanding the information in LLP and LLP. Column (6) presents the regression results on the components of LLP and LLP (NLLP, DLLP, NLLP, and DLLP). The coefficients on NLLP, NLLP, and DLLP in column (6) are negative and significant. The magnitude and significance level of coefficients on NLLP and NLLP are much larger than that for DLLP and the coefficients on NLLP and NLLP have similar magnitudes. These results in Panel A of Table 8 suggest that analysts do not properly impound the information in the level of and change in LLP information, particularly, those of NLLP and NLLP. Panel B of Table 8 reports the Fama-MacBeth regression results. Consistent with Panel A, coefficients on LLP and LLP are significant in the level or change analysis or both. The difference in results between Panel A and Panel B is that NLLP is negative and significant in only change analysis and it is negative but insignificant in the level-change analysis. This also occurs in Panel B of Table 5. Another difference is that DLLP in Panel B is not significant in both the change analysis and the level-change analysis while DLLP in 22

Panel A is significant in both analyses. The low statistical power in Panel B may be due to a small number of years (17 or 16). Overall, Table 8 indicates that analysts do not fully utilize information in LLP, particularly, NLLP and NLLP, when they forecast banks earnings. VII. Conclusion This study investigates whether two type of market participants equity investors and sell-side analysts completely use information in LLP into their decisions. We find that both investors and sell-side analysts equity market participants do not fully appreciate the loanrelated risk information in LLP. Our study provides valuable implications for various market participants such as equity investors, analysts, regulators, and standard-setters. First, equity investors and analysts should be more knowledgeable about the information in LLP. Second, regulators should improve the current loan loss disclosure system so as to enhance market participants understandability of risks in bank loans. Third, standard-setters such as FASB and IASB should develop a loan loss provisioning model which objectively measures the expected loan loss under consideration. Our study is subject to the following limitations. First, we use only post-basel period data due to data availability. If pre-basel period data were available, we could have examined the effect of BASEL on the market valuation of LLP. Second, we cannot rule out the possibility that the discretionary loan loss provision model we use is subject to measurement errors. There is no common DLLP model in the banking literature. However, we use various versions of the DLLP model and find that our results are robust. Our study could be extended into the following areas. First, it can be interesting to consider how credit market participants use information in LLP. Because LLP is a type of 23

credit risk information, credit market participants are likely to better appreciate information in LLP. Second, the degree of mispricing due to LLP can vary across countries and their regulatory regimes. Numerous studies document that accounting mispricing changes across countries and their enforcement environments. Because banks are subject to regulations, it will be interesting to examine how different regulations internationally affect LLP mispricing. We leave these to future studies. 24

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