Accruals, Heterogeneous Beliefs, and Stock Returns

Transcription

1 Accruals, Heterogeneous Beliefs, and Stock Returns Emma Y. Peng An Yan* and Meng Yan Fordham University 1790 Broadway, 13 th Floor New York, NY Feburary 2012 *Corresponding author. Tel: (212) For helpful comments, we thank C. S. Agnes Cheng, Guojin Gong, Joshua Livnat, Zvi Singer, John Shon, Eric Yeung, and the participants at the 2010 American Accounting Association Annual Meeting and the 2011 AAA Financial Accounting and Reporting Section Mid-year Meeting. All remaining errors are our own responsibility. 1

2 Accruals, Heterogeneous Beliefs, and the Stock Return ABSTRACT In the paper, we study how a firm s accounting accruals affect the heterogeneity of investor beliefs on the firm s value. We also study how the effect of accounting accruals on the heterogeneity of investor beliefs affects the firm s stock returns. We document three findings. First, we find that the level of heterogeneity in investor beliefs on a firm s value is higher when the firm experiences a larger increase in its accounting accruals. Second, we find that future stock returns following earnings announcement are lower when the firm s accounting accruals increases the heterogeneity of investor beliefs to a larger degree. Finally, we also find that the effect of accruals-induced heterogeneous investor beliefs on future stock returns is more pronounced when short-sale constraints are more binding. Overall, our empirical findings suggest a channel of investor beliefs in which accruals affects future stock returns by affecting the heterogeneity of investor beliefs. Keywords: heterogeneous beliefs, accruals, mispricing, accrual anomaly. JEL Classification: M41; G12; G14 1

3 1. Introduction Investors have heterogeneous prior beliefs on a firm s value. How does the heterogeneity of investor beliefs affect the valuation of the firm s securities has been studied in depth in the finance literature. This research dates back to Miller (1977) (and subsequently, Harrison and Kreps (1978), Mayshar (1983), and Morris (1996)). Miller (1977) argues that, when investors with heterogeneous beliefs are subject to short-sale constraints, stocks would sell at a premium over their fundamental values. This is because short-sale constraints prevent pessimistic investors from trading in the stock market so that stock prices reflect the beliefs of optimistic investors. Recently, Chen, Hong, and Stein (2002) and Diether, Malloy, and Scherbina (2002) find empirical evidence supporting Miller s predictions. However, it is still not well understood what causes the heterogeneous investor beliefs. In this paper, we study one factor that may affect the heterogeneity of investor beliefs. We conjecture that different interpretations of a firm s accounting information could cause heterogeneous investor beliefs on the firm s value. Specifically, we focus on accounting accruals. We study how accounting accruals affect the heterogeneity of investor beliefs. We also study how the effect of accruals on investor beliefs could affect future stock returns. To the best of our knowledge, our paper is the first to provide empirical evidence on the impact of accounting accruals on the heterogeneity of investor beliefs. It is also the first to study how this impact affects future stock returns. We first propose that high accruals could increase the heterogeneity of investor beliefs on the firm value. The accrual system allows managers to shift the recognition of cash flows over time. It relies on managers assumptions and judgment and it is hard to be objectively verified. 1 1 As Bernstein (1993) points out, the accrual system relies on accruals, deferrals, allocations, and valuations, all of which involve higher degree of subjectivity. Francis and Krishnan (1999) suggest that accruals cannot be 2

4 We argue that this subjectivity and unverifiability nature of accruals would induce disagreement among investors on the value implication of accruals. In particular, some investors could believe that accruals reveal managers private information and improve earnings ability to predict future cash flows. 2 These investors accordingly would take accruals into valuation by face value. Other investors, on the other hand, could believe that the quality of accruals is compromised by earnings manipulations. They could believe that managers engage accruals in active incomeinflating earnings management to beat earnings thresholds and to avoid disappointing the market (Graham, Harvey and Rajgopal (2005); Chan, Jegadeesh, and Lakonishok (2006)). Under this skeptical view, these investors would associate high accruals with upward earnings management and they would more or less ignore accruals when valuing the firm. Thus, manager discretion on accruals would inevitably lead to different interpretations among investors on the value implication of the accruals, and consequently cause heterogeneous opinions among investors on the firm value. When accruals increase, investor would become more heterogeneous in their beliefs on the firm value. This is the first hypothesis (H1) we test in the paper. As a part of test of hypothesis H1, we also study whether or not the positive relation between accruals and heterogeneity of investor beliefs is monotonic. While we focus on the income-inflating upward earnings management in developing hypothesis H1, it is possible that the income-deflating downward earnings management could also play a role. In particular, we argue in the development of hypothesis H1 that an increase in accruals is viewed by investors as an outcome of an increased degree of upward earnings management, thereby increasing objectively verified by auditors and that auditors feel uncertain about the reliability of high accruals compared to low accruals. 2 Statement of Accounting Concepts No. 1 (FASB 1978, paragraph 44) states that Information about an enterprise earnings based on accrual accounting generally provides a better indication of enterprises present and continuing ability to generate favorable cash flows than information limited to the financial aspects of cash receipts and payments. 3

5 heterogeneity of investor beliefs. However, it is also possible that an increase in accruals could be caused by a reduced degree of downward earnings management, thereby reducing heterogeneity of investor beliefs. This is especially so in the case of negative accruals. Thus, we also test hypothesis H1 for both the subsample of positive and the subsample of negative accruals. If downward earnings management is important, we expect to find a negative relation between accruals and heterogeneity of investor beliefs at least for the subsample of negative accruals. Next, we examine how the impact of accounting accruals on heterogeneous investor beliefs could affect future stock returns. Following Miller (1977), we argue that the heterogeneity of beliefs generated by high accruals would boost the firm s contemporaneous equity price. Over time, as firm value gradually converges to its fundamental value, the firm would experience a lower future stock return. In other words, we propose an investor belief channel through which accounting accruals could affect future stock returns. A high level of accruals could increase the level of the heterogeneity of investor beliefs, which subsequently leads to negative future stock returns. The higher the level of the accrual-induced heterogeneity of investor beliefs is, the lower future stock returns are. This is the second hypothesis (H2) we test in the paper. Finally, we also study how short-sale constraints play a role in the investor belief channel discussed above. In particular, we study whether the impact of accounting accruals on heterogeneous investor beliefs affects future stock returns differently for firms with various degrees of short-sale constraints. In Miller s (1977) framework, a key condition for heterogeneous investor beliefs to affect stock pricing is that investors are subject to short-sale constraints. The effect of heterogeneous investor beliefs on stock pricing is greater when short- 4

6 sale constraints are more binding. See Boehme, Danielsen, and Sorescu (2006), Sadka and Scherbina (2007), and Hirshleifer, Teoh, and Yu (2011) for the empirical findings. Thus, we hypothesize that the effect of the accruals-induced heterogeneous investor beliefs on future stock returns is more pronounced when short-sale constraints are more binding. This is the third hypothesis (H3) we test in the paper. A central variable in our test of the above three hypotheses is the level of investors heterogeneous beliefs. We follow the literature and use the dispersion in analysts earnings forecasts to measure the degree of heterogeneous beliefs among market participants. A higher dispersion in analyst forecasts indicates a higher level of heterogeneity in investor beliefs (see, e.g., Diether, Malloy, and Scherbina (2002)). Using analyst dispersion as the heterogeneity variable, we find evidence consistent with all three hypotheses. First, as expected from hypothesis H1, we find that financial analysts disagree more on their earnings forecasts when accruals increase to a larger degree from the previous quarter. 3 We also find that the positive relation between the accrual change and the heterogeneity of investor beliefs holds for both positive accruals and negative accruals. Second, we show that the lower future stock return experienced by a firm with increased accruals is more pronounced if the firm faces a higher level of dispersion in analysts earnings forecasts in the month of increased accruals. This result supports hypothesis H2, suggesting that accounting accruals could affect future stock returns through the investor belief channel (by affecting the heterogeneity of investor beliefs). To ensure the robustness of our result above, we run various robustness tests. We show that our result is unlikely to be driven by the common return predictors, such as size, book-to-market, momentum, illiquidity, etc, as well as the growth 3 The majority of our empirical tests are based on the change in accruals rather than the level of accruals. The use of accruals could be effectively a firm characteristic. We use change in accruals to purge firm fixed effects. 5

7 anomaly (Fairfield et al. 2003) and the post-announcement earnings drift. We also address the potential concern of sample selection. In the paper, we use a proprietary sample consisting of firms that disclose net operating cash flows in their preliminary earnings announcements. By using this proprietary sample, we ensure that investors are able to infer the amount of accruals from earnings and operating cash flows at the earnings announcement date. However, this proprietary sample is only a subset of the universe of firms announcing earnings, since many firms do not announce operating cash flows at earnings announcements. To check whether or not the sample selectivity affects our empirical results, we run Heckman s (1979) selection model. Our results from the selection model are consistent with hypothesis H2, demonstrating that our finding on the relation among the heterogeneity of investor beliefs, accruals, and stock returns is robust to the selection of our sample. In another robustness check, we further study whether the relation among the heterogeneity of investor beliefs, accruals, and stock returns is asymmetric. Miller (1977) predicts that the stocks with a high level of heterogeneous beliefs will underperform in the future, while the converse, that the stocks with low heterogeneity will outperform in the future, need not be true. 4 Thus, it is possible that the investor belief channel on the pricing effect of accruals is effective when the accrual-induced heterogeneity of investor beliefs is high. The investor belief channel may not be effective when the accrual-induced heterogeneity of investor beliefs is low. Our findings are consistent with this conjecture. We find that the relation among accruals, heterogeneity of investor beliefs, and future stock returns is more pronounced when analyst dispersion is higher in the contemporaneous year. This finding suggests that accruals could affect 4 The contemporaneous overpricing of the high-heterogeneity stocks is due to the existence of short-sale constraints. However, while there may exist short-sale constraints on the stock, there is no constraint on buying a stock. Thus, the low-heterogeneity stocks in Miller s framework may not necessarily be underpriced. 6

8 future stock returns in a way consistent with Miller s framework of heterogeneous investor beliefs. Finally, to test the third hypothesis, we use stock holdings by institutional investors and Amihud s (2002) illiquidity measure to proxy for how tightly short-sales constraints bind. Prior studies show that the stocks with more institutional investor holdings are easier to short and that the illiquid stocks are hard to short (Nagel (2005), Berkman et al. (2009), Sadka and Scherbina (2007) and Banerjee and Graveline, (2012)). Using institutional investor holdings and stock illiquidity as measures for short-sales constraints, we find that the accrual-induced heterogeneous investor beliefs affects future stock returns to a larger degree for the stocks with lower institutional investor holdings and for the stocks with higher stock illiquidity. Overall, our results suggest that accounting accruals are a key determinant of the heterogeneity of investor beliefs. They also suggest that accounting accruals could affect future stock returns by affecting the heterogeneity of investor beliefs. These results extend the literature on heterogeneous investor beliefs and stock valuation. The literature was set forth originally by Miller (1977) (see earlier discussions). 5 However, none of the studies in the literature provide indepth analysis of whether and how earnings attributes affect the heterogeneity of investor beliefs. Our paper fills the void. By linking the impact of accounting accruals on investors heterogeneous beliefs to future stock returns, our paper also extends the accrual anomaly research which is well documented in the accounting literature. The accrual anomaly is first documented by Sloan (1996), who shows that the stocks of high accrual firms earn negative abnormal returns in the future. Sloan (1996) argues that the accrual anomaly occurs since investors natively fixate on accounting earnings and 5 Several papers incorporate Miller s insight in more formal and refined models. For example, Scheinkman and Xiong (2003) and Hong, Scheinkman, and Xiong (2004) further develop dynamic models with heterogeneous beliefs and shorting constraints to study the joint behavior of volume and overpricing. 7

9 overestimate the persistence of accruals. 6 Bradshaw, Richardson, and Sloan (2001) further show that sell-side analysts do overestimate the persistence of accruals and fail to anticipate the subsequent earnings declines for firms reporting high accruals. Our paper identifies a different channel through which accruals could affect future stock returns. We propose that an increase in accruals could cause lower future stock returns because it increases the heterogeneity of investor beliefs regarding firm value contemporaneously in the period of increased accruals. Thus, unlike the fixation explanation, which focuses on investors average (biased) belief in response to the accruals information, our paper focuses on the heterogeneity or the dispersion of investors beliefs. 7 We find that the negative stock return following an increase in accruals is related to a higher degree of investors heterogeneous beliefs even after we control for forecast errors, the average level of analyst beliefs as suggested by the fixation explanation. Thus, it is our view that, while the consideration of the average (biased) investor belief is important in determining the accrual anomaly, the heterogeneity in investor beliefs characterizing the stock market may be equally (if not more) important. 8 6 In recent years, alternative explanations on the accrual anomaly emerge in the literature. For instance, researchers suggest that the accrual anomaly can be a special case of the growth anomaly (e.g., Fairfield et al., 2003; Desai et al., 2004; Zhang, 2007). Khan (2008) proposes a risk-based explanation, suggesting that risk can at least partially explain the accrual anomaly. Other studies on accrual anomaly include Hirshleifer, Hou, Teoh, and Zhang (2004), Dechow and Ge (2006), Dechow, Richardson, and Sloan (2008), Levi (2008), and Louis, Robinson, and Sbaraglia (2008). 7 Recently, Ree and Thomas (2010) find that the change in dispersion of investor beliefs negatively affects the 3-day stock return around the earnings announcement. They attribute this negative effect to the information risk as proxied by the dispersion of investor beliefs. In contrast, we study the effect of dispersion of investor beliefs on future longrun stock returns following the earnings announcement. We argue that our empirical findings cannot be explained by the information risk argument. In particular, the information risk argument would predict that firms with higher information risk, such as firms with higher accruals and higher analyst dispersion, should have higher expected stock returns in the long run. This prediction is not supported by our findings. 8 Our findings that accruals affect future stock returns through affecting the heterogeneity of investor beliefs are based on the change in accruals, while the accrual anomaly literature is mostly based on the level of accruals. Thus, our findings only suggest that the heterogeneity of investor beliefs can explain the part of the accrual anomaly that is caused by the increased level of accruals. However, our results do not have any implication on the part of the accrual anomaly that is caused by high accruals that represent decreases from (or the same levels as) the last quarter. Nevertheless, our paper still complements the literature by showing that the heterogeneity in investor beliefs is another important channel in explaining the accrual-driven future stock returns. 8

10 The remainder of the paper is organized as follows. Section 2 develops the hypotheses on accruals, heterogeneity of investor beliefs, and ex-post stock returns. Section 3 describes the sample selection and variable construction. Section 4 reports the results from our empirical tests. Section 5 discusses the other potential explanation on our findings. Section 6 concludes. 2. Hypotheses The literature on heterogeneous investor beliefs originates from the work of Miller (1977) who considers two realities of the stock market. First, investors have heterogeneous beliefs regarding a stock s intrinsic value, and second, there exist short-sale constraints. He argues that when pessimistic investors are prevented from selling short, stock prices reflect the beliefs of optimistic investors and the securities would sell at a premium over their fundamental values. When the heterogeneity of investor beliefs on a stock s value increases, the stock will be purchased by investors with higher valuations and therefore is priced at a higher level. In this paper, we extend this heterogeneous belief theory to study the effect of accounting accruals on the heterogeneity of investor beliefs and further on future stock returns. Accounting accruals include revenues and expenses recognized in a period of time either before or after when cash is received and paid. They are subject to managerial judgment and discretion. 9 Thus, accruals are difficult to be completely quantified and needs investors discretion to interpret the value implication. Some investors could perceive accruals as a signal of managers private information about the firm s future cash flows and take accruals by face value into firm valuation. Other investors would adopt a skeptical view that managers could 9 For instance, companies making credit sales are expected to recognize bad debts expense in each accounting period, but how much to recognize depends on managers estimates about future uncollectible accounts. In another example, for a long-term contract, managers can choose to recognize revenue when the contract is completed, or in interim periods based on the progress toward completion. Further judgment is required in terms of how to measure progress at a particular interim date. 9

11 opportunistically manipulate accruals to manage earnings. Under this skeptical view, these investors would more or less ignore accruals when valuing the firm. Thus, manager discretion on accruals would lead to different interpretations among investors on the underlying reasons for accruals, thereby causing heterogeneous opinions among investors on the firm value. We further argue that high accounting accruals leads to a high level of the heterogeneity in investor beliefs. Accounting accruals could result from either income-inflating upward earnings management or income-deflating downward earnings management. As suggested in Chan, Jegadeesh, and Lakonishok (2006), managers face more pressure to boost reported earnings to meet the market s expectations than to defer current earnings to the future. Thus, investors would be more likely to view an increase in accruals as an outcome of an increased degree of upward earnings management rather than a decreased degree of downward earnings management. Under this view, an increase in accruals would induce more concerns on (upward) earnings management for some investors, thereby causing a higher level of heterogeneous investor beliefs on the value of the firm. This is our first hypothesis (H1) to test. In one of the robustness checks, we also check whether or not the relation on accruals and heterogeneity of beliefs (i.e., hypothesis H1) holds for both positive accruals and negative accruals. An increase in accruals could arise from either an increase in the income-inflating upward earnings management, or a decrease in the income-deflating downward earnings management, or both. In the development of hypothesis H1, we argue that the downward earnings management is less likely to happen compared to the upward earnings management. Thus, an increase in accruals is viewed by investors as an outcome of an increased degree of the upward earnings management, thereby increasing the heterogeneity of investor beliefs. However, it is also possible that an increase in accruals could be caused by a reduced degree of the 10

12 downward earnings management, thereby reducing the heterogeneity of investor beliefs. This possibility is especially likely to happen in the case of negative accruals, since the downward earnings management is likely associated with negative accruals. Thus, as part of the test of Hypothesis H1, we also test hypothesis H1 for both the subsample of positive accruals and the subsample of negative accruals. If the downward earnings management is important, we expect to find a negative relation between accruals and the heterogeneity of investor beliefs at least for the subsample of negative accruals. Next, we examine whether the impact of accruals on heterogeneous investor beliefs could affect future stock returns. As discussed earlier, investors could be more heterogeneous in their valuations of the firm s stock when a firm announces higher level of accruals. According to Miller (1977), this higher level of the heterogeneity of investor beliefs would cause the firm s stock to be valued contemporaneously at a higher level. Over time, the value of the highheterogeneity stock will converge to the fundamental value, leading to a negative ex-post long run stock return. Thus, we predict a negative future stock return following higher accruals. We also predict that the negative relation between future stock return and accruals is more pronounced if higher accruals cause a higher level of heterogeneous investor beliefs. This is our second hypothesis (H2) to test. As part of the test of hypothesis (H2), we also study whether or not there is an asymmetry on the relation among accruals, heterogeneity of investor beliefs, and future stock returns. Miller (1977) predicts that the stocks with a high level of heterogeneity will underperform in the future, while the converse, that the low heterogeneity stocks will outperform in the future, need not be true. In Miller s framework, the contemporaneous overpricing of the high-heterogeneity stocks is due to the existence of short-sale constraints. However, while there may exist short-sale 11

13 constraints on the stock, there is no constraints on buying. Thus, the low-heterogeneity stocks in Miller s framework may not necessarily be underpriced. Following this logic, we also study whether or not hypothesis (H2) holds for both the high-heterogeneity stocks and the lowheterogeneity stocks. Finally, we examine if the above relation among accruals, heterogeneity of investor beliefs, and stock returns are stronger when short-sale constraints are more binding. One necessary condition in Miller s (1977) framework is the existence of short-sale constraints. A high level of heterogeneity of investor beliefs would cause a higher level of contemporaneous price and be followed by a lower ex-post future stock return only when the existence of shortsale constraints prevents the pessimistic investors from selling short the high-heterogeneity stock. The relation between the heterogeneity of investor beliefs and future stock return would be more pronounced if short-sale constraints are more binding. Thus, our third hypothesis (H3) is that the impact of accounting accruals on the heterogeneity of investor beliefs affects future stock returns to a larger extent if the stock faces more binding short-sale constraints. 3. Sample Selection and Variable Construction 3.1. Sample Selection To study the impact of accruals on heterogeneity of investor beliefs and stock returns subsequent to the preliminary earnings announcement, we need to calculate accruals at the earnings announcement date. Since accruals are the difference between earnings and operating cash flows, we obtain a proprietary database of firms that voluntarily disclose operating cash 12

14 flows in the preliminary earnings announcement. 10 Using this sample ensures that investors have sufficient information to infer firms accruals amount at the earnings announcement date. 11 Our proprietary sample covers years 1994 to We exclude utilities and financial services firms (two-digit SIC codes 49 and 60-67). We further extract stock prices from the Center for Research in Securities Prices (CRSP), and financial analysts forecasts from I/B/E/S. Our final sample consists of 1,257 firms and 10,694 firm-quarters. In the following empirical analysis, there may be sample attrition due to incomplete information from missing lagged variables. Table 1 reports the annual breakdown of our sample as well as the average and the median market capitalization every year Measures of Total Accruals Following the accounting literature, we calculate total accruals (ACCA) as firms quarterly net income before extraordinary items and discontinued operations minus quarterly net operating cash flows, scaled by the average total assets during the quarter. We calculate the change in total accruals (ΔACCA) as the change of accruals from the previous quarter q-1 to the current quarter q. All our empirical tests will be based on total accruals. In the paper, we focus mainly on the change in total accruals (i.e., accrual growth). We study specifically the relation between accrual growth, heterogeneity of investor beliefs, and stock returns. We work with change in accrual rather than the level of accruals to purge firm fixed effects. First, the effect of accruals on heterogeneity of investor beliefs could vary among 10 We thank Joshua Livnat for providing us with the proprietary database. 11 For firms without such voluntary disclosure, investors have to find out about the amount of operating cash flows and hence the amount of accruals from quarterly filings. Quarterly fillings are usually filed within a month after earnings announcements (Easton and Zmijiewski, 1993). In an unreported robustness check with the whole universe of firms, we assume that firms file their 10-Q (K) reports within two month subsequent to the fiscal quarter end. We rerun all tests with stock returns in windows starting from 60 days subsequent to the fiscal quarter end to ensure that investors have access to the accruals information. The results based on this new sample are qualitatively the same. They are available upon request from readers. 13

15 various firms. For example, a highly-reputable firm with a high level of accounting accruals could still enjoy a lower level of heterogeneity of investor beliefs compared to a firm with bad reputation and a low level of accruals. Second, the proportion of the accrual component in earnings could also effectively be a permanent firm characteristic. For example, firms with a longer operating cycle could have a higher level of accruals. Recently, many papers argue that accruals are correlated with certain firm characteristics and that it is these characteristics that predict future stock returns (see, e.g., Fairfield et al., 2003; Desai et al., 2004; Khan, 2008; Zhang, 2007). In unreported results, we also find that accruals are positively correlated to lagged operating performance, lagged stock return performance, and market-to-book ratio, and are negatively correlated to firm size. These correlations suggest that small firms, growth firms, firms with high profitability, and firms with high stock return performance are more likely to have high accruals. In an effort to purge the above firm fixed effects, we use the change in accruals ΔACCA rather than the level of accruals ACCA in our tests. In addition to the change in total accruals, we have also tested our hypotheses using discretionary accruals. Our results based on discretionary accruals are similar to those reported in the paper. Due to space constraint, we choose not to report the results based on discretionary accruals in the paper. These results are available upon request from readers Measures of Heterogeneous Beliefs We measure the degree of heterogeneous investor beliefs on a firm s value by the dispersion of financial analysts forecasts on the firm s one-year-ahead earnings (see Diether, Malloy, and Scherbina, 2002). 12 The higher the dispersion in analysts earnings forecasts, the 12 The data we use in the calculation of earnings forecasts come from the Summary History file of I/B/E/S. Diether et al. (2002) report a rounding bias due to stock splits, but they find that the bias does not affect their results. 14

16 higher the level of heterogeneity in investor beliefs. We calculate analyst forecast dispersion (Dispersion) as the standard deviation of analysts earnings forecasts in the month subsequent to the earnings announcement date, scaled by the absolute value of the firm s actual earnings. We code Dispersion as missing if there are less than three financial analysts covering the firm. In the main tests, we focus on the level of analyst dispersion and study how the accrual change affects analyst dispersion (and further future stock returns). In several robustness checks, we also examine the change in analyst dispersion and study how the accrual change affects the change in analyst dispersion Measures of Stock Returns We measure the future stock return in various trading day event windows. We first measure two-month, three-month, and six-month stock returns starting from earnings announcement date: [0, 42], [0, 63], and [0, 126], where 0 denotes the earnings announcement date, 42 denotes 42 trading days, i.e., two months subsequent to the earnings announcement date, etc. We also measure stock returns excluding the period around the earnings announcement date: [6, 42], [6, 63], and [6, 126], where 6 denotes the sixth trading day subsequent to the earnings announcement date, i.e., the day after the first week of earnings announcement. We study these three trading day windows to ensure that our results are not driven by the short run announcement period return and that they are indeed driven by the long run ex-post stock returns. Finally, we also measure stock returns after financial analysts report their earnings forecasts to I/B/E/S: [a, 42], [a, 63], and [a, 126], where a denotes the date subsequent to the reporting date of analysts forecasts. One potential concern for the windows starting from day 0 or day 6 is that they could overlap with the measurement window of analyst dispersion, which is 15

17 measure in the first month right after the earnings announcement. This overlapping would cause ambiguity on the causality between analyst dispersion and stock return. Specifically, this ambiguity could arise since the heterogeneity of investor beliefs could cause a certain pattern of stock returns and a certain pattern of stock returns could also cause investors to be heterogeneous in their beliefs. In the paper, we intend to study how the heterogeneity of investor beliefs induced by the accrual change affects stock returns in the future. Thus, to ensure the causality from analyst dispersion to stock return and not the other way around, we also measure stock returns starting subsequent to the report date of analysts earnings forecasts Measures of Short-sale Constraints We use two proxies to capture how tightly short-sale constraints bind. The first one is the fraction of the stock holdings by institutional investors. Institutional investors lend shares in the stock lending markets, from which short-sellers borrow to sell short. Thus, the stocks with low institutional investor ownership are hard to be located in the stock lending market and thus hard to sell short (Nagel 2005; Berkman et al. 2009). The second proxy for short-sale constraints is the level of stock illiquidity (Amihud 2002). Stock illiquidity (Illiquidity) is calculated as the ratio of the absolute value of daily return to the value of daily trading volume, averaged in the year prior to day -6. Prior literature suggests that the illiquid stocks are more costly to sell short (see, Sadka and Scherbina (2007) and Banerjee and Graveline (2012)) Construction of Other Variables We calculate the following control variables. Firm size (Size) is the log of the market value of equity at the end of the previous quarter, i.e., quarter q-1. Book-to-market ratio (BM) is 16

18 the ratio of the book value to the market value of equity at the end of quarter q-1. Stock return momentum (Momentum) is the stock return in trading day window [-21, -6]. Stock beta (Beta) is the beta estimate based on a period of 200 days ending 6 days prior to the earnings announcement date. We will control for Size, BM, Beta, Momentum, as well as Illiquidity, in our empirical studies since these variables are the common return predictors as documented in the literature. To control for a firm s growth, we use growth in long-term net operating assets (GrLTNOA). It is calculated as the growth in non-accrual net operating assets scaled by average total assets. We also calculate two earnings variables. We calculate standardized unexpected earnings (SUE) as (E q E q-4 c q )/s q, where E q and E q-4 are earnings in the current quarter and in the same quarter a year ago, respectively; and c q and s q are the mean and standard deviation, respectively, of (E q E q 4 ) over the preceding eight quarters. We calculate return on assets (ROA) as the ratio of net income to total assets in quarter q-1. Finally, we calculate two variables based on the information from I/B/E/S. We calculate the number of analysts' one-year-ahead earnings forecasts reported in I/B/E/S (NForecast). We also calculate forecast error (Error) as the difference between the average earnings forecast and the actual earnings per share, scaled by absolute value of the actual earnings per share. It is worth noting that our forecast error is based on the signed difference between the forecasted EPS and the actual EPS, rather than unsigned difference as in many studies. Our results would remain qualitatively the same if we use signed forecast error. However, we choose to use signed forecast error in the paper since we want to proxy for the average of analyst beliefs. If analysts on average are more optimistic, signed forecast error would be larger and more likely to be positive. If analysts on average are more pessimistic, signed forecast error would be smaller and more likely to be negative. Table 2 17

19 provides the sample statistics on the key variables in our study. To minimize the influence of outliers, we winsorize all variables at the top and bottom 1 percent of the distribution. 4. Empirical Findings In this section, we study the impacts of accruals on the heterogeneity of investor beliefs and consequently future stock returns by testing hypotheses H1-H Accruals and Investors Heterogeneous Beliefs Our first hypothesis (H1) is that an increase in accruals causes a higher level of heterogeneous beliefs among investors on the value of the firm. We test H1 by running the following regression: Analyst Dispersion = ΔACCA + 2 Control variables +. (1) In regression (1), the dependent variable is Dispersion, proxied for the level of heterogeneous beliefs. We measure Dispersion based on analysts forecasts in the first month subsequent to earnings announcement date. We measure ΔACCA based on the cash flow information announced in the previous and the current earnings announcement dates. In other words, we measure Dispersion at a time subsequent to the measurement window of ΔACCA. In doing so, we ensure the causality is from ΔACCA to Dispersion, not the other way around. The control variables consist of ROA, SUE, GrLTNOA, Error, NForecast, Size, BM, Beta, Illiquidity, and Momentum. Return on assets (ROA) and earnings surprise (SUE) are measured in the current quarter q. We use these two variables to control for the effect of reported earnings on investors heterogeneous beliefs. Forecast error (Error) and number of analysts following (NForecast) are measured in the current quarter q as well. We use Error to control for the effect 18

20 from the average level of analyst beliefs (as suggested by the fixation consideration). We use NForecast since many studies show that analyst dispersion is affected by the number of analyst following. Finally, we control for growth in long-term net operating assets (GrLTNOA) to ensure that our findings are not affected by the growth anomaly as documented in Fairfield et al. (2003). According to hypothesis H1, we expect 1 to be positive. We try various econometric techniques for regression (1) to ensure the robustness of our results. In particular, we run ordinary least square regressions (OLS), Fama-MacBeth regressions, and the fixed effect regression. In Fama-MacBeth regressions, we first run separate regressions for each year. We then average the regression coefficients across years as in Fama and MacBeth (1973) and estimate the statistical inference based on the Newey-West standard errors. In OLS regressions, we control for year dummies. We also allow correlated residuals within each firm in all OLS regressions (i.e., clustering based on firms). Significance tests are conducted based on heteroskedasticity-consistent standard errors following Huber-White procedure. We report the results in Table 3. In columns (1) to (4), we report results from Fama- MacBeth regressions. We first control for the two earnings variables ROA and SUE in column (1), followed by regressions gradually adding more controls in columns (2) to (4). In columns (5) and (6), we report results from OLS regressions without and with time dummies, respectively. Finally, in column (7), we report the results from the fixed-effect regression. As can be seen, 1, the coefficient of ΔACCA, is positive in all seven columns. It is significant at 1% in five of the seven columns and significant at 5% in the rest of the two columns. These results in Table 3 show that an increase in accruals is associated with a higher level of analyst dispersion. They also show that the effect of accruals on analyst dispersion is incremental to the earnings effect, i.e., the effect of the reported earnings on analyst dispersion. 19

21 The effect is also independent of the effect of accruals on the average analyst beliefs (measured by the signed forecast error). Thus, our results support hypothesis H1. They suggest that higher accruals cause investors to be more heterogeneous in their beliefs on the value of the firm Robustness Checks on Accruals and Investors Heterogeneous Beliefs We run three robustness tests. First, we run regressions of the change in analyst dispersion, Dispersion, against the accrual change, ACCA, rather than using the level of dispersion as in Table 3. In these regressions where the dependent variable is Dispersion, we choose to control for Error and NForecast rather than the level variables Error and NForecast as in regression (1) where the dependent variable is Dispersion. In some regressions, we also control for Lagged ACCA, Lagged Dispersion, Lagged Error, and Lagged NForecast. The other control variables are the same as in regression (1). 13 We report the results from this robustness check in Table 4. In column (1), we control for just the two earnings variables and we gradually add more controls in columns (2) through (6). In all specifications, we run Fama-MacBeth regressions. As predicted, 1, the coefficient of ΔACCA, remains positive and significant in all columns. The evidence provides additional support to H1. It suggests that our results on the positive relation between the accrual change and analyst dispersion are robust to the alterative change specifications. In the second robustness check, we address the concern of sample selectivity. Our sample consists of the firms disclosing both the earnings and the operating cash flow information at the earnings announcement date. However, not all the firms report the operating cash flow 13 In regressions where we control for both Lagged ACCA and Lagged Dispersion, the specification is equivalent to the specification that regress Dispersion against ACCA, both as level variables. 20

22 information at the earnings announcement date. Thus, our sample is only a subset of the universe of Compustat firms. If our sample is not a truly random sample, then the estimates from the above regressions could be biased. To address the sample selection concern, we estimate Heckman's (1979) selection model. The Heckman selection model consists of a selection equation and a dispersion equation. To estimate the selection equation, we run a probit model on whether or not a firm reports the operating cash flow information at the earnings announcement date. The sample in the estimation of the selection equation consists of all firms that are covered by Compustat and I/B/E/S. The independent variables in the selection equation include the lagged variables of ACCA, ACCA q-1, and ACCA q-2, lagged Error, lagged NForecast, Beta, lagged Size, lagged Illiquidity, lagged Momentum, lagged capital expenditures/ assets, and lagged stock trading turnover. The sample in the estimation of the dispersion equation consists of the firms disclosing both the earnings and the cash flow information at the earnings announcement date. The specification of the dispersion equation is the same as in the previous regressions. We report the results from the Heckman selection model in Table 5. Due to space constraint, we report only the results on the dispersion equation. The dependent variable in the first three columns is the level of analyst dispersion (Dispersion); and it is the change in analyst dispersion ( Dispersion) in columns (4) to (6). In general, the results from the Heckman model are similar to those reported in the previous tables. The coefficient of ΔACCA is positive. It is also significant in all columns. Thus, it is evident that our results on accruals and analyst dispersion are unlikely to be driven by the factors that cause the selectivity of our sample. In the third robustness check, we study whether the relation between the accrual change and analyst dispersion is nonlinear and asymmetric. We first include the square of ΔACCA, ΔACCA 2, as an additional independent variable in regression (1). If the relation between the 21

23 accrual change and analyst dispersion is non-linear, we expect this non-linear variable to be significant. We present the results in columns (1), (4), and (7) in Table 6. The coefficients of ΔACCA 2 are insignificant in all three columns. Next, we disaggregate the whole sample to the subsamples of positive and negative accruals. We run regression (1) separately for each of both subsamples. We present the results based on the subsample of positive accruals in columns (2), (5), and (8), and the results based on the subsample of negative accruals in columns (3), (6), and (9). As can be seen, the coefficients of ΔACCA are positive and significant in all columns, regardless of the subsamples of positive or negative accruals. These results suggest that the relation between the accrual change and analyst dispersion is linear and symmetric. They also suggest that the relation is driven by the income-inflating upward earnings management rather than the income-deflating downward earnings management Accruals, Investors Heterogeneous Beliefs, and Future Stock Returns In hypothesis H2, we predict a negative future stock return following an increase in accruals. We also predict that the negative relation between future stock return and increased accruals is more pronounced if the increase in accruals causes a higher level of heterogeneous investor beliefs. We run the following regression to test this hypothesis: Ret = ΔACCA + 2 Analyst Dispersion + 3 ΔACCA Analyst Dispersion + 4 Control variables +. (2) The dependent variable in Equation (2) is the ex-post long-run stock return (Ret). We first measure stock returns in two trading day windows: [0, 63] and [6, 63], starting from either the earnings announcement date or one week after the earnings announcement date. However, as we discussed earlier, these two stock return windows [0, 63] and [6, 63] could overlap in month 1 22

24 with the measurement window of our analyst dispersion variable. To eliminate this overlapping, we also measure stock returns starting after the report date of analysts earnings forecasts, in window [a, 63]. In other words, window [a, 63] helps ensure that the causality is from analyst dispersion to ex-post stock returns. In the paper, we use all three event windows for ex-post stock returns to demonstrate the robustness of our results. We measure the heterogeneity of investor beliefs by analyst dispersion, Dispersion. We also interact Dispersion with ΔACCA. The control variables include the well-documented return predictors: Size, BM, Beta, Momentum, and Illiquidity. We also control for the earnings variable SUE and ROA to control for other stock anomalies such as the post-earnings announcement drift. Finally, we control for Error, as well as NForecast, to purge the effect from average analyst forecast on stock returns so that we can focus on the effect from the heterogeneity of analyst forecasts on stock returns. According to hypothesis H2, we expect the coefficient of the interaction term ΔACCA Dispersion to be negative. We present the results in Table 7, with the first three columns based on future stock return in window [0, 63], the next three columns based on future stock return in window [6, 63], and the last three columns based on future stock return in window [a, 63]. In column (1), (4), and (7), we first run Fama-MacBeth regressions on ex-post long-run stock returns against ΔACCA. As can be seen, the coefficient of ΔACCA in these three columns is negative and significant. These results show that an increase in accruals is followed by lower stock returns in the future. They are consistent with the previous findings in the literature on the accrual anomaly. In columns (2), (5), (8), we report results with the interaction term ΔACCA Dispersion as one of the independent variable in the Fama-MacBeth regressions. The coefficients of the interaction term are negative in all three columns. They are significant at either the 1% or the 5% 23

25 level. In columns (3), (6), and (9), we further present the results based on OLS regressions with year dummies as additional control variables. Again, the coefficients of the interaction term are negative and significant. Overall, our results in Table 6 show that the negative relation between an increase in accruals and future stock return is more pronounced if financial analysts disagree more with one another in the month following the accrual growth. They are robust to the different controls and different econometric techniques. They hold across various measurement windows of stock returns. They also do not seem to be driven by the predictability powers of the other common return predictors, such as firm size, momentum, illiquidity, and the difference between value and glamour stocks. Thus, our results are consistent with hypothesis H2, suggesting that the stock price reversal following an increase in accruals is more pronounced when heterogeneity of investor beliefs increases to a larger degree in response to the increase in accruals Robustness Checks on Accruals, Heterogeneous Beliefs, and Future Stock Returns We run several robustness checks on the relation between accruals, dispersion, and future stock returns. First, we run regression (2) in two subsamples: the subsample with a high level of analyst dispersion and the subsample with a low level of dispersion. We include in the highdispersion subsample those firms with their levels of analyst dispersion above the median of the whole sample. We include in the low-dispersion subsample those firms with their analyst dispersion below the median. If the relation between accruals, dispersion, and future stock returns follows Miller s (1977) framework, then we expect the relation between accruals, dispersion, and future stock returns as hypothesized in H2 is stronger in the subsample of high analyst dispersion, compared to the subsample of low analyst dispersion. 24