# Explaining the Accrual Anomaly: Evidence from Firm Size and Market Conditions.

I. IntroductionSince the accrual anomaly was documented in Sloan (1996), a large body of literature attempts to explore the causes of the anomaly. There has been an extended debate on whether the abnormal returns from the accrual anomaly are attributed to investors' fixation on reported earnings and their failure to understand the lower persistence of accruals (Richardson, Sloan, Soliman and Tuna 2005 and Shi and Zhang 2012) or exists due to limits to arbitrage (Pontiff 2006). Contributing to this debate is a stream of research that examines whether the accrual anomaly exists for all firms across the board or is caused by a small group of firms with certain characteristics or outlier observations in the sample (Collins, Cong and Hribar 2003; Kraft, Leone and Wasley 2006; Lev and Nissim 2006; Mashruwala, Ragjopal and Shevlin 2006; Taylor and Wong 2012 and Givoly, Hayn and Lourie 2016). The current study intends to reconcile the alternative explanations for the accrual anomaly by investigating whether the accrual anomaly is a robust phenomenon that exists for firms of all sizes and whether the accrual anomaly exhibits different behavior during the financial crisis in comparison to the normal market conditions, after controlling for firm characteristics that correlate with future returns.

There are several reasons why it is important to examine whether the accrual anomaly depends on firm size. First, our study would be helpful

to reconcile the diverging explanations for accrual anomaly documented in prior research. If the accrual anomaly only exists in small firms, investors' earnings fixation would not likely be the major underlying driver for the anomaly. Instead, it would lend support to the view that limits on arbitrage constrain the exploitation on the accrual mispricing. As small firms tend to have higher risk and higher transaction costs, they could be expected to exhibit stronger accrual anomaly (Collins, Gong and Hribar 2003; Mashruwala, Ragjopal and Shevlin 2006 and Hafzalla, Lundholm and van Winkle 2011). Second, Lev and Nissim (2006) note that the accrual anomaly involves trading in the extreme-accruals firms, which tend to be smaller in size. A more recent work by Givoly, Hayn and Lourie (2016) contends that several well documented anomalies, including the accrual anomaly, are subject to a small-firm-bias in that the anomalies are limited to smaller firms that represent a minor fraction of the market value of equity markets. (1) Similarly, Taylor and Wong (2012) demonstrate that the accrual abnormal returns could be sensitive to the handling of a small group of firms with extremely large returns. They argue that it is important to verify that the accrual anomaly is a robust phenomenon to justify the tremendous effort devoted to searching for detailed explanations. From an investment perspective, an anomaly that only manifests itself in small firms is not likely the result of mispricing and may not constitute any practical trading opportunities (Givoly, Hayn and Lourie 2016).

Some prior studies (Palmon, Sudit and Yezegel 2008 and Givoly, Hayn and Lourie 2016) show that the abnormal returns of accrual anomaly are not independent of firm size. They provide evidence that although the magnitude of abnormal returns decreases with firm size, the accrual anomaly still exists among the larger firms. A limitation of these studies is that they fail to provide direct test of whether the accrual mispricing is indeed attributed to small firms or not, while controlling for the disparity in firm characteristics, such as idiosyncratic risk and transaction costs, that affect future returns and probably correlate with firm size. (2)

The 2008 financial crisis offers a unique setting to examine the alternative explanations for the accrual anomaly. During the recent financial crisis, the capital market endured a severe credit shock and extreme liquidity restrictions (Rosch and Kaserer 2013). Such market conditions drastically increased transaction costs and reduced arbitrage activities. On the other hand, there has been a sharp decline in the trading activities of sophisticated institutional investors relative to those of native individual investors, which could also lead to more pronounced mispricing of accruals due to naive investors' inability to distinguish between the persistence of the accrual and cash flow components in earnings (Teo 2011 and Boyson, Helwege and Dindra 2014). To explore the effect of arbitrage costs and accrual mispricing, we examine the behaviors of the accrual anomaly during the financial crisis versus non-crisis normal period under normal market conditions and compare the magnitude of the accrual anomaly for small firms and large firms in those two different periods.

We undertake the hedge portfolio test and multivariate regression test using both annual buy-and-hold returns and announcement window returns (the three-day period surrounding the quarterly announcement date) (Sloan 1996 and Cheng and Thomas 2006). (3) We perform independent sorting on both total accruals and firm size. Specifically, we sort firms into deciles each year based on their total level of accruals; we also perform independent sorting of firms into deciles based on their market value. We define small (large) firms as those with market value at fiscal-year-end in the bottom (top) 20 percent of the sample year. (4) We then create a hedge portfolio long (short) in the lowest (highest) accrual firms and hold it for one year. We perform this hedge portfolio test for the full sample, the small firm sample, the medium-sized firm sample and the large firm sample, respectively. The magnitude of abnormal returns for hedge portfolios measures the extent of accrual mispricing. Since abnormal returns from the hedge portfolios are subject to the effect of various factors, we also conduct a multivariate regression analysis by regressing future risk-adjusted buy-and-hold hedge returns and announcement window returns, separately, on ranks of accruals while controlling for trading costs and ERC in an attempt to evaluate whether these factors can explain the difference in the accrual mispricing between the small and large firms, if any. We perform these tests for the entire sample using size dummy variables to assess the effect of size on the trading strategy.

We find evidence that the accrual anomaly is not driven by small firms. A hedge portfolio long (short) in low (high) accrual firms consisting of only small firms earns an insignificant abnormal return, averaging 10.7 percent, which is not significantly different from the 7.1 and 8.1 percent hedge portfolio returns of large firms and medium-sized firms, respectively. (5) In the multivariate regression analysis using annual buy-and-hold abnormal returns and announcement returns, we do not find that size has any significant impact on accrual mispricing either. This finding is robust to including controls for firms' price response to earnings (the ERC) and alternative measures of trading costs.

The tests of accrual anomaly surrounding the 2008 financial crisis reveal interesting results. We find that the accrual anomaly is stronger during the financial crisis period than during the non-crisis periods both before and after the crisis, as evidenced by significantly higher abnormal returns for firms with extreme accruals during the 2007-2008 financial crisis period. On the other hand, there is no significant difference in the abnormal returns between small firms and large firms, during both the financial crisis and the non-crisis periods.

This study contributes to the accrual anomaly literature in a number of ways. First, we provide direct evidence on the association between firm size and accrual anomaly. Contrary to the implications drawn from previous studies (e.g., Collins, Gong and Hribar 2003; Mashruwala, Ragjopal and Shevlin 2006 and Lev and Nissim 2006), the accrual anomaly is not driven by a group of small firms, nor is it more exacerbated for small firms than for large firms. Rather, the accrual anomaly is prevalent among firms of all sizes. Second, we contribute to the debate on the causes of the accrual anomaly. Our analysis of the behavior of accrual anomaly surrounding the recent financial crisis reveals that the accrual anomaly is more pronounced during the financial distress than during the non-crisis period. The extreme market conditions during the financial crisis, including credit freeze, evaporation of liquidity and significantly reduced transactions by professional investors, would likely cause higher transaction costs and barriers to arbitrage than under normal market conditions during the non-crisis period (Boyson, Helwege and Jindra 2014). Therefore, transaction costs and limits to arbitrage could be a major driver for the prolonged existence of significant abnormal returns from the accrual anomaly. On the other hand, after controlling for the difference in firm characteristics associated with idiosyncratic risk and transaction costs between small firms and large firms, a hedge portfolio of large firms earns roughly the same abnormal return as that of small firms, both in market distress during the financial crisis and under normal market conditions during the non-crisis period. Such results suggest that limits to arbitrage cannot fully explain the accrual anomaly. Rather, the evidence indicates that earnings fixation may also play a role in the accrual anomaly.

The rest of the paper is organized as follows. Section 2 reviews the literature and develops the hypothesis, section 3 outlines the research design, section 4 discusses our sample, section 5 contains the empirical results and section 6 concludes.

II. Review of Prior Literature and Discussion of Research Questions

In a seminal paper, Sloan (1996) shows that the accrual component of earnings is less persistent than the cash component. Sloan then shows that a hedge portfolio long (short) in the low-accrual (high-accrual) stocks earns abnormal returns averaging over 10 percent per annum. Sloan's explanation for this finding was that investors are naively fixating on earnings, failing to distinguish between the differential persistence of accruals and cash flows.

Several follow-up studies provide support for the earnings fixation hypothesis. Richardson, Sloan, Soliman and Tuna (2005) show that mispricing is strongest for the least persistent accruals. Shi and Zhang (2012) find that firms with the least persistent accruals relative to cash flows exhibit the greatest mispricing. (6) They further show that firms with greater price response to earnings (i.e., higher ERC) exhibit greater accrual mispricing. Hui, Nelson and Yeung (2016) find that greater persistence in the industry-wide component of earnings than that of the firm-specific component of earnings is not fully reflected in stock prices. A number of studies find evidence that managers use accruals to manage earnings and investors cannot unravel this earnings management, resulting in a predictable stock return pattern as the accruals reverse (Xie 2001; Pincus, Ragjopal and Shevlin 2007 and Keskek 2011).

Another stream of literature argues that the accrual anomaly is a manifestation of a more general growth anomaly (e.g., Fairfield, Whisenant and Yohn 2003; Zhang 2007 and Li, Lundholm and Minnis 2011). Investors misprice growth firms by over extrapolating past growth, failing to understand the diminishing rate of return to new investment (Lakonishok, Shleifer and Vishney 1994). However, Lewellenand Resutek (2016) show that investment and growth cannot fully explain the accrual anomaly.

While it is not implausible that individual traders fixate on earnings, it seems unlikely that sophisticated investors would be so naive. Since sophisticated investors, such as institutional investors, account for the majority of the trading volume in the U.S. stock market, the earnings fixation hypothesis must be able to provide evidence that sophisticated investors do not understand accruals. There is some prior research that suggests that sophisticated investors, as well as the market as a whole, do not fully understand accruals (Bradshaw, Richardson and Sloan 2001; Bhojraj and Swaminathan 2009 and Xu 2010).

Still, it is a puzzle how a simple trading strategy relying on accounting accruals could earn consistently significant abnormal returns, long after being widely documented in the literature. One stream of literature argues that the accrual anomaly persists because trading costs prevent traders from arbitrating it away. Arbitrageurs are constrained from eliminating mispricing by two costs: transaction costs and holding costs (Pontiff 2006). Transaction costs include commissions paid to the broker, the bid-ask spread and any price impact the trader has on the stock price. Holding costs refer to idiosyncratic risk exposure. (7)

The 2008 financial crisis offers a perfect setting to examine the role of limits to arbitrage in accrual anomaly. Prior studies (Rosch and Kaserer 2013 and Boyson, Helwege and lindra 2014) show that the capital market experienced severe distress during the financial crisis, with market liquidity drying up, credit largely frozen and trading activities by institutional investors significantly reduced. Such extreme market conditions would naturally induce substantially higher transaction costs and more barriers to arbitrage than under normal market conditions in the non-crisis period. We compare the behavior of the accrual anomaly during the crisis period and the non-crisis period. If the accrual anomaly is stronger during the financial crisis period, we would provide evidence that arbitrage costs play a significant role in the prolonged existence of accrual anomaly.

However, there is a limitation with comparing the behavior of accrual anomaly during the financial crisis and the non-crisis period. It could not provide relevant evidence on whether other factors, such as investors' earning fixation, drive accrual mispricing. To distinguish between the limits-to-arbitrage perspective and the earnings fixation perspective for the accrual anomaly, we also examine the interaction between the accrual anomaly and firm size. Firms with the lowest accruals are typically small firms with low-price, high bid-ask spread; low liquidity and high idiosyncratic risk (Collins, Gong and Hribar 2003; Lev and Nissim 2006; Mashruwala, Ragjopal and Shevlin 2006 and Hafzalla, Lundholm and van Winkle 2011). As a result, there are more limits-to-arbitrage on these stocks, which dissuade even the most sophisticated investors from trading them. (8)

The limits-to-arbitrage perspective predicts accrual mispricing will only exist for small firms with high trading costs because trading costs prevent traders from arbitraging the anomaly away. Indeed, if sophisticated investors, such as institutions, do trade on accruals information, leaving the anomaly non-existent for large liquid firms, the accrual anomaly is not a market anomaly. Instead, it is a consequence of limits-to-arbitrage preventing traders from correcting the mispricing. However, if the accrual anomaly exists among both small firms and large firms and yields similarly significant abnormal returns for these two groups, after controlling for factors such as idiosyncratic risk and transaction costs, it would provide clear evidence that the underlying driver of accrual mispricing is investors' inability to fully understand the information content in the accruals component of earnings, which is consistent with the earnings fixation perspective.

It should be noted that our study is different from some recent research that examines the interaction between the accrual anomaly and firm size. Givoly, Hayn and Lourie (2016) show that the accrual anomaly is more pronounced among small firms, which account for the majority of all firms in number but only a fraction of total market value, whereas the accrual anomaly is less significant among large firms, which account for a small fraction of firms in number but a majority of total market value. None of the commonly documented market anomalies produces significant abnormal hedge portfolio returns when they weight firm returns with firm value, which they interpret as evidence that these common market anomalies documented in prior research are all subject to the small-firm-bias. However, value weighting firm returns in calculating portfolio returns would give disproportionally large weight to the small group of extremely large firms and actually lead to a large-firm-bias. Such a bias that lends undue weight to extremely large firms probably explains why all of the well documented market anomalies in the literature fail to produce significant abnormal returns when the authors do value weighting. Moreover, the study ignores firm characteristics that correlate with firm and affect future returns in comparing abnormal returns between large and small firms.

III. Research Design

In testing the hypothesis, we use total accruals calculated from the statement of cash flows. Richardson, Sloan, Soliman and Tuna (2005) show that this measure captures more accruals of low reliability, which are more closely associated with mispricing. Total accruals are calculated as follows:

[mathematical expression not reproducible] (1)

where

TACC = total accruals,

EARN = earnings before extraordinary items, and

OCF = operating cash flows before extraordinary items and discontinued operations.

Subscripts i and t indicate firm and year, respectively. All variables are deflated by average total assets.

A. Test Designs

To test whether the relationship between accruals and future returns varies by firm size, we use two main tests, the hedge portfolio test and the multivariate regression analysis. We conduct the above tests using annual as well as announcement period returns. (9)

In the hedge portfolio test, we form portfolios based on accruals and calculate the hedge returns for large and small firms separately. Since we rank firms into accrual deciles based on the full sample of firms, this results in an unequal amount of large, medium and small firms in each decile. We define small (large) firms as those whose market value of equity falls below (above) the 20th (80th) percentile of all stocks in the fiscal year. The rest of the sample are classified into the medium-sized-firm group. While these cutoffs are admittedly arbitrary, our inferences remain unchanged when using the 10th and 90th percentiles. As in previous studies, we observe each accrual decile's average return over the 12-month holding period beginning four months after the fiscal year-end to ensure financial statement information is available. The hedge return is then the average return from going long in the low-accrual decile plus the average return from shorting the high-accrual decile.

Hedge [Return.sup.t+1] = (Low Decile [Return.sup.t+1]) - (High Decile [Return.sup.t+1]) (2)

We use abnormal returns in our tests. Abnormal returns are calculated as a firm's stock return less the return on a value-weighted portfolio of stocks in the same size decile for the 12 months beginning four months after the firm's fiscal year-end. Size breakpoints are calculated each December using all NYSE/AMEX/NASDAQ stocks on CRSR Firms are then placed in the appropriate size decile for the following 12 months.

The first main test is to examine whether the hedge return is greater for small firms than for large firms. In addition to comparing the hedge portfolio returns of large and small firms, we also conduct regression analyses to control for other factors that may affect accrual mispricing. Specifically, we estimate the following multivariate regression:

[mathematical expression not reproducible] (3)

where

Return = abnormal returns;

TACC = decile rank of total accruals;

SD = small firm dummy, with an indicator variable set equal to 1 if the firm is classified as small, 0 otherwise;

LD = large firm dummy, with an indicator variable set equal to 1 if the firm is classified as large, 0 otherwise; and

Control = ranks of control variables.

All independent variables are decile rank variables ranging from 0 to 1, with 0 being the lowest rank. We control for a firm's ERC to control for any discrepancy in firms' stock price response to earnings news. We follow the methodology of Shi and Zhang (2012) to calculate the ERC. We also control for trading costs to ascertain whether any difference in returns of large and small firms can be attributed to limits-to-arbitrage. We anticipate that mispricing for smaller firms would be significantly lower after controlling for trading costs. We adopt two measures of trading costs, idiosyncratic volatility (IV) and price impact on stock (PRC J). The two measures of trading costs are as follows:

IV=The standard deviation of [[epsilon].sub.i,t] in the following model:

[mathematical expression not reproducible] (4)

and

[mathematical expression not reproducible] (5)

where

IV = idiosyncratic volatility. This measure equals the standard deviation from the residual of a regression of a firm's stock return on CRSP's value-weighted market index. Largervalue of IV indicates higher holding costs for the firm's stock. The model is estimated separately for each firm using the past 36 months of return data.

R = stock return;

MKT = the return on the market;

PRC I = price impact measure based on Amihud (2002), which is the average ratio of daily absolute stock return to the trading volume in dollar on that day, and larger value of PRC J indicates less stock liquidity;

VOL = trading volume; and

DT = the number of trading days during the test period for which the stock returns are available.

Subscripts i, t and s denote firm, month and day, respectively. Idiosyncratic volatility is meant to capture the holding costs associated with arbitrage (Lev and Nissim 2006; Mashruwala, Ragjopal and Shevlin 2006 and Hafzalla, Lundholm and van Winkle 2011). An arbitrageur holding a stock bears holding costs as she waits for the mispricing to correct itself. PRC_I calculates the price change per dollar of trading volume and is meant to capture a stock price's sensitivity to trading. Abnormal returns of stocks with high PRC J could be overstated because the stock returns are sensitive to the potential price impact the trading could have on the stock price.

Following Bernard, Thomas and Wahlen (1997) and Cheng and Thomas (2006), we also test mispricing using announcement period returns. Bernard, Thomas and Wahlen (1997) propose that if anomalous returns are attributable to investor mispricing, then returns should be centered on future earnings announcement dates. In the context of the accrual anomaly, the reversal of the extreme accruals is revealed during subsequent earnings announcements (Sloan 1996). Therefore, we examine the percentage of the annual abnormal return occurring during the earnings announcements. The announcement period consists of the three-day period surrounding (i.e., one day before the earnings announcement through one day after the earnings announcement) each of the four quarterly earnings announcements in the subsequent one-year period (in total 12 days). This interval constitutes approximately 5 percent (12/255) of the annual window. Accordingly, if the abnormal returns associated with the accrual anomaly are truly mispricing, the portion of abnormal returns occurring at the earnings announcement interval will be substantially larger than 5 percent of the annual buy and hold returns. We re-run all of the above tests using the announcement return as the dependent variable.

IV. Sample

The sample includes all firm-year observations with the necessary financial data from the COMPUSTAT fundamentals annual file and stock return data from the Center for Research in Security Prices (CRSP) database from 1988-2014, resulting in 95,472 firm-year observations. (10) Our sample starts in 1988 because the statement of cash flows data was not available prior to that year. Consistent with prior research, we exclude financial firms (SIC codes 6000-6999) and firms with negative book values. We also exclude firms with sales less than one million dollars. We do not require the firm to have non-missing future accruals or earnings in order to guard against the look-ahead bias discussed in Kraft, Leone and Wasley (2006). (11) For regression analyses, we truncated all continuous variables at the 1st and 99th percentiles. Our results are not sensitive to this truncation; all inferences remain unchanged when using abnormal returns, which are not truncated or winsorized.

Table 1 displays the mean (median) of the relevant variables used in our study for the full sample as well as the Large and Small firm subsamples. The absolute magnitude of scaled total accruals is larger for small firms than for large firms. Compared to large firms, small firms also have much lower liquidity (PRCJ) and higher idiosyncratic volatility (IV) (median 10.505 vs. 0.048 and 0.173 vs. 0.078, respectively), consistent with prior findings that small firms tend to have higher transaction costs and greater limits-to-arbitrage (Marshruwala, Ragjopal and Shevlin 2006). Large firms on average have greater earnings response coefficient (median 3.096 vs 1.174), probably because they have better information environment (Collins, Kothari and Rayburn 1987 and Collins and Kothari 1989).

Table 2 presents Pearson and Spearman correlation coefficients for selected variables used in our analysis. Total accruals are negatively related to both annual and announcement abnormal returns (-0.039 and -0.048 respectively), consistent with the recent accrual anomaly literature (e.g., Cheng, Thomas and Liu 2012). As expected, firm size is positively related to ERC (0.114) but negatively related to price impact (-0.520) and idiosyncratic volatility (-0.440), our proxies for limits to arbitrage. The correlation suggests that large firms have higher ERC, greater stock liquidity and lower idiosyncratic risk. Annual abnormal returns are positively correlated with announcement period returns (0.275), yet the correlation is low enough to suggest these two variables provide unique pieces of information.

V. Empirical Results

A. Hedge Portfolio Test

We first use the hedge-portfolio test to examine whether the accrual mispricing differs for small and large firms. Each year we sort firms into 10 equal deciles based on the level of total accruals and form a hedge portfolio that is long in the lowest accrual decile and short in the highest accrual decile. Table 3 displays the mean of the annual abnormal size-adjusted returns for each accrual decile over the 1988-2014 sample period, as well as the abnormal returns to the hedge portfolio for the full sample and the large/medium/small firm subsamples. Consistent with prior studies, results in the full sample indicate that the size-adjusted abnormal returns for the highest accrual decile are significantly negative in years t+1 (-0.067, t=-4.72), while the size-adjusted abnormal returns for the lowest accrual decile are positive in years t+1 but not statistically significant (0.029, t=0.83). In other words, mispricing occurs mostly in extreme high-accrual portfolio but not so much in the low accrual portfolio, as evidenced in Kraft, Leone and Wasley (2006) and Zach (2007), among others. The hedge portfolio yields positive size-adjusted abnormal returns of 9.6 percent (t=2.52). (12)

In order to examine whether the accrual anomaly is mostly driven by small firms, we subsequently sort firms into deciles independently by total accruals and firm size. Each size-accrual decile portfolio is the interaction of two independent rankings. Large, Medium and Small Firms consist of firms in the top 2, middle 6 and bottom 2 size deciles, respectively. The size-adjusted abnormal returns for the highest and the lowest accrual deciles formed with the Small Firm subsample are -0.039, t=-1.44 and 0.068, t=1.70, respectively, yielding a significant total hedge portfolio return of 10.7 percent (t=2.21). Our untabulated data analysis shows a large portion of Small Firms has extreme accruals--nearly 30 percent of Small Firms are concentrated in the top and bottom accrual deciles. Given that the accrual anomaly is most evident in extreme accrual firms and Small Firms have a large proportion of extreme accrual firms, such finding might lead to the perception that the accrual anomaly is driven by Small Firms.

The size-adjusted abnormal returns for the highest and lowest accrual deciles of Large Firms are not statistically significant (-0.042, t=0.58 and 0.029, t=0.64, respectively). The hedge portfolio also yields a size-adjusted abnormal return of 7.1 percent (t=1.35), which is statistically insignificant but economically substantial. In contrast to Small Firms, Large Firms have relatively fewer firms with extreme accruals. Untabulated data analysis shows only 8.3 percent of those in the Large Firm subsample fall into the top and bottom accrual deciles.

Finally, the abnormal returns between the Large and Small Firms are only statistically different for 1 out of the 10 deciles (decile 5, t=2.71), indicating that abnormal returns across accrual deciles are not significantly different between Large and Small Firms. Moreover, the total abnormal hedge returns are not significantly different between the two groups of firms. Overall, our hedge portfolio test using size adjusted abnormal returns shows that the accrual mispricing is not driven by Small Firms. In fact, the accrual anomaly is manifested in both Small Firms and Medium Firms.

Table 4 reports the results for the hedge portfolio test using abnormal announcement-window returns. Both Sloan (1996) and Cheng and Thomas (2006) have shown that the accrual anomaly is more of an earnings-based anomaly than a risk-based anomaly because the returns to accrual strategies tend to cluster around future earnings announcements rather than occur smoothly over the year. We find that announcement returns are much more significant at the lowest and highest deciles for the full sample in comparison to any of the subsamples (0.019, t=2.88 and -0.017, t=-6.63, respectively), which is consistent with prior research. The hedge return is a significant 3.5 percent (t=5.13), which constitutes more than one third of the 10.3 percent annual abnormal return (0.035/0.096=36.4 percent). This is consistent with investors mispricing prior accruals, which reverses on the announcement days. Turning to the results for the Large Firm subsample, we find that the hedge strategy earns an insignificant abnormal announcement return of 1.3 percent (t=0.91) when trading on the announcement-window. In contrast, the Small Firm subsample earns a statistically significant announcement return of 2.6 percent (t=2.32). The evidence indicates the accrual anomaly returns are more concentrated in the announcement return window for small firms than for large firms. This result is consistent with the prices of large firms leading quarterly earnings announcements more than the prices of small firms. However, the announcement return in each decile is not significantly different between large and small firms in eight out of 10 deciles. Similarly, there is no significant difference in total abnormal announcement returns between large and small firms. Similar to small firms, medium-sized firms also earn significant abnormal returns in the extreme accrual deciles, yielding a total abnormal announcement return of 2.7 percent (t=4.02).

B. Fama and MacBeth (1973) Cross-sectional Regressions

We use Fama and MacBeth (1973) cross-sectional regressions to compare large and small firms in the relation between future returns and the scaled portfolio rank of accruals, controlling for factors that relate to future abnormal returns. We begin by first estimating the following equation as a benchmark of our data against prior literature:

[mathematical expression not reproducible] (6)

Next we add the interaction terms between TACC and dummy variable for small firms (SD) and large firms (LD) to the regression model:

[mathematical expression not reproducible] (7)

We estimate the regression models using the annual abnormal returns ([AbRet.sub.t+1]) and the announcement abnormal returns ([AnncRet.sub.t+1]) as the dependent variables, respectively.

B.7. Annual Abnormal Returns

Table 5 presents the results of estimating Equations (6) and (7) using annual abnormal returns. We interact TACC with our size dummies, SD and LD, to examine whether the return to the accrual strategy differs

between small and large firms. In column 1, we focus on the accruals and their interactions with the two size dummies. The coefficient on TACC is significantly negative at -0.081 (t=-2.84), suggesting that the accrual strategy could generate 8.1 percent return for medium-sized firms. The coefficient on the interaction terms, TACC*LD, is positive and marginally significant (0.047, t= 1.75), while the coefficient on TACC*SD is negative but insignificant (-0.009, t=-0.25), suggesting that large firms earn a slightly lower abnormal returns than medium-sized firms do. However, the difference in the sum of the coefficients of the TACC for small and large firms is not significant (diff. =0.056, F-statistic=1.59, p-value=0.21), suggesting that there is no statistically significant difference in the degree of the accrual anomaly for small firms and large firms. (13)

In column 2, we add the interaction between TACC and ERC to control for the effect of (ERC) on the accrual anomaly. Consistent with the expectation that the return to the accrual strategy should be higher for firms with higher ERC (Shi and Zhang 2012), the coefficient on the interaction term TACC*ERC remains significantly negative (-0.088, t=-3.29). Recall that the earnings fixation hypothesis predicts greater accrual mispricing for large firms because of the higher ERCs of large firms. After controlling for the effect of ERC on accrual mispricing, which is more likely to affect large firms, we expect to find less significant mispricing for large firms. Consistent with this argument, after controlling for ERC, the coefficient for TACC*LD loses its significance (0.037, t=1.60), in comparison to its coefficient in column 1. On the other hand, the difference in the sum of the coefficients of the TACC for small and large firms, TACC+TACC*SD and TACC+TACC*LD, is not significant (difference=0.047, F-statistic=1.16, p-value=0.29). The results indicate that accrual mispricing is not significantly different for large and small firms after controlling for the effect of ERC, the earnings response coefficient.

In colums 3 and 4, we control for limits-to-arbitrage via price impact (PRCJ) and idiosyncratic volatility (IV), respectively. Prior research (Mashruwala, Ragjopal and Shevlin 2006 and Hafzalla, Lundholm and van Winkle 2011) suggests higher returns to the accrual strategy for firms facing more limits to arbitrage. Both the coefficients of TACC*SD and TACC*LD are positive and insignificant when we control for PRCJ or IV. Further, the differences in the sum of the coefficients of the TACC for small and large firms are insignificant as well (diff.=0.000, F-statistic=0.00, p-value=0.99) for the test using PRC_I as a proxy for arbitrage costs; diff.=0.046, F-statistic=0.85, p-value=0.36 for the test using IV as a proxy for arbitrage costs). These results suggest that after controlling for limits to arbitrage, there is no significant difference in the level of accrual mispricing between small and large firms.

In column 5, the regression model includes all three control variables, namely ERC, PRC_I and IV The results are similar to those in columnc 2, 3 and 4, where the regression model contains one control variable at a time. The coefficient on TACC is significantly negative at -0.062 (t=-2.15), suggesting that the accrual strategy could generate 6.2 percent return for medium-sized firms after controlling for the effect of arbitrage costs and the discrepancy in firms' ERCs. The coefficients on the interaction terms of TACC*LD and TACC*SD are positive and insignificant (0.037, t=1.33 and 0.006, t=0.22). Further, the difference in the sum of the TACC for small and large firms is not significant (diff. =0.031, F-statistic=0.27, p-value=0.60), suggesting that there is no statistically significant difference in the degree of the accrual anomaly for small firms and large firms.

B.2. Announcement Returns

Prior research documents that a large portion of the abnormal returns from the accrual anomaly concentrate in the earnings announcement window periods. Therefore, we repeat the Fama-MacBeth (1973) regression analysis using announcement-window abnormal returns, Anne [Ret.sub.(i,t+1)] as the dependent variable. The test results are presented in Table 6. column 1 shows that the coefficient on the interaction term TACC*SD is insignificant (-0.005, t=-0.66), while the coefficient of TACC*LD is significantly positive (0.012, t=1.84), indicating that the announcement abnormal returns are significantly lower for large firms. Further, the difference in the sum of the coefficients on TACC between small and large firms is also statistically significant (diff.=0.017, F-statistic=3.30, p-value=0.08), suggesting that more of small firms' announcement abnormal returns to the accrual anomaly are realized during earnings announcements compared to large firms.

In column 2, we control for the ERC, which tends to have more substantial effect on the abnormal returns for large firms than for small firms, given that large firms on average have higher ERCs. We find that after controlling for the ERC, neither large nor small firms earn any extra significant announcement abnormal returns from accruals beyond those of medium-sized firms. The coefficients for TACC*SD and TACC*LD are both positive and insignificant (0.008, t=1.14 and 0.008, t=1.61, respectively). Furthermore, the difference in the sum of the coefficients of TACC+TACC*SD and of TACC+TACC*LD (diff.=0.001, F-statistic=2.60, p-value=0.12) is statistically insignificant, suggesting that there is no significant difference in the abnormal announcement returns for large firms and small firms.

In columns 3 and 4, we control for the price impact (PRCJ) and idiosyncratic risk (IV), respectively. After controlling for PRCJ, the coefficient of TACC*SD is significantly positive (0.016, t=2.31), while that of TACC*LD is insignificant, which indicates that when the effect of transaction costs is controlled for, small firms earn lower abnormal returns in the announcement window from the accrual anomaly than the medium-sized firms. However, the difference in the sum of the coefficients of TACC+TACC*SD and of TACC+TACC*LD (diff.=0.012, F-statistic=0.08, p-value=0.78) is statistically insignificant, suggesting that there is no significant difference in the abnormal announcement returns between large firms and small firms. In column 4, we control for idiosyncratic volatility IV. The results suggest both large firms and small firms earn similar abnormal announcement returns to those of the medium-sized firms, and there is no significant difference in the abnormal announcement returns of large firms and small firms.

In column 5, we control for all three variables, ERC, PRC_I and IV, in the regression model, and the results are similar to those in regressions where the control variables are added to the model one at a time. Large firms and small firms earn similar abnormal announcement returns to those of the medium-sized firms, and there is no significant difference in the abnormal announcement returns of large firms and small firms.

C. Analyses of the Accrual Anomaly Surrounding the Financial Crisis

The recent financial crisis of 2007-2008 offers a perfect setting to examine the role of arbitrage and earnings fixation in the accrual anomaly. During the crisis, the market liguidity dried up, and it became exceedingly difficult to obtain credit financing. Stock volatility spiked. As a result of the extreme market conditions, transactions by professional traders and hedge funds decreased significantly. Therefore, the transaction costs and limits to arbitrage increased significantly in comparison to the non-crisis period.

We examine the behaviors of the accrual anomaly during the financial crisis and non-crisis periods. In Table 7, we present the buy-and-hold 12-month hedge portfolio returns for the two periods in panel A. The hedge returns for Large Firms and Small Firms are 22.2 and 25.3 percent, respectively, during the 2007-2008 period. In the non-crisis period (in 2002-2006 and 2009-2014, i.e., five years before and after the crisis) the hedge returns are 5.1 and 4.5 percent for Large Firms and Small Firms, respectively. The returns are similar for small and large firms in both periods. However, abnormal returns are much higher in the crisis period. The announcement returns in panel B show similar results to the buy and hold annual returns. The announcement returns for Small Firms and Large Firms are 7.8 and 7.7 percent, respectively, during the crisis period, while the announcement returns for these two groups of firms are 3.2 and 1.8 percent, respectively, during the non-crisis period.

We conduct regression analysis using separate samples for the financial crisis period (2007-2008) and for the non-crisis period (2002-2006 and 2009-2014). Table 8 panel A reports the regression analysis using the one-year buy-and-hold abnormal returns as the dependent variable. For simplicity, the control variables are omitted from the table. The sum of coefficients for TACC and TACC*SD measures the total abnormal returns attributed to the small firms, and the sum of coefficients for TACC and TACC*LD measures the total abnormal returns attributed to the large firms. The total coefficients for TACC + TACC*SD and for TACC + TACC*LD in regression for the financial crisis period are 0.428 and 0.405, respectively, both significant at the 5 percent level. In contrast, in the regression using the non-crisis sample period, the coefficients for TACC + TACC*SD and for TACC + TACC*LD are 0.125 and 0.095, respectively, both significant at the 10 percent level. The coefficients are similar for small firms and large firms. However, the regression coefficients from the financial crisis sample period are significantly larger than the coefficients in regression using the non-crisis sample. The regression analysis in panel B using the announcement abnormal returns as the dependent variable yields similar results to those in panel A. The findings suggest that while the accrual anomaly is stronger during the financial crisis in comparison to the non-crisis period, the behaviors of the accrual anomaly are similar for small firms and large firms in both periods. Such evidence is consistent with the role of transaction costs and limits to arbitrage in explaining the prolonged existence of the accrual anomaly. Further, the results again demonstrate that the accrual anomaly is not driven by small firms. Rather, it seems to exist across firms of all sizes during both normal market period and the financial crisis.

D. Additional Analyses

We perform additional analyses as robustness checks. First, we re-run our tests using the 10 (th) and 90 (th) percentiles of market value of equity as breakpoints to define firm size. The regression analysis using the annual buy-and-hold abnormal returns as dependent variables is reported in panel A of Table 9. We omit control variables from the table for ease of exposition. After controlling for ERC and limits to arbitrage, we find small firms actually have weaker accrual mispricing in comparison to medium-sized firms. There is no evidence that the accrual anomaly is weaker for large firms. However, we find no significant difference in the degree of accrual anomaly between large firms and small firms. Panel B reports results from estimating the regression using announcement window abnormal returns. Again the results suggest that the accrual anomaly is not significantly different between large and small firms, even though we find some evidence that large firms earn lower abnormal announcement returns than medium-sized firms.

In addition to using alternative measures for small and large firms, we also performed the following robustness tests:

1. Re-ran our main analyses using percent accruals in place of total accruals;

2. Used working capital accruals in place of total accruals; and

3. To mitigate concerns about truncating the dependent variable, we used abnormal returns, which were winsorized instead of being truncated at 1 percent. We also used abnormal returns, which were not winsorized or truncated.

Our inferences remain unchanged when performing these additional analyses. The accrual anomaly is pervasive across firms of all sizes.

VI. Conclusion

In this study, we evaluate whether the accrual anomaly exists in firms of all sizes or is concentrated in small firms and whether the accrual anomaly demonstrates different behaviors during financial crisis in comparison to normal market conditions. Several recent papers suggest the anomaly is traded on by active institutional investors and is likely to exist only in small firms (e.g., Collins, Gong and Hriban 2003; Lev and Nissim 2006 and Mashruwala, Ragjopal and Shevlin 2006). On the other hand, during the 2008 financial crisis, the capital market experienced extreme market conditions, including liquidity drying up, heightened volatility and substantial reduction in transaction activities by sophisticated investors (Rosch and Kaserer 2013 and Boyson, Helwege and Jindra 2014). Such market conditions would induce higher transaction costs and limits to arbitrage. We find that the accrual anomaly is prevalent among firms of all sizes, both under normal market conditions and during the financial crisis. Our inferences remain unchanged when controlling for proxies for limits to arbitrage and the ERC.

We contribute to the literature on firm size and the accrual anomaly (Palmon, Sudit and Yezegel 2008 and Givoly, Hayn and Lourie 2016) by demonstrating that the accrual anomaly is not concentrated in small firms and does not depend on firm size. Our study also sheds light on the debate over the causes of the accrual anomaly. We find that the accrual anomaly is stronger during the financial crisis in comparison to the non-crisis period. With higher arbitrage costs during the financial crisis, the accrual anomaly became stronger. Such evidence is consistent with the role of transaction costs and limits to arbitrage in explaining the prolonged existence of the accrual anomaly. However, the fact that both small firms and large firms in extreme accruals experience similarly significant abnormal returns, after controlling for disparity in idiosyncratic risk and other firm characteristics between the two groups, indicates that limits to arbitrage may not fully explain the accrual anomaly. Investors' fixation on reported earnings could also play a role in the mispricing of accruals.

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Shanshan Pan

University of Houston-Clear Lake

Randall Zhaohui Xu

University of Houston-Clear Lake

(1) Givoly, Hayn and Lourie (2016) weight firm observations by their market value in calculating portfolio returns. Such a methodology would give undue weight to a small group of extremely large firms, causing in effect a large-firm-bias. Moreover, weighting firm observations by firm size would essentially deviate from the definition of the accrual anomaly per se. Sloan (1996) originally documents the accrual anomaly as such that firms with relatively low (high) levels of accruals during a given period tend to earn positive (negative) future abnormal returns in the following period. Please see section 2, Review of Prior Literature, for more details on the issue.

(2) Palmon, Sudit and Yezegel (2008) are mainly concerned with the effects of the interaction between company size and accruals on future abnormal returns and investigate whether firm size generates abnormal returns incremental to accruals. Consistent with their objectives, they adopt a double sorting method on size and accruals. In contrast, we perform independent sorting on size and accruals aimed at examining whether the accrual anomaly is more prominent in large firms versus small firms. See footnote 1 and the literature review for discussions on the limitation with the research approach of Givoly, Hayn and Lourie (2016).

(3) The hedge portfolio test referred to here is essentially a zero-investment portfolio investment strategy whereby we simultaneously long (short) $1 in the lowest (highest) accrual firms and examine whether this strategy yields any significant returns. In the seminal paper on the accrual anomaly, Sloan (1996) used the term "hedge portfolio" in describing such an investment strategy. Since then this term has been widely adopted in the accrual anomaly literature.

(4) In the sensitivity analysis, we also define small (large) firms as those in the bottom (top) 10 percent in market value and find gualitatively similar results.

(5) The hedge return for the full sample is 9.6 percent, which is similar to the 10.4 percent reported in Sloan (1996).

(6) Shi and Zhang (2012) measure the persistence of accruals relative to cash flows using a firm's past eight years of data. They show that using a hedge portfolio of firms with the least persistent accruals relative to cash flows earns a hedge return of 17.83 percent, as opposed to 9.37 percent when using firms with the most persistent accruals.

(7) Holding costs are incurred because the arbitrageur does not know when the mispricing will be corrected. If the correction takes too long, the holding costs will be greater than the profits earned, resulting in a net loss on the arbitrage. See Pontiff (2006) for an excellent discussion on this topic.

(8) Mashruwala, Ragjopal and Shevlin (2006) document that the hedge portfolio strategy earns a 14.4 percent return when using the sub-sample of stocks with the highest idiosyncratic risk but only 3.6 percent when using the stocks with the lowest idiosyncratic risk (a proxy for arbitrage risk).

(9) As a robustness check, we perform a Mishkin (1983) test of mispricing (untabulated). The results from the Mishkin test are consistent with those reported in the paper.

(10) The observation count is reduced for subsequent tests that require additional variables.

(11) In addition, we do not require the firm to have nonmissing stock return data for all 12 months. Missing returns are set to zero. We also use CRSP to assign stock exchange codes (See Kraft, Leone and Wasley 2006).

(12) Green, Hand and Soliman (2011) found that the hedge returns to the accrual anomaly have declined in the U.S. stock markets in recent years, possibly due to extensive exploitation of this trading strategy by hedge funds. An implication of their findings would be that the hedge funds are profiting from the mispricing of the accruals information by firms and investors. Moreover, the magnitude of our hedge portfolio return is similar to earlier studies on the accrual anomaly, e.g., Sloan (1996) and Xie (2001), even though the accrual anomaly is not as consistently significant as it was in the 20th century.

(13) The sum of the coefficients of TACC for the small groups (TACC+TACC*SD) is -0.090 (-0.081-0.009) and for the large firms (TACC+TACC*LD) is -0.034 (-0.081+0.047), resulting in a difference of 0.056.

TABLE 1 Mean (Median) of Selected Characteristics for a Sample of 95,472 Firm-years from 1988-2014 Table 1 displays the mean (median) of all variables used in our analysis. All variables are truncated at 1 and 99 percent. TACC is total accruals, calculated as earnings (ib) less OCF, where OCF is operating cash flows (oancf - xidoc). OCF/P is the operating cash ftows-to-price ratio ((oancf - xidoc)/(prcc_f*csho)); B/M is the book-to-market ratio (ceq/(prcc f*csho)); SG is the average sales growth over the past three years (sale) and ERC is the earnings response coefficient, calculated as in Shi and Zhang (2012). AbRet is the annual abnormal return, calculated as the raw buy-and-hold return on the firm less the value-weighted return on a portfolio of firms with similar market value. AnncRet is the abnormal announcement-window return, calculated as the size-adjusted return during the four three-day intervals surrounding the firm's subsequent four quarterly earnings announcements in year t+1. PRC_I is price impact, calculated as in Amihud (2002), multiplied by 1,000 for ease of interpretation. IV is idiosyncratic risk, calculated as the residual from a time-series regression of the firm's return on CRSP's value-weighted market index (vwretd) using up to 36 months of prior stock return data. Size is the log of market equity (prcc_f*csho). The full sample contains 95,472 firm-year observations. Small (large) firms are defined as those with market value in the bottom (top) 20 percent of all firms for that year. Diff is the difference in mean (median) between large and small firms. (*), (**) and (***) denote statistical significance at the 10, 5 and 1 percent levels, respectively. Variable Full Large Small TACC -0.055 -0.052 -0.075 (-0.049) (-0.048) (-0.061) ERC 3.716 4.293 1.981 (2.375) (3.096) (1.174) PRC_I 6.264 0.257 17.656 (0.705) (0.048) (10.505) IV 0.140 0.092 0.188 (0.123) (0.078) (0.173) Size 5.150 7.943 2.441 (5.088) (7.872) (2.491) [AbRet.sub.t+1] 0.001 -0.002 0.026 (-0.080) (-0.031) (-0.16) [AnncRet.sub.t+1] 0.011 0.010 0.037 (0.005) (0.009) (0.009) N 95,472 20,080 18,783 Variable Diff. TACC 0.022 (***) (0.012) (***) ERC 2.312 (***) (1.922) (***) PRC_I -17.399 (***) (-10.457) (***) IV -0.095 (***) (-0.095) (***) Size 5.502 (***) (5.381) (***) [AbRet.sub.t+1] -0.028 (***) (0.131) (***) [AnncRet.sub.t+1] -0.027 (***) (-7.059) N TABLE 2 Pearson (Upper Diagonal) and Spearman (Lower Diagonal) Correlation Coefficients for Selected Variables for a Sample of 95,472 Firm-years from 1988-2014 Table 2 displays the average yearly Pearson (Spearman) correlation coefficients above (below) the diagonal. T-statistics are reported in parenthesis below. The sample spans 1988-2014. Variable definitions are provided in Table 1. TACC ERC PRC_I IV Size TACC 0.068 -0.013 -0.118 0.039 (0.001) (0.001) (0.001) (0.001) ERC 0.075 -0.056 -0.119 0.114 (0.001) (0.001) (0.001) (0.001) PRCJ 0.046 -0.058 0.102 -0.520 (0.001) (0.001) (0.001) (0.001) IV -0.098 -0.148 0.283 -0.440 (0.001) (0.001) (0.001) (0.001) Size 0.014 0.139 -0.853 -0.486 (0.001) (0.001) (0.001) (0.001) [AbRet.sub.t+1] -0.021 0.048 -0.071 -0.133 0.105 (0.001) (0.001) (0.001) (0.001) (0.001) [AnncRet.sub.t+1] -0.037 0.036 0.030 -0.027 -0.011 (0.001) (0.001) (0.001) (0.001) (0.001) [AbRet.sub.t+1] [AnncRet.sub.t+1] TACC -0.039 -0.048 (0.001) (0.001) ERC 0.009 0.025 (0.022) (0.001) PRCJ 0.012 0.082 (0.001) (0.001) IV -0.007 -0.016 (0.033) (0.001) Size -0.013 -0.051 (0.001) (0.001) [AbRet.sub.t+1] 0.275 (0.001) [AnncRet.sub.t+1] 0.311 (0.001) TABLE 3 Time-Series Means(t-statistics) of Annual Size-Adjusted Buy-and-Hold Returns for Each Portfolio Ranked by Total Accruals Table 3 reports time-series average of the mean annual size-adjusted buy-and-hold abnormal return for the portfolio of firms in the respective accrual decile. Each year firms are ranked into 10 equal deciles based on the level of total accruals (TACC). Then, the mean size-adjusted buy-and-hold return is calculated for each decile. Abnormal returns are the 12-month raw return beginning in the fourth month after the fiscal year-end less the value-weighted return on a portfolio of firms with similar market value. FM t-statistic is the t-value for the hedge return (HEDGE) calculated as in Fama and MacBeth (1973). Separate statistics are provided for the full sample, the medium firm, large firm and small firm subsamples. Small (large) firms are defined as those with market value in the bottom (top) 20 percent of all firms for that year. Medium firms are those in between. (*), (**) and (***) denote statistical significance at the 10, 5 and 1 percent levels, respectively. Portfolio Accrual Ranking Lowest 1 2 3 Full Sample 0.029 0.033 (**) 0.025 0.019 (0.83) (1.71) (1.93) (1.95) Medium Firms 0.002 0.038 (**) 0.024 0.016 (0.07) (1.90) (1.74) (1.57) Large Firms 0.029 -0.008 0.010 0.008 (0.64) (-0.42) (0.72) (0.98) Small Firms 0.068 (*) 0.045 (*) 0.047 (*) 0.051 (1.70) (1.67) (1.72) (1.58) Diff. between -0.039 -0.052 -0.037 -0.043 Large vs Small (-0.65) (-1.62) (-1.20) (-1.30) 4 5 6 7 8 Full Sample 0.007 0.014 0.010 -0.009 -0.024 (**) (0.92) (1.51) (1.43) (-1.15) (-2.32) Medium Firms 0.011 0.007 0.007 -0.015 -0.035 (***) (1.54) (0.64) (0.72) (-1.65) (-3.24) Large Firms 0.007 -0.000 0.004 -0.005 -0.010 (0.85) (-0.01) (0.41) (-0.52) (-0.59) Small Firms -0.006 0.080 (***) 0.031 -0.001 -0.007 (-0.15) (2.79) (0.87) (-0.03) (-0.32) Diff. between 0.013 -0.080 (***) -0.028 -0.005 -0.003 Large vs Small (0.34) (-2.71) (-0.19) (-0.10) (-0.09) Highest Hedge Full Sample -0.067 (***) 0.096 (**) (-4.72) (2.52) Medium Firms -0.078 (***) 0.081 (**) (-4.77) (2.04) Large Firms -0.042 0.071 (-0.58) (1.35) Small Firms -0.039 0.107 (**) (-1.44) (2.21) Diff. between -0.003 Large vs Small (-0.54) TABLE 5 Fama-MacBeth(1973) Regressions of One-year Ahead Size-adjusted Buy-and-hold Returns on the Portfotio Ranks of Accruals and Other Predictors of Return Table 5 displays the average yearly coefficients from a linear regression estimated as in Fama and MacBeth (1973). In panel A, the dependent variable in all regressions is the firm's one-year ahead size-adjusted buy-and-hold returns. All other independent variables are rank variables, ranging from 0 to 1, with 0 being the low rank. The last row displays the adjusted R2 from each model. There are 27 firm-years estimated using the 1988-2014 time period. Variable definitions are provided in Table 1. In panel B, the dependent variable in all regressions is the firm's earnings announcement window returns. SD and LD are interacted with all control variables. SD (LD) is an indicator variable set equal to! if the firm is classified as a small firm (large firm), zero otherwise. (*), (**) and (***) denote statistical significance at the 10, 5 and 1 percent levels, respectively. Model: [AbRet.sub.t+1] = [[lambda].sub.0] + [[lambda].sub.1] TACC, + [[lambda].sub.2]SD + [[lambda].sub.3]LD + [[lambda].sub.4] [TACC.sub.t] *SD + [[lambda].sub.5] [TACC.sub.t]*LD + [[lambda].sub.6][TACC.sub.t] *[ERC.sub.t] + [[lambda].sub.7] [TACC.sub.t]* PRC_[l/.sub.t] +[[lambda].sub.8][TACC.sub.],*lv, + [[lambda].sub.9][ERC.sub.t] + [[lambda].sub.10] PRC_[l.sub.t], + [[lambda].sub.11][V.sub.t] + [[lambda].sub.t+1] Variable (1) (2) (3) Estimate Estimate Estimate (t-stat) (t-stat) (t-stat) Intercept 0.038 (**) 0.019 0.012 (1.88) (0.71) (0.28) TACC -0.081 (***) -0.086 (***) -0.063 (*) (-2.84) (-2.93) (-2.17) SD 0.032 (*) 0.036 (*) 0.014 (1.79) (2.00) (0.51) LD -0.021 -0.023 -0.001 (-1.36) (-1.58) (-0.03) TACC*SD -0.009 -0.010 0.017 (-0.25) (-0.27) (0.45) TACC*LD 0.047 (*) 0.037 0.017 (1.75) (1.60) (0.56) TACC*ERC -0.088 (***) (-3.29) TACC*PRC_I -0.009 (**) (-2.32) TACC* IV ERC 0.071 (***) (3.02) PRC_I 0.006 (0.95) IV Adj. [R.sub.2] 0.58% 0.69% 1.20% Test of the Difference in the Sum of the Coefficients of TACC+TACC* SD and of TACC+TACC*LD Difference 0.056 0.047 0.000 F-Statistic 1.59 1.16 0.00 P-Value 0.21 0.29 0.99 Variable (4) (5) Estimate Estimate (t-stat) (t-stat) Intercept 0.069 (**) 0.010 (2.10) (0.16) TACC -0.106 (***) -0.062 (**) (-3.20) (-2.15) SD 0.032 0.043 (1.51) (1.91) LD -0.026 0.010 (-1.61) (0.64) TACC*SD 0.002 0.037 (0.04) (1.33) TACC*LD 0.047 0.006 (1.62) (0.22) TACC*ERC -0.105 (***) (-4.85) TACC*PRC_I -0.007 (*) (-1.69) TACC* IV 0.003 0.009 (***) (0.84) (2.89) ERC 0.091 (***) (5.99) PRC_I 0.006 (1.25) IV -0.004 -0.012 (**) (-0.49) (-2.69) Adj. [R.sub.2] 1.83% 2.44% Test of the Difference in the Sum of the Coefficients of TACC+TACC* SD and of TACC+TACC*LD Difference 0.046 0.031 F-Statistic 0.85 0.27 P-Value 0.36 0.60 TABLE 6 Fama-MacBeth(1973) Regressions of Announcement Return on the Portfolio Ranks of Accruals and Other Predictors of Returns Table 6 displays the average yearly coefficients from a linear regression estimated as in Fama and MacBeth (1973). The dependent variable in all regressions is the firm's announcement returns. SD (LD) is an indicator variable set equal to one if the firm is classified as a small firm (large firm), 0 otherwise. All other independent variables are rank variables, ranging from 0 to 1, with 0 being the low rank. The last row displays the adjusted [R.sup.2] from each model. In panel B, SD and LD are interacted with all control variables. These interactions are omitted to save space. There are 27 firm-years estimated using the 1988-2014 time period. Variable definitions are provided in Table 1. (*), (**) and (***) denote statistical significance at the 10, 5 and 1 percent levels, respectively. Model: [AnncRet.sub.t+1] = [[lambda].sub.0] + [[lambda].sub.1] TACC, + [[lambda].sub.2]SD + [[lambda].sub.3]LD + [[lambda].sub.4][TACC.sub.t] *SD + [[lambda].sub.5] [TACC.sub.t]*LD + [[lambda].sub.6][TACC.sub.t]*[ERC.sub.t] + [[lambda].sub.7][TACC.sub.t]*PRC_[l/.sub.t] + [[lambda].sub.8][TACC.sub.],*lv, + [[lambda].sub.9] [ERC.sub.t] + [[lambda].sub.10] PRC_[l.sub.t], + [[lambda].sub.11][V.sub.t] + [[lambda].sub.t+1] Variable (1) (2) (3) Estimate Estimate Estimate (t-stat) (t-stat) (t-stat) Intercept 0.016 (***) 0.002 -0.005 (3.55) (0.60) (-1.30) TACC -0.024 (***) -0.017 (***) -0.017 (***) (-5.25) (-3.51) (-3.29) SD 0.032 (***) 0.011 (*) -0.011 (**) (4.25) (1.90) (-2.23) LD 0.001 0.001 0.020 (***) (0.19) (0.31) (5.40) TACC*SD -0.005 0.008 0.016 (**) (-0.66) (1.14) (2.31) TACC*LD 0.012 (*) 0.008 0.004 (1.84) (1.61) (0.63) TACC*ERC -0.016 (**) (-2.36) TACC*PRC_I -0.001 (-1.61) TACC*IV ERC 0.031 (***) (6.37) PRCJ 0.005 (***) (7.78) IV Adj. R2 0.90% 0.80% 0.93% Test of the difference in the Sum of the Coefficients of TACC+TACC*SD and of TACC+TACC*LD Difference 0.017 0.001 0.012 F-Statistic 3.30 (*) 2.60 0.08 P-Value 0.08 0.12 0.78 Variable (4) (5) Estimate Estimate (t-stat) (t-stat) Intercept 0.037 (***) 0.001 (7.34) (0.03) TACC -0.033 (***) -0.021 (***) (-5.24) (-2.29) SD 0.009 -0.001 0.67) (-0.06) LD -0.006 0.010 (**) (-1.57) (2.33) TACC*SD 0.010 0.011 (1.92) (1.22) TACC*LD 0.009 0.006 (1.60) (0.80) TACC*ERC -0.015 (**) (-2.33) TACC*PRC_I -0.001 (-0.74) TACC*IV 0.001 0.001 (1.40) (1.01) ERC 0.026 (***) (6.04) PRCJ 0.004 (***) (5.86) IV -0.004 (***) -0.003 (***) (-5.83) (-4.04) Adj. R2 0.83% 1.08% Test of the difference in the Sum of the Coefficients of TACC+TACC*SD and of TACC+TACC*LD Difference 0.001 0.005 F-Statistic 2.24 0.00 P-Value 0.14 0.99 TABLE 7 Time-Series of Hedge Returns to Accrual Anomaly during Financial Crisis and Non-financial Crisis Periods by Firm Size Table 7 reports the time-series average of the abnormal returns to the accrual anomaly during the financial crisis period (2007-2008) and the non-financial crisis period (2002-2006 and 2009-2014). Panel A reports the results based on [AbRet.sub.t+1], the firm's one-year ahead size-adjusted buy-and-hold returns; panel B reports the results based on [AnncRet.sub.t+1], the firm's announcement returns. See Table 3 and 4 for details on the method.3 (*), (**) and (***) denote statistical significance at the 10, 5 and 1 percent levels, respectively Financial Crisis Period Non-financial Crisis Period 2007-2008) (2002-2006 and 2009-2014) Penal A Means of (t-statistic) Annual Size-adjusted Buy-and-hold Hedge Returns Lowest Highest Hedge Lowest Accruals Accruals Returns Accruals Decile Decile Decile Full 0.154 (***) -0.043 0.197 (***) 0.021 (2.86) (-1.08) (2.94) (1.35) Medium 0.166 (**) -0.002 0.168 (*) 0.012 (2.49) (-0.03) (1.93) (0.66) Large 0.180 (**) -0.042 0.222 (**) 0.037 (2.25) (-1.00) (2.46) (1.10) Small 0.126 0.126 (***) 0.253 (*) 0.036 (1.14) (-2.69) (1.90) (1.54) Diff. 0.054 0.085 -0.031 0.001 Between Large vs Small (0.39) (1.00) (0.85) Panel B Means of (t-statistic) Announcement Hedge Returns Lowest Highest Hedge Lowest Accruals Accruals Returns Accruals Decile Decile Decile Full 0.032 (**) -0.021 (**) 0.053 (***) 0.004 (2.25) (-2.12) (3.06) (0.82) Medium 0.034 (**) -0.002 0.036 (*) 0.003 (2.02) (-0.19) (1.75) (0.52) Large 0.037 -0.040 0.077 (**) 0.002 (1.35) (-1.84) (2.20) (0.19) Small 0.030 -0.049 (**) 0.078 (**) 0.005 (1.01) (-2.37) (2.20) (0.62) Diff. Between 0.007 -0.009 -0.001 -0.003 Large vs Small (0.18) (0.34) (-0.22) Financial Crisis Period Non-financial Crisis Period 2007-2008) (2002-2006 and 2009-2014) Penal A Means of (t-statistic) Annual Size-adjusted Buy-and-hold Hedge Returns Highest Hedge Accruals Returns Decile Full -0.017 0.036 (*) (-1.19) (1.74) Medium -0.019 0.031 (-1.40) (1.17) Large -0.013 0.051 (*) (-0.48) (1.70) Small -0.004 0.045 (*) (-1.13) (1.68) Diff. -0.009 0.006 Between Large vs Small (0.79) Panel B Means of (t-statistic) Announcement Hedge Returns Highest Hedge Accruals Returns Decile Full 0.024 (***) 0.028 (***) (-5.93) (4.70) Medium 0.025 (***) 0.027 (***) (-4.94) (3.86) Large -0.016 (**) 0.018 (*) (-2.18) (1.67) Small 0.027 (***) 0.032 (***) (-2.99) (2.57) Diff. Between 0.011 -0.014 Large vs Small (0.93) TABLE 8 Fama-MacBeth (1973) Regressions of Stock Returns on Accruals during Financial Crisis and Non-financial Crisis Periods Table 8 reports the average yearly coefficients from a linear regression estimated as in Fama and MacBeth (1973) during the financial crisis period (2007-2008) and the non-financial crisis period (2002-2006 and 2009-2014). The dependent variable in Panel A is [AbRet.sub.t+1], the firm's one-year ahead size-adjusted buy-and-hold returns. The dependent variable in Panel B is [AnncRet.sub.t+1] the firm's announcement returns. SD (LD) is an indicator variable set equal to 1 if the firm's market value of equity falls in the bottom 20 percent (top 20 percent) of all firms in year t, and 0 otherwise. The regression models are the same as in Panel B of Table 5 and 6. The differences in coefficients between the financial crisis period and non-financial crisis period are testing using an indicator variable for the financial period observations. We present results separately to make the results for each subsample more evident. In addition, only TACC related variables are reported in the table for brevity. (*). (**) and (***) denote statistical significance at the 10. 5 and 1 percent levels, respectively. Panel A One-year Ahead Size-adjusted Buy-and-hold Returns Financial Non-financial Crisis Period Variable Crisis Period (2002-2006 and 2009-2014) Estimate Estimate TACC -0.263 (**) -0.061 (*) TACC*SD -0.165 -0.064 TACC*LD -0.142 -0.034 Difference P-Value -0.428 (**) -0.125 (*) 0.303 (**) 0.03 TACC+TACC*LD -0.405 (**) -0.095 (*) 0.310 (**) 0.04 Difference 0.023 0.030 P-Value 0.12 0.10 Panel B Announcement Returns Financial Non-financial Crisis Variable Crisis Period Period (2007-2008) (2002-2006 and 2009-2014) Estimate Estimate TACC -0.052 (**) -0.019 (**) TACC*SD -0.013 -0.017 TACC*LD -0.080 (*) 0.014 Difference P-Value TACC+TACC*SD -0.065 (**) -0.036 (*) 0.029 (*) 0.08 TACC+TACC*LD -0.132 (**) -0.005 0.127 (**) 0.02 Difference 0.067 0.031 P-Value 0.27 0.11 TABLE 9 Robustness Check Using 10th and 90th Percentiles to Define Small and Large Firms Table 9 displays the average yearly coefficients from a linear regression estimated as in Fama and MacBeth (1973). The dependent variable in panel A is [AbRet.sub.t+1], the firm's one-year ahead size-adjusted buy-and-hold returns. The dependent variable in panel B is [AnncRet.sub.t+1] the firm's announcement returns. SD (LD) is an indicator variable set equal to 1 if the firm's market value of equity falls in the bottom 10 percent (top 10 percent) of all firms in year t. and 0 otherwise. The regression models are the same as in Panel B of Table 5 and 6. Only TACC related variables are reported in the table for brevity. (*). (**) and (***) denote statistical significance at the 10, 5 and 1 percent levels, respectively. Panel A: Fama-MacBeth (1973) Regressions of One-year ahead Size-adjusted Buy-and-hold Returns on the Portfolio Ranks of Accruals and Other Predictors of Returns (1) (2) (3) Variable Estimate Estimate Estimate (t-stat) (t-stat) (t-stat) TACC -0.078 (***) -0.075 (***) -0.057 (**) (-2.78) (-2.73) (-2.69) TACC*SD -0.010 0.049 (**) 0.082 (***) (-0.21) (2.24) (3.22) TACC*LD 0.063 0.014 -0.004 (1.70) (0.50) (-0.16) Adj. [R.sup.2] 0.69% 0.92% 1.21% Test of the Difference in the Sum of the Coefficients of TACC+TACC* SD and of TACC+TACC*LD Difference 0.073 0.035 0.087 F-Statistic 1.54 1.76 0.02 P-Value 0.23 0.19 0.89 Panel B: Fama-MacBeth (1973) Regressions of Announcement Return on the Portfolio Ranks of Accruals and Other Predictors of Returns Variable (1) (2) (3) Estimate Estimate Estimate (t-stat) (t-stat) (t-stat) TACC -0.021 (***) -0.016 (***) -0.033 (***) (-6.12) (-3.54) (-5.18) TACC*SD 0.010 0.004 0.001 (1.48) (0.48) (0.14) TACC*LD 0.018 (**) 0.021 (**) 0.029 (***) (2.09) (2.68) (2.75) Adj. [R.sup.2] 0.40% 0.66% 0.53% Test of the Difference in the Sum of the Coefficients of TACC+TACC* SD and of TACC+TACC*LD Difference 0.008 0.017 0.028 F-Statistic 0.91 1.83 2.70 P-Value 0.94 0.21 0.11 Panel A: Fama-MacBeth (1973) Regressions of One-year ahead Size-adjusted Buy-and-hold Returns on the Portfolio Ranks of Accruals and Other Predictors of Returns (4) (5) Variable Estimate Estimate (t-stat) (t-stat) TACC -0.106 (***) -0.059 (**) (-5.54) (-2.60) TACC*SD 0.039 (*) 0.063 (**) 0.73) (2.71) TACC*LD 0.038 0.001 (1.34) (0.04) Adj. [R.sup.2] 1.59% 2.42% Test of the Difference in the Sum of the Coefficients of TACC+TACC* SD and of TACC+TACC*LD Difference 0.002 0.062 F-Statistic 0.95 0.44 P-Value 0.33 0.52 Panel B: Fama-MacBeth (1973) Regressions of Announcement Return on the Portfolio Ranks of Accruals and Other Predictors of Returns Variable (4) (5) Estimate Estimate (t-stat) (t-stat) TACC -0.034 (***) -0.025 (***) (-5.88) (-2.81) TACC*SD 0.010 (**) 0.003 (1.60) (0.43) TACC*LD 0.019 (**) 0.022 (*) (2.15) (1.86) Adj. [R.sup.2] 0.75% 1.36% Test of the Difference in the Sum of the Coefficients of TACC+TACC* SD and of TACC+TACC*LD Difference 0.009 0.019 F-Statistic 0.73 0.85 P-Value 0.45 0.48

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Author: | Pan, Shanshan; Xu, Randall Zhaohui |
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Publication: | Quarterly Journal of Finance and Accounting |

Date: | Jan 1, 2019 |

Words: | 12682 |

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