Evaluating the accrual-fixation hypothesis as an explanation for the accrual anomaly

Evaluating the accrual-fixation hypothesis as an explanation for the accrual anomaly Tzachi Zach * Olin Business School Washington University in St. Louis St. Louis, MO 63130 Tel: (314)-9354528 zach@wustl.edu First version: August 2004 This version (2.0): September 2007 Abstract. In this study, I directly examine whether the accrual-fixation hypothesis explains the accrual anomaly, first documented in Sloan (1996). The accrual-fixation hypothesis posits that investors fixate on earnings without taking into account accruals tendency to reverse. Thus, the returns to an accrual-based strategy are related to accruals reversals. I use the reversal property of the accrual-fixation hypothesis to generate testable empirical predictions. I find that extreme accrual firms are sticky and tend to remain in extreme deciles in two consecutive years. Sticky firms are associated with future abnormal returns only in the low accruals decile. In contrast, in the high accruals decile, abnormal returns are related to accruals reversals. This asymmetry between low and high accrual deciles suggests that the causes of the accrual anomaly differ across the two groups. Evidence on firm characteristics reveals that in the high accruals decile future abnormal returns are related to high abnormal accruals, while in the low accruals decile future abnormal returns are related to high bankruptcy risk. Overall, the evidence implies that the accrual-fixation hypothesis is descriptive of the behavior of high accrual firms but not of low accrual firms. * This paper is based on parts of my dissertation completed at the University of Rochester. I would like to thank the members of my dissertation committee: Bill Schwert, Jerry Warner, Ross Watts (chair) and Jerry Zimmerman for their valuable comments and suggestions. I also benefited greatly from the insights of an anonymous referee, Sudipta Basu, Daniel Cohen, Nick Dopuch, Philip Joos, Ron King, S.P. Kothari, Andy Leone, Thomas Lys (the editor), Richard Sloan, Michela Verardo and Charles Wasley. I also thank seminar participants at University of California at Berkeley, University of Chicago, Columbia University, Emory University, MIT, Northwestern University, Washington University in St. Louis and University of Washington. Finally, I thank the Deloitte Foundation for generous financial support. All errors are my own.

1 1. Introduction Sloan (1996) and a number of subsequent studies report that a trading strategy based on publicly available information about operating accruals earns abnormal returns of approximately 10% in the year following its initiation. The strategy is based on firms in the extreme high and low deciles of accruals cross-sectional distribution. This empirical regularity has been termed the accrual anomaly. Sloan (1996) also shows that accruals and cash flows exhibit differential persistence with respect to future earnings. He attributes the return predictability to the market s inability to take the differential persistence into account. More specifically, he argues that stock prices act as if investors fixate on earnings, failing to distinguish fully between the differential properties of the accrual and cash flow components of earnings. In this study I directly examine Sloan s (1996) explanation for the causes of the accrual anomaly. I label this explanation the accrual-fixation hypothesis. According to this hypothesis, return predictability arises because market participants treat accruals and cash flows similarly, without taking into account accruals tendency to reverse in the following year. Investors misprocessing of the reversal properties of accounting information is central to the accrual-fixation hypothesis. Under the accrual-fixation hypothesis, and based on the results of Mishkin (1983) tests of rational pricing, investors overprice (underprice) firms with high (low) accruals. As a result, firms with extreme accruals are associated with abnormal returns in the following year. Since abnormal returns appear in extreme accrual deciles and because under the accrualfixation hypothesis returns arise from accruals reversals, I expect that firms in these deciles

2 will exhibit reversal patterns similar to those of accruals. Under this scenario accrual extremeness is expected to be transitory. Thus, the accrual-fixation hypothesis predicts that extreme accrual deciles are likely to be composed of different firms in adjacent years. In addition, the accrual-fixation hypothesis predicts that no abnormal returns will be associated with firms that do not exhibit reversals because reversals are the primary cause of abnormal returns. If reversals are associated with future returns, the accrual-fixation hypothesis does not specify the degree or type of reversals that are more likely to result in predicable return patterns. In my analysis, I use the reversal feature of the accrual-fixation hypothesis to generate testable empirical predictions for it. I then perform several empirical tests to evaluate whether the data is consistent with these predictions. First, I examine the time-series pattern of firms with extreme accruals to see whether these firms tend to leave the top and bottom accrual deciles in the following period or whether they are sticky. 1 In other words, do these firms habitually reside in extreme deciles in successive years? The accrual-fixation hypothesis, together with the fact that the top and bottom accrual deciles are associated with abnormal returns, predicts that extreme accrual firms will leave the extreme accrual deciles in the following year. Second, I investigate the sources of abnormal returns earned by extreme accrual firms. Are these returns related to habitual extremes or to firms that exhibit reversal patterns? Because under the accrual-fixation hypothesis the returns are a result of accrual reversals, it predicts that no returns will be associated with sticky firms. 1 Throughout this paper, sticky refers to firms that belong to an extreme accrual decile (high or low) in two consecutive years.

3 Summary of results. In the time-series analysis, I find that extreme accrual firms are habitual extremes. About 25% of firms in portfolios of extreme high (low) accruals were in the same portfolios in the previous year. Such stickiness is observed across various measures of accruals, including working capital accruals and investing accruals. This frequency is higher than 10%, a benchmark which assumes independence across years and ignores the tendency of accruals to reverse. After considering accruals reversals, which are an important element in the accrual-fixation hypothesis, the expected frequency is even lower than 10%. One shortcoming of this analysis is that the specification of the transition matrix under the null hypothesis is unclear. Since I also find that stickiness is related to past growth rates in sales and to the length of firms operating cycles, it is possible that under the accrual-fixation hypothesis the expected stickiness frequency is higher than 10%. To address this, the second set of tests investigates the future abnormal returns of sticky and non-sticky firms. When I examine the sources of returns to an accrual-based strategy, I find an asymmetry between high and low accrual firms. In high accrual firms, future returns largely arise from accrual reversals. The degree of reversals varies by sample. In the non- NYSE/AMEX sample, some of these reversals are from the highest accrual decile in one year to the lowest accrual decile in the following year. In the NYSE/AMEX sample the reversals are less dramatic, from the highest accrual decile in one year to the second and third lowest deciles in the following year. Since the accrual-fixation hypothesis does not specify the degree of reversals that are expected to generate abnormal returns, the NYSE/AMEX evidence is important in highlighting the various sources of returns to an accrual strategy. In

4 both samples, abnormal returns do not arise to sticky high accrual firms. Overall, the evidence regarding high accrual firms is consistent with the accrual-fixation hypothesis. In low accrual firms, abnormal returns are not associated with strong reversals from the lowest decile in one year to any one of the three highest deciles in the following year. There is some evidence of abnormal returns related to weaker reversal patterns, from the bottom decile in one year to the second and third lowest deciles in the following year. Further, I find some evidence that abnormal returns are associated with sticky firms, inconsistent with the accrual-fixation hypothesis. The documented asymmetry in the sources of abnormal returns to low and high accrual firms suggests that the causes of the anomaly in each extreme decile are different. To shed light on the potential different sources of the anomaly, I report some characteristics of firms that are the drivers of returns to an accrual strategy. In the NYSE/AMEX sample, abnormal returns to high accrual firms are not associated with the fastest-growing firms. The high accrual firms that drive the returns have the highest book-to-market ratios but not the lowest market capitalizations or the highest rates of growth in sales. These firms also do not have the highest abnormal accruals. In the non-nyse/amex sample, a successful accrual strategy is exposed to smaller stocks with higher bankruptcy risk. These firms have significantly larger abnormal accruals suggesting that at least some of the returns are related to reversals of accrual manipulations (Xie, 2001). The low accrual firms that drive the returns in the NYSE/AMEX sample are larger and do not have the lowest book-to-market ratios. Moreover, they have the lowest (in absolute value) abnormal accruals, suggesting that the causes of the accrual anomaly in this set are not

5 related to accounting discretion. Finally, low accrual firms that drive the strategy s returns have higher bankruptcy risk. This raises the possibility that an alternative explanation for the accrual anomaly in low accrual firms is bankruptcy risk. Similar findings regarding abnormal accruals and bankruptcy risk also emerge in the non-nyse/amex sample. This study contributes to the debate regarding the potential explanations for the accrual anomaly. I extend the literature by providing direct evidence on the sources of returns to an accrual strategy, and on whether these returns are related to accruals reversals. I show that abnormal returns are associated with firms that exhibit varying degrees of reversals, and not necessarily strong reversals from one extreme decile to the other extreme decile. This is important because the accrual-fixation hypothesis does not specify the degree or type of reversals that are more likely to result in predicable return patterns. My results support the accrual-fixation hypothesis in high accrual firms but not in low accrual firms. By highlighting the asymmetry between high and low accrual firms, I conclude that the sources of anomaly differ across the two groups. In particular, there is evidence that high accrual firms that reverse have higher abnormal accruals than other high accrual firms, suggesting that accounting discretion may explain the accrual anomaly in these firms. Low accrual firms that are associated with future returns have higher bankruptcy risk than other low accrual firms, suggesting that bankruptcy risk may explain the anomaly in these firms. This asymmetry is important and is related to other recent studies that examine the accrual anomaly (for example, Dechow and Ge, 2006). The rest of this paper is organized as follows. Section 2 provides a brief overview of the relevant literature and a discussion of the reversal property of the accrual-fixation

6 hypothesis used in this study. The data are described in Section 3. I present the results in Section 4 and conclude in Section 5. 2. The accrual-fixation hypothesis 2.1 Literature background Sloan (1996) reports two results. First, he shows that abnormal returns are predictable based on current information about accruals. Second, he shows that accruals and cash flows exhibit differential persistence with respect to future earnings. To link the return predictability result with the persistence result, Sloan (1996) performs Mishkin (1983) tests. They reveal that the persistence coefficients of accruals and cash flows that are implied in market prices are different from the true coefficients obtained from a predictive regression of future earnings on current accruals and cash flows. More specifically, the market assigns a higher persistence to the accrual component of earnings than the one implied by the predictive regression and, as a result, over (under)-prices firms whose earnings contain high (low) accrual components. The conclusion is that return predictability is due to investors processing accounting information in a particular, yet incorrect, way. The conclusion is essentially Sloan s (1996) original interpretation for the accrual anomaly, which has become the most widely accepted explanation for the phenomenon. I call this explanation the accrual-fixation hypothesis. According to the accrual-fixation hypothesis, return predictability is due to mispricing driven by investors mis-interpreting accrual information. When pricing securities investors do not consider the future reversals of accruals. Sloan views future reversals to be a result of aggressive or bad accounting that originally inflated or deflated accruals. Investors, for some reason, do not process the

7 information correctly leading to mispricing. An important tenet underlying this hypothesis is the link between the reversals of accruals and the reversals of prices. It is also important to note that the accrual-fixation hypothesis originated from the results of the Mishkin tests. In that sense, the hypothesis is descriptive in nature and does not stem from predictions of an information misprocessing theory. A large body of literature has explored the anomaly since Sloan (1996). However, there is still no consensus about the causes of the anomaly. In my discussion below I survey the literature from the perspective of the three potential explanations for the anomaly. The first explanation argues that the anomaly does not stem from true mispricing. Instead, the anomaly is a manifestation of problems in asset pricing models such as inappropriate controls for risk (Zach, 2003; Khan, 2007). Zach (2003) finds that the accrual strategy still produces abnormal returns, even after controlling for size, book-to-market and momentum. Khan (2007), on the other hand, implements a different asset pricing model and argues that the strategy s returns can be explained by the use of a naïve asset pricing model. 2 Alternatively, the anomaly can be a result of selection biases and lack of control for outlying observations (Kraft, Leone and Wasley, 2006). The second explanation for the accrual anomaly is the accrual-fixation hypothesis. It argues that the anomaly represents true mispricing which is caused by investors misprocessing of accrual information. The existing evidence supporting the accrual-fixation 2 Related studies in this category examine whether the calculated abnormal returns are realizable (Lev and Nissim, 2006; Mashruwala, Rajgopal and Shevlin, 2006). Both studies argue that implementing an accrual strategy is too costly for arbitrageurs. As a result, predictability remains observable. However, these studies do not comment on the causes of the anomaly. Rather, they examine the factors responsible for the existence and persistence of abnormal returns.

8 hypothesis is indirect. Several studies have looked for variation in the accrual strategy s returns across accrual components. The association of mispricing with abnormal accruals (Xie, 2001), with inventory accruals (Thomas and Zhang, 2002), and with less reliable accruals (Richardson, Sloan, Soliman and Tuna, 2005), led researchers to conclude that investors are misled by accrual manipulation. This provides indirect evidence supporting the accrual-fixation hypothesis. Other studies examine the behavior of analysts and institutional investors (Bradshaw, Richardson and Sloan, 2001; Ali, Hwang and Trombley, 2000; Collins, Gong and Hribar, 2003; Barth and Hutton, 2004). These investors are presumably less subject to any processing biases implied by the accrual-fixation hypothesis. The studies seek to exploit cross-sectional variation in the presumed processing bias to generate predictions about the nature of the anomaly across groups of investors. The evidence is mixed. While Ali, Hwang and Trombley (2000) do not find evidence consistent with naïve fixation, Collins, Gong and Hribar (2003) show that returns to an accrual strategy vary with the level of institutional (or sophisticated) investors in a manner consistent with naïve fixation. Bradshaw, Richardson and Sloan (2001) find evidence that analysts are subject to the same misprocessing bias as the market. Francis and Smith (2005) question the accrual-fixation hypothesis indirectly. Their results suggest that accruals and cash flows do not possess differential persistence. By extension, if that is the case, then the accrual-fixation hypothesis, which relies on the different persistence properties of accruals and cash flows, no longer has merit. The third explanation for the accrual anomaly can be characterized generally as a correlated omitted variable problem. That is, accruals are correlated with a variable that is

9 associated with abnormal returns. The generation of abnormal returns could be due to a misspecification in existing asset pricing models with respect to the omitted variable. This explanation, although related to the first explanation, is distinct from it because the associated variable is not known to be a priced-risk factor. In that sense, its discovery is important to the asset pricing literature. The association of the omitted variable with abnormal returns could also be due to investors mispricing securities with respect to that variable. This is related to the second explanation because both argue true mispricing. However, the important difference is that the information set over which investors make mistakes is different. The accrualfixation hypothesis is very specific in positing that investors make mistakes in interpreting accrual information. The third explanation does not limit the information set exclusively to accruals, but rather to any variable correlated with accruals. This is an important difference that has implications on how researchers and practitioners interpret the anomaly. Desai, Rajgopal and Venkatachalam (2004) find that the accrual anomaly is related to the value-glamour anomaly. Since accruals are correlated with growth, Fairfield, Whisenant and Yohn (2003) argue that the accrual anomaly is a special case of a more general growth anomaly. Ng (2005) suggests that some of the anomaly s returns are associated with increased exposure to distress risk. The correlation of accruals with corporate financing events is discussed in Zach (2003) and Bradshaw, Richardson and Sloan (2006). In summary, there is no agreement in the literature about any of the three explanations. 3 Moreover, there is no direct evidence supporting or refuting the accrual- 3 There are other studies that pertain to the accrual anomaly but whose conclusions do not sway readers to one particular explanation. For example, Collins and Hribar (2002) argue that the anomaly is distinct from the postearnings announcement drift. Other examples include studies that examine the anomaly in an international

10 fixation hypothesis. In this paper I take a more direct approach in investigating the validity of this hypothesis. Direct evidence supporting or refuting it is an important step in understanding the accrual anomaly. 2.2 The accrual-fixation hypothesis and reversals Under the accrual-fixation hypothesis, and stemming from the Mishkin (1983) tests results, market participants treat accruals and cash flows similarly ignoring the transitory nature of accruals (i.e. accruals tendency to reverse). As a result, firms with extreme high (low) accruals are over- (under-) priced and future abnormal returns are generated. Since abnormal returns appear in extreme accrual deciles and because abnormal returns under the accrual-fixation hypothesis are driven by accruals reversals, I expect that firms in extreme deciles will exhibit reversal patterns similar to those of accruals. Thus, under this scenario accrual extremeness is expected to be transitory. Further, if aggressive accounting is related to accrual-fixation then, for a given firm, accruals are not likely to remain extreme in the following period because of disciplinary mechanisms such as auditor oversight. Thus, my first testable prediction is that under the accrual-fixation hypothesis, extreme accrual deciles are likely to be composed of different firms across periods. To test my first prediction, I examine the time-series properties of extreme accrual firms. I look at whether extreme accrual firms tend to leave the extreme accrual deciles in the following year as implied by the accrual-fixation hypothesis. Alternatively, these firms could reside in extreme deciles in successive years. I label such firms as sticky. context (Pincus, Rajgopal and Venkatachalam, 2007; LaFond, 2005) and those that examine the anomaly as a function of the disclosure of accrual information at the time of an earnings announcement (Levi, 2006).

11 A second implication of the accrual-fixation hypothesis is that the returns associated with an accrual strategy are a result of accruals reversals. Thus, not only does the accrualfixation hypothesis predict reversals of firms from extreme deciles, but it also predicts that no abnormal returns will be associated with sticky firms that do exist. The accrual-fixation hypothesis does not stipulate the degree of reversals that would be associated with abnormal returns. To explore this property of the accrual-fixation hypothesis, I identify the firms that are the drivers of abnormal returns to an accrual strategy. I investigate whether these firms are sticky or whether they experience accrual reversals. If so, I examine what is the degree of these reversals. 3. Data 3.1 Sample selection and variable measurement For my main analysis, I use two samples: (1) NYSE and AMEX firms and (2) NASDAQ firms. My main sample period is 1988-1999. In cases, where I calculate accruals using the balance sheet approach, I use the 1970-1999 sample period. Accounting variables. Accounting variables are drawn from the COMPUSTAT primary, secondary and tertiary files. First, I use differences between successive balance sheet accounts according to the following formula (COMPUSTAT item numbers in parentheses, Δ stands for annual changes in the corresponding items): Balance-sheet accruals: Δcurrent assets(#4)-δcash(#1)-δcurrent liabilities(#5)+ Δdebt in current liabilities(#34)-depreciation(#14). I also calculate accruals directly from the statement of cash flows, according to the following formula:

12 Cash-flow-statement accruals: Earnings before extraordinary items from the Cash Flow Statement (#123) Cash flows from operations (#308). All accounting variables are deflated by average total assets (at year t-1 and year t). Stock returns. I obtain stock returns from the Center for Research in Security Prices (CRSP) tapes as of 2001. I choose equal-weighted, size- and book-to-market adjusted buyand-hold returns as my reference normal return benchmark. I use NYSE cutoffs to assign firms to non-equal-sized size and book-to-market portfolios at the end of fiscal year. I calculate abnormal returns after compounding monthly returns of both firms raw returns and benchmark portfolio returns. Benchmark portfolios are implicitly rebalanced every month and their composition may change after the ranking period. Accrual strategy. To apply the accrual strategy, at the end of each year firms are ranked into deciles based on the magnitude of their deflated accruals. Once the rankings are determined, abnormal returns for each accrual decile are calculated by averaging the annual average abnormal returns of all firms in a particular accrual decile. Like other studies in the literature, I start the calculation period four full months after the end of the fiscal year. This assures that all the information in the financial statements is available to implement the strategy. 3.2 Descriptive statistics Table 1 reports medians and means of several variables of interest by deciles of accruals calculated from the cash flow statement and deflated by average total assets. In general, the descriptive statistics are similar to those reported in previous studies. First, the negative correlation between accruals and cash flows is immediately apparent. Cash flows

13 from operations decrease monotonically as we move from the low accrual decile (median of 0.22) to the high accrual decile (median of 0.02). Second, it is evident that firms with extreme accruals, those that occupy the top and bottom accrual deciles, are smaller in terms of market capitalization. A similar pattern is also present for total assets or total revenues (not reported). All these variables exhibit an inverted U-shaped pattern with respect to the accrual deciles. Moreover, the median size of low accrual firms is smaller than that of high accrual firms (p-value smaller than 1%), but the mean size of low accrual firms is larger than the mean size of high accrual firms. Third, high accrual firms have lower book-to-market ratios. Starting with the eighth decile, there is a decrease in the median book-to-market ratio. It falls from around 0.55 to 0.51 in the eighth decile, to 0.48 in the ninth decile and to 0.45 in the high accrual decile. The difference in median book-to-market ratios between the low and high accrual deciles is significant at conventional levels. Fourth, firm performance measured in terms of both contemporaneous stock performance and accounting rates of return and growth, is increasing monotonically with accruals. For example, the median raw return in the fiscal year for which accruals are measured increases from 3.2% in the low accrual decile to 16.6% in the high accrual decile. The median return on assets starts at 5.5% in the low accrual decile and increases to 10.5% in the high accrual decile. The median growth in sales is 1.9% for the low accrual decile and 23.4% for the high accrual decile. This difference may be slightly misleading because of the larger preponderance of mergers in the high accrual deciles and of divestitures in the low accrual deciles. After controlling for these factors, however, the median sales growth remains different across the extreme accrual deciles (1.4% for the low

14 decile versus 20.2% for the high decile). Fifth, compared to firms in the middle accrual deciles, analysts forecasts of long-term growth are slightly larger for low accrual firms (13.5% vs. 12%), whereas they are much larger for high accrual firms (18% vs. 12%). Finally, I report summary statistics on Altman s (1968) Z-score, which measures a company s financial strength. Altman s Z is negatively correlated with the probability of bankruptcy. Table 1 reveals that the ex-ante probability of bankruptcy is monotonically decreasing as we move from the low to the high accrual deciles. That is, low accrual firms have a higher bankruptcy probability than high accrual firms. The median Z-score of low accrual firms is 2.7 and it reaches 3.9 in the high accrual decile. All the patterns mentioned above (size, book-to-market, performance, bankruptcy risk) are present in the unreported summary statistics of non-nyse/amex firms. 4. Empirical results In section 4.1 I test whether extreme accrual firms are habitual extremes (i.e. sticky) or whether reversal patterns of firms across deciles are observed. In section 4.2 I investigate whether there is a relation between stickiness and future abnormal returns. I explore characteristics that distinguish firms that drive the anomaly s returns from firms that do not drive the returns in section 4.3. 4.1 Are extreme-accrual firms sticky? Recall from section 2.2 that the accrual-fixation hypothesis predicts that extreme accrual firms will tend to move away from the extreme accrual portfolios in the following year. Table 2 reports transition matrices containing frequencies of firms that occupy decile i in

15 year t-1 and decile j in year t. I use the traditional definition of working capital accruals as in Sloan (1996) and many subsequent studies. I measure these working capital accruals using both the balance-sheet approach (Panel A) and the cash-flow-statement approach (Panel B). 4 The results in Table 2 are for NYSE firms. Similar (unreported) results apply for non-nyse firms. 5 Panel A of Table 2 indicates that there is a tendency for extreme accrual firms in year t-1 to remain in the extreme accrual deciles in year t. For example, 26.4% of firms in the bottom balance-sheet accrual decile remain in that decile in the following year. Similarly, 27.1% of firms in the top accrual decile in year t-1 remain in that same decile in year t. Based on chi-squared tests, these frequencies are significantly higher than a frequency of 10%, which assumes independence across years and ignores the tendency of accruals to reverse. 6 Taking accrual reversals into account yields an expected frequency that is even lower than 10%. In fact, inventory accruals, which are part of working capital accruals, are likely to be the most transitory, reinforcing this lower expected frequency. However, the null hypothesis of expected frequency under accrual reversals is not readily and easily specified. As Hribar and Collins (2002) argue, measuring accruals using the cash-flow approach is preferable in the context of the accrual anomaly. Thus, it is worth noting that when accruals are measured using this approach, they exhibit an even stronger stickiness. Panel B shows that in the bottom (top) accrual deciles, 31.7% (30.7%) of firms remain in their respective accrual deciles in the subsequent year compared to 26.4% (27.1%) in panel A, wherein accruals are 4 In similar unreported results (available from the author upon request) I also use the more comprehensive measure of total accruals that includes working capital accruals, investing accruals and financing accruals (see Richardson, Sloan, Soliman and Tuna, 2005). 5 In my discussions of the results, the NYSE sample includes firms from both NYSE and AMEX. 6 P-values from chi-squared tests were lower than 0.01.

16 measured using the balance-sheet approach. Part of this increased frequency, compared to balance-sheet accruals, is because many firms are in the bottom (top) balance-sheet accrual decile as a result of divestitures (mergers) which are presumably transitory events (Zach, 2003). In Table 3, I examine two characteristics that can contribute to accrual stickiness: growth and the length of the operating cycle. I report medians of these variables, measured at the end of year t across different cells of accrual rankings in years t-1 and t. Consistent with the analyses in the next section, I construct five uneven groups: The High and Low groups correspond to firms in extreme accrual deciles. The non-extreme firms are divided into three groups as follows: (i) firms in the 2 nd or 3 rd accrual deciles (Mid1), (ii) firms in accrual deciles 4 through 7 (Mid2), and (iii) firms in accrual deciles 8 and 9 (Mid3). For brevity, I do not report results of differences-in-medians tests. All the comparisons I discuss below are significant at conventional levels. It is evident from Table 3 that sticky low firms in the NYSE sample (as well as Low- Mid1 firms) have a significantly shorter operating cycle than Low-High firms, which fully reverse (84.3 days compared to 118.2 days). Sticky low firms have lower growth rates than Low-High firms (6.5% versus 9.7%). The difference in growth rates is much starker in the non-nyse sample (1.7% versus 12.7%). Sticky high accrual firms do not have a significantly larger operating cycle than High-Low in both samples. However, growth rates of sticky high accrual firms are significantly higher in both the NYSE and non-nyse samples (22.5% and 38.3%, respectively). This is consistent with the evidence in Fairfield, Whisenant and Yohn (2003). Thus, stickiness of high accrual firms is more related to high growth rates and less

17 related to the length of the operating cycle. Stickiness of low accrual firms is related to the length of the operating cycle (especially in NYSE firms), and, to a lesser extent to growth rates (stronger in the non-nyse sample). In summary, Table 2 shows that extreme accrual firms, regardless of the type of accruals, are sticky. Recall that, under the accrual-fixation hypothesis, extreme accrual firms are expected to be transitory. Thus, the results reported in Table 2 are not consistent with this hypothesis. One shortcoming of this set of tests is that the specification of the transition matrix under the null hypothesis is unclear. This makes the interpretation of the transition frequencies somewhat subjective. While I benchmark my results against a naïve expectation of an even distribution of firms (i.e. 10%) from year t-1 across the accrual deciles in year t, and argue that under the accrual-fixation hypothesis accruals are expected to reverse, this interpretation of the results can still be construed as subjective. It can be argued that the evidence is still consistent with the accrual-fixation hypothesis because the majority of firms do not reside in the same decile in two consecutive years. Moreover, as Table 3 shows, this stickiness is related to actual growth rates, especially in high accrual firms. Thus, it is possible that under the accrual-fixation hypothesis the expected stickiness frequency is higher than 10%. To address this, the second set of tests in the next section investigates another prediction of the accrual-fixation hypothesis regarding the future abnormal return patterns of sticky and non-sticky firms. 4.2 Extreme accrual stickiness and abnormal returns Given the documented evidence of accruals stickiness in section 4.1, I now explore a second implication of the accrual-fixation hypothesis. I examine whether abnormal returns

18 earned during year t to portfolios of extreme accrual firms formed at the end of year t-1, vary depending on whether an extreme accrual firm is sticky or not in year t. Under the accrualfixation-hypothesis, sticky firms are not expected to be associated with abnormal returns. Rather, the returns are expected to result from the reversals of accruals of extreme accrual firms, although the degree of reversals is not stipulated by the accrual-fixation hypothesis. Table 4 reports the strategy s abnormal returns stratified by a five-by-five partition of accrual groups in both year t-1 and year t. 7 The table allows us to observe the sources of the returns to an accrual strategy that is implemented at the end of year t-1. The High and Low groups correspond to firms in extreme accrual deciles in either year t-1 or year t. The nonextreme firms are divided into three groups as follows: (i) firms in the 2 nd or 3 rd accrual deciles (Mid1), (ii) firms in accrual deciles 4 through 7 (Mid2), and (iii) firms in accrual deciles 8 or 9 (Mid3). The abnormal returns in the table are adjusted for both size and bookto-market and the t-statistics are calculated based on the standard deviation of the time-series average of annual abnormal returns. I base my analysis on the traditional measures of working capital accruals, calculated using the cash-flow-statement approach and corresponding to panel B in Table 2. Similar (unreported) results emerge for working capital accruals calculated using the balance-sheet approach. The table reports results separately for the NYSE sample in Panel A and for the non-nyse sample in Panel B. 7 In unreported results I construct three-by-three partitions, where extreme high and low accrual groups are defined as in Lys and Sabino (1992). According to this classification scheme, the extreme high and low groups each contain 27% of firms and the remaining middle group contains 46% of firms. This scheme maximizes the power of the tests to detect abnormal stock return performance. The results using this alterative classification scheme are similar. I chose to report five-by-five partitions because they provide more information on the reversal patterns of accruals.

19 It is important to emphasize that the returns reported in Table 4 are not returns to implementable trading strategies. Notice that as of the end of year t-1, investors do not have information about the future accrual grouping to which a firm will belong at the end of year t. Without such information, investors cannot earn the returns that are reported in Table 4. Instead, Table 4 helps researchers identify the firms that drive the returns to an accrual strategy. To the extent that at the end of year t-1 it is possible to predict which firms will reverse and which firms will remain sticky in year t, the returns reported in Table 4 can be used to potentially enhance the returns to an accrual trading strategy (See the analysis in section 4.3). 4.2.1 High accrual firms in year t-1 I first discuss firms with high accruals in year t-1. Past studies (e.g., Sloan, 1996) show that these firms earn negative abnormal stock returns in the following year. Table 4 investigates whether these returns differ depending on the future path that high accrual firms take. High-Low firms. Consider first firms that are ranked in the highest accrual group in year t-1 and experience a complete reversal to the lowest accrual decile in year t (High-Low firms). 8 High-Low firms earn significantly negative abnormal returns of -9.53% (t-statistic of -2.08) in the NYSE sample and -35.5% (t-statistic of -8.32) in the non-nyse sample. 9 However, firms in the lowest decile of accruals in year t may experience poor stock price 8 Throughout my discussion, I first refer to the accrual ranking in year t-1 and then to the ranking in year t. Thus, High-Low firms are those with high accruals in year t-1 and low accruals in year t. 9 Zach (2003) shows that the returns to high accrual firms in the non-nyse sample are higher (in absolute values) than in the NYSE sample. The significantly higher returns earned by non-nyse firms may be related to the greater difficulty of short selling firms in this subsample (e.g. Mashruwala, Rajgopal and Shevlin 2006) or to a greater difficulty of asset pricing models to capture expected returns in this group (e.g. Khan, 2007).

20 performance in that year because of true sub-par economic performance, and not because of accruals reversals due to, for example, past manipulations. The reason is that accruals, earnings and stock returns are all positively correlated (e.g. Dechow, 1994). Thus, when evaluating whether accruals reversals are the source of returns to High-Low firms, it is important to control for firm performance in year t. In effect, there needs to be a control for the look-ahead bias that is present in Table 4, because of the foreknowledge of the accrual rankings at time t. To separate the effects of true poor performance from the effects of accrual reversals, and control for the look-ahead bias, I compare the returns of High-Low firms with the returns of two groups: Mid3-Low and Mid2-Low. Firms in both Mid3-Low and Mid2-Low have low accruals in year t (i.e. they perform as poorly as High-Low firms in year t), and moderate levels of accruals in year t-1, which are closest to the accrual levels of High-Low firms in year t-1. Mid3-Low (Mid2-Low) firms earn in year t an insignificant abnormal return of -5.16% (-4.10%) in the NYSE group and a marginally significant (significant) abnormal return of -11.36% (-15.75%) in the non-nyse group. The difference in returns between the High-Low group and the two comparison groups is reported in the right side of Table 4, under the columns titled Hi-Mid3 and Hi-Mid2. These differences (4.36% and 5.42%) are insignificant (with t-statistics of 0.56 and 1.27) in the NYSE sample. Thus, in this sample, there is no evidence that the returns to an accrual strategy are a result of complete reversals of high accrual firms in one year to the lowest accrual decile in the following year. Note that the earnings performance at time t of High-Low firms (reported in brackets) is lower than the comparison groups (0.6% vs. 2.2% and 2.0%).

21 Thus, it is possible that the benchmark return performance of Mid3-Low and Mid2-Low is too high. The results in the non-nyse are different. The return differential between the High- Low group and both comparison groups is significant (24.15% and 19.76%). This difference represents the returns to High-Low firms that are not attributable to year t s performance. 10 Instead, these returns are attributed to the high levels of accruals in year t-1 that completely reversed to the other extreme in year t, consistent with the accrual-fixation hypothesis. High-Mid1 and High-Mid2 firms. Consider next firms that are ranked in the high accrual group in year t-1 and experience partial reversals to non-extreme deciles (Mid1 or Mid2) in year t. High-Mid1 firms earn a negative and significant abnormal return of -8.36% (t-statistic of -2.76) in the NYSE sample. Compared to firms with similar accrual levels in year t, the differential return of High-Mid1 firms is positive and significant (9.16% relative to Mid3-Mid1 firms and 8.53% relative to Mid2-Mid1 firms). Note that the earnings performance in year t of High-Mid1 firms is similar (4.1%) to that of the benchmark firms (4.1% and 3.9%), indicating that the control for year t s performance is effective. This evidence suggests that the returns to an accrual strategy taking short positions in high accrual NYSE firms are mostly attributed to partial reversals from the top accrual decile in one year to the second or third lowest deciles in the following year. The evidence in the non-nyse sample is slightly weaker. High-Mid1 firms earn a negative return of -14.67% (with a t- statistic of -2.46) in the non-nyse sample. The differential return with respect to the Mid3-10 While I try to control for the performance in year t, the earnings performance of High-Low firms (-21.7%) is inferior to the earnings performance of Mid3-Low (-18.2%) and Mid2-Low (-15.5%). This could be a source of the differential return that may not be fully attributed to accruals reversals.

22 Mid1 groups is an insignificant 3.33%, but it is significant with respect to the Mid2-Mid1 group (15.36%). Note, however that the earnings performance at time t of High-Mid1 firms is -3.8% compares with a superior 0.1% of Mid2-Mid1 firms. Thus, the control for contemporaneous performance may not be as effective in this group. I next examine abnormal returns associated with reversal patterns of high accrual firms to the middle deciles (4 through 7). High-Mid2 NYSE firms earn a negative and significant abnormal return of -9.07% (with a t-statistic of -3.66). Controlling for the general performance of Mid2 firms in year t, we observe that the differential return of High-Mid2 firms is insignificant (4.27% and a t-statistic of 1.31) relative to Mid3-Mid2 firms. It is significant (7.85% and t-statistic of 2.53) relative to Mid2-Mid2 firms. Thus, there is some evidence that part of the returns to the high-accrual firms is attributed to mild reversals to the middle deciles of accruals in year t. This evidence is weaker in the non-nyse sample. High-Mid3 and High-High (sticky) firms. Finally, I look at the returns to the high accrual decile associated with firms that either remain in the top decile (sticky firms) or move slightly down to the 8 th or 9 th deciles (Mid3) in the following year. In the NYSE sample these firms do not earn significant returns in year t (-1.62% for High-Mid3 and 0.13% for High- High). Further, there is no evidence that the differential returns of these firms, relative to other firms with similar accrual performance in year t, are significantly different from zero. Thus, there appears to be no evidence that firms with very mild reversal patterns or sticky firms are driving the returns of the short positions of the accrual strategy in the NYSE sample. The evidence is slightly different in the non-nyse sample. High-Mid3 firms earn a significant abnormal return of -9.29% (with a t-statistic of -3.25) and the differential returns between

23 them and Mid3-Mid3 or Mid2-Mid3 firms are significant (13.02% and 10.16%). This suggests that some of the returns to an accrual strategy in the non-nyse sample are a result of very mild reversals from the highest accrual decile to the second and third highest deciles of accruals. With respect to sticky firms, there is no evidence of abnormal returns in the non- NYSE sample as well. In summary, the sources of returns to an accrual strategy that takes short positions in high accrual firms vary by sample. In the NYSE sample, most of the returns are driven by firms with high accruals in year t-1 that reverse to the second and third lowest deciles in year t. In the non-nyse sample, there is evidence of abnormal returns associated with both complete reversals (from the highest decile to the lowest one) as well as with very mild reversals (from the highest decile to the two next-to-highest deciles). In both samples, there is no evidence that abnormal returns are due to sticky firms, consistent with the accrual-fixation hypothesis. 4.2.2 Low accrual firms in year t-1 In this section, I examine firms that belong to the lowest accrual decile in year t-1. Based on prior studies, these firms earn positive abnormal stock returns in the following year. Low-High firms. Consider low accrual firms in year t-1 that experience a complete reversal to the highest accrual decile in year t (Low-High firms). Low-High firms earn insignificant abnormal returns in both the NYSE sample (2.82%) and the non-nyse sample (33.99%). Note that the number of firms in this group is quite small (111 over a 12-year period in the NYSE sample). However, these returns are also insignificant in unreported

24 results, where the groupings are based Lys and Sabino s (1992) most powerful classification scheme, wherein the extreme portfolios contain 27% of firms. Firms in the high decile of accruals in year t may experience good stock price performance in year t because of true above-par economic performance. To control for this issue, and as I did in the case of High-Low firms, I examine the differential returns between Low-High firms and other high accrual firms in year t. In both samples, the differential returns reported in Table 4 under the columns titled Low-Mid1 and Low-Mid2 are insignificant (-4.68% and 2.15% in the NYSE sample and 24.10% and 15.99% in the non- NYSE sample). Thus, in both samples, and unlike in the case of high accruals, there is no evidence that the returns to low accrual firms are related to complete reversals from the lowest accrual decile in year t-1 to the highest accrual decile in year t. Low-Mid3 and Low-Mid2 firms. Consider low accrual firms in year t-1 that experience partial reversals to non-extreme deciles (Mid3 or Mid2) in year t. In both the NYSE and non- NYSE samples, Low-Mid3 firms earn an insignificant abnormal return (5.56% and 1.59%, respectively). When compared to firms with similar accrual levels in year t, the differential returns of Low-Mid3 firms are also insignificant in both samples. I next examine abnormal returns associated with mild reversals of low accrual firms to the middle deciles (4 through 7). Low-Mid2 NYSE firms exhibit a positive and significant abnormal return of 8.39% (with a t-statistic of 1.94). Controlling for the general performance of Mid2 firms in year t, we observe that the differential return of Low-Mid2 firms is positive and marginally significant (8.05% and a t-statistic of 1.70) relative to Mid1-Mid2 firms. The differential return is a significant 9.61% (t-statistic of 2.29) relative to Mid2-Mid2 firms. This

25 suggests that the positive abnormal returns to low accrual firms are a result of mild reversals to the middle deciles of accruals in year t. Similar evidence is observed in the non-nyse sample, in which Low-Mid2 firms earn a significant abnormal return of 27.4% in year t. Low-Mid1 and Low-Low (sticky) firms. Finally, I examine the returns of firms in the low accrual decile that either remain in the low accrual decile in the following year (sticky firms) or move to the second or third lowest deciles (Mid1). In the NYSE sample, Low-Mid1 firms earn a significant return of 7.50% and sticky firms earn an insignificant return of 6.02%. The differential returns of Low-Mid1 firms, after controlling for the performance of Mid1 firms in year t, is positive and significant (6.27% with a t-statistic of 1.78 relative to Mid1- Mid1 firms, and 7.32% with a t-statistic of 2.43 relative to Mid2-Mid1 firms). While sticky firms do not earn statistically significant returns, the difference between their returns and the returns of similar low accrual firms is positive and significant (10.83% with a t-statistic of 2.08 relative to Mid1-Low firms, and 10.13% with a t-statistic of 2.15 relative to Mid2-Low firms). This suggests that the returns to the accrual strategy s long positions in low accrual firms are partially due to sticky firms and partially due to very mild reversals of low accrual firms to the second and third lowest deciles of accruals. The evidence is similar (albeit slightly weaker) in the non-nyse sample. Low-Mid1 firms earn significant abnormal returns of 8.51% (t-statistic of 1.96). The difference between this return and the returns to similar Mid1 firms is also positive and significant (7.81% and 6.31%). Sticky Low-Low firms do not earn a significant abnormal return, but their differential return relative to one of the benchmark groups, Mid2-Low firms, is positive (15.17%) and significant, providing some evidence of returns associated with sticky firms in the non-nyse sample as well.