Explaining the accrual anomaly by market expectations of future returns and earnings

Advances in Accounting, incorporating Advances in International Accounting 25 (2009) 190–199

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Advances in Accounting, incorporating Advances in International Accounting j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a d i a c

Explaining the accrual anomaly by market expectations of future returns and earnings☆ Randall Zhaohui Xu, Michael J. Lacina ⁎ University of Houston-Clear Lake, School of Business, 2700 Bay Area Blvd, Box 42, Houston, TX 77058, United States

a r t i c l e Keywords: Accrual anomaly Campbell model Easton model Return news Cash flow news

i n f o

a b s t r a c t This study examines the accrual anomaly under the framework of the Campbell [Campbell, J.Y. (1991). A variance decomposition for stock returns. Economic Journal 101 (405), 157–179.] model. The Campbell (1991) model shows that realized asset returns are a joint function of 1) expected returns, 2) revisions in market expected future returns (i.e., return news), and 3) revisions in market expected future cash flows (i.e., cash flow news). The current study adopts the Easton [Easton, P. (2004). PE ratios, PEG ratios, and estimating the implied expected rate of return on equity capital. The Accounting Review 79 (1), 73–96.] model to estimate proxies for expected returns, return news, and cash flow news. The results show that firms with low accruals have lower expected returns than firms with high accruals, which is contradictory to prior research that argues that firms with low accruals are more risky. However, investors underestimate (overestimate) future earnings growth, a proxy for cash flow growth, for low (high) accrual firms. Further analysis demonstrates that earnings news (proxy for cash flow news) plays a major role in explaining abnormal returns associated with the accrual anomaly. © 2009 Elsevier Ltd. All rights reserved.

1. Introduction Prior research (Sloan, 1996; Pincus, Rajgopal, & Venkatachalam, 2007) has documented that firms with low accruals tend to have higher stock returns than firms with high accruals. Trading strategies that hold a portfolio of low accrual firms and short a portfolio of high accrual firms generate significantly positive returns even after controlling for differences in risk with measures such as CAPM beta or firm size. The extant accounting literature contains a large body of research exploring the causes for the abnormal returns associated with the accrual anomaly. One stream of research contends that the accrual anomaly is a spurious phenomenon in the sense that the abnormal returns are compensations for risk that is either unaccounted for or improperly measured (Ng, 2005; Kraft, Leone, & Wasley, 2006; Beaver, McNichols, & Price, 2007; Khan, 2008). The other stream of research argues that the accrual anomaly is not related to risk. Instead, it arises because naive investors in the market fail to efficiently incorporate certain information contained in accruals. The more popular explanations include (1) the market fixates on reported earnings and ignores the fact that the accrual

☆ We gratefully acknowledge the comments and suggestions from Richard Morton (Associate Editor), three anonymous referees, Anup Agrawal, Wael Aguir, Keji Chen, Mike Dugan, Robert Ingram, Mary Stone, and Gary Taylor. Further, we thank participants at the University of Alabama workshop and at the 2009 Southwest Region American Accounting Association Annual Meeting for helpful comments and suggestions. Also, we acknowledge Thomson Financial for providing I/B/E/S analysts' earnings forecasts. ⁎ Corresponding author. E-mail addresses: [email protected] (R.Z. Xu), [email protected] (M.J. Lacina). 0882-6110/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.adiac.2009.06.002

component of earnings is less persistent than the cash component of earnings (Sloan, 1996; Xie, 2001; Richardson, Sloan, Soliman, & Tuna, 2006; Pincus, et al., 2007);1 and (2) the market fails to properly incorporate growth-related information contained in accruals (Fairfield, Whisenant, & Lombardi Yohn, 2003a; Fairfield, Whisenant, & Lombardi Yohn, 2003b; Cohen & Lys, 2006; Dechow, Richardson, & Sloan, 2008). In either case, the market would need to revise its expectations as firms reveal their true performance in subsequent periods.2 Both streams of research find some evidence supporting their assertions, but none is conclusive. We argue that each of the two streams may catch only one side of the story. As shown by Campbell (1991), these two lines of arguments actually represent different factors that affect asset returns. Campbell (1991) shows that an asset's realized returns are a function of not only the asset's current period expected returns, but also of revisions in the market's expectation of the asset's future returns and future cash flows (i.e., “return news” and 1 Xie (2001) finds that the lower persistence of accruals is mainly caused by firms with high discretionary accruals. Further, Xie (2001) and Pincus, et al. (2007) show that discretionary accruals and not non-discretionary accruals cause abnormal returns. Since high discretionary accruals are likely produced by earnings management, the previous findings suggest that the accrual anomaly may be induced by earnings management. We do not explicitly examine earning management in the current paper. 2 Mashruwala, Rajgopal, and Shevlin (2006) show that the stocks of firms with extreme accruals on-average have high idiosyncratic risk and are traded at a low volume, making it risky and costly to arbitrage away abnormal returns associated with extreme accruals. This could be an explanation for the mispricing of firms with extreme accruals. In the current paper, we examine overall risk (expected returns) and thus do not explicitly examine idiosyncratic risk. Also, we do not examine transaction costs in the paper.

R.Z. Xu, M.J. Lacina / Advances in Accounting, incorporating Advances in International Accounting 25 (2009) 190–199

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“cash flow news”). Thus, unexpected returns (the difference between realized returns and expected returns) occur when there are changes in investors' expectations about the asset's future returns and/or changes in investors' expectations about its future cash flows. The Campbell model demonstrates that unexpected returns are positively related to cash flow news and negatively related to return news. This relationship can be illustrated using stock as an example. Stock is in theory priced as the present value of future dividends, and stock return is the change in stock price plus the dividend for the period, deflated by the beginning price. If investors' expectations about the stock's returns and dividends remain constant over time, the realized stock return for a given period should be equal to the expected or required stock return. However, higher expected returns, which are caused by higher risk, lead to a lower stock price. Consequently, if investors learn of information suggesting higher risk associated with the firm's business and accordingly revise upward their stock's required future returns (holding future dividend payouts constant), stock price would go down, which would lead to negative unexpected returns in the period. On the other hand, if investors learn of information suggesting improvements in the firm's future performance and accordingly revise upward their expectations about the stock's future dividend payouts (holding risk constant), stock price would go up, which would lead to positive unexpected returns. From the previous discussion, we can see that the aforementioned two streams of research on the accrual anomaly are related to different factors in the Campbell (1991) model. The first group of researchers who argue that abnormal returns are compensations for risk is conveying that low accrual firms are more risky than high accrual firms and that the common asset pricing models used in the market anomaly studies fail to properly assign higher levels of current period expected returns for low accrual firms. The second group of researchers argues that investors do not fully understand firms' true performance due to either a fixation on earnings or an inability to properly price growth. As subsequent events such as earnings announcements reveal new information about firms' prospects, investors change their expectations of future returns and/or future cash flows. Thus, in accordance with the Campbell (1991) framework, there is return news and/or cash flow news about a firm, which causes abnormal returns. The purpose of the study is to utilize the framework of Campbell's (1991) return decomposition model to explore the accrual anomaly. This study adopts the Easton (2004) approach to simultaneously estimate 1) expected returns and 2) future earnings growth (to proxy for expected cash flow growth),3 using stock price and analyst earnings forecasts. The expected return generated from the Easton model is constant in perpetuity. Therefore, we are able to use this measure as a proxy for current period expected returns. Hence, expected returns are generated for high and low accrual firms to test the risk-based explanation for the accrual anomaly. A higher current period expected return for low accrual firms would support a riskbased explanation for the accrual anomaly. To test the errors in

expectations explanation for the accrual anomaly, estimates for cash flow news and return news are constructed. Specifically, we measure the difference in estimated expected earnings growth rates and the difference in estimated returns generated by the Easton model between the time of portfolio formation and one year after portfolio formation. If high accrual firms have a negative change in expected earnings growth over the year and low accrual firms have a positive change in expected earnings growth, this would convey that the accrual anomaly is at least partially explained by investors initially over-estimating earnings growth for high accrual firms and initially under-estimating earnings growth for low accrual firms. Similar arguments apply for inferring errors in investors' expectations of risk from changes in expected returns during the one-year period.4 There are several advantages in using the Easton (2004) model to estimate the key variables for this study. Prior research (Botosan & Plumlee, 2005) shows that cost of capital (expected return) estimated with the Easton (2004) model is consistently positively related to risk and is more reliable than other estimates of cost of capital in accounting research (e.g., Gordon & Gordon, 1997; Gebhardt, Lee, & Swaminathan, 2001). Also, the Easton (2004) model simultaneously estimates both expected return and (abnormal) earnings growth that are implied by market data (stock price and analyst earnings forecasts). As a result, it avoids making an ad hoc assumption on one of the measures and solving for the other.5 Campbell and Vuolteenaho (2004) and Khan (2008) use the VAR model to estimate return news and cash flow news and apply these estimates under the Campbell (1991) framework to examine market anomalies. However, as shown by Chen and Zhao (2006), the VAR approach has serious limitations and can lead to counter-intuitive conclusions. Specifically, the VAR model estimates the return news in the first step and then backs out the cash flow news as the residual of the model. As a result, the estimated cash flow news is very sensitive to omitted variables in the VAR model.6 The current study runs the Easton (2004) model for portfolios formed by accrual levels and finds that firms with low accruals, on average, have an expected return of 11.9% at the time of portfolio formation (the current period), lower than the expected return of 14.7% for firms with high accruals. The difference is both economically and statistically significant. This result for current expected returns runs counter to a risk-based explanation for higher returns from lower accrual firms.7 An analysis of the change in expected returns and the change in expected earnings growth between the time of portfolio formation and one year after portfolio formation reveals different patterns for firms with extreme accruals. For firms with low accruals, there is a significant increase of 6.9% in expected earnings growth during the year following portfolio formation. For firms with high accruals, the expected earnings growth rate decreases by 5.0% during the year. The expected return basically remains the same during the one year period after portfolio formation for firms with different levels of accruals. These findings suggest that investors initially underestimate (overestimate) earnings growth for low (high) accrual firms,

3 The future earnings growth rate estimated by the Easton (2004) model is actually the growth rate of future abnormal earnings, which is in accordance with Vuolteenaho's (2002) version of Campbell's (1991) stock returns decomposition model. Abnormal earnings is cum-dividend earnings minus normal earnings. Normal earnings is defined as prior period earnings multiplied by one plus the firm's expected return. For simplicity, we use the term future earnings growth instead of growth rate in future abnormal earnings. Although Campbell (1991) expresses his stock returns decomposition model using dividend growth to proxy for cash flows, Vuolteenaho (2002) and Easton and Monahan (2005) demonstrate that the returns decomposition model can be derived using accounting earnings. Whether one chooses to express cash flow news in the return decomposition model “…in terms of dividend growth or ROE is a matter of taste” (Vuolteenaho, 2002). Vuolteenaho (2002) expresses the proxy for cash flows as return-on-equity (ROE) minus interest rate, which is equivalent to abnormal earnings deflated by book value of equity. See Appendix A for details on derivations of the return decomposition model using accounting earnings.

4 We measure current expected return to test whether there is a risk-based explanation for the accrual anomaly because it is the ex ante expected return that is included in the current stock price. The change in expected return (i.e., return news) measures the ex post change in investors' consensus on the risk of the firm between the current time period and a future date (e.g., one year later). Thus, the return news is not compounded in the current (initial) stock price, and it measures errors in investors' initial expectations about future returns. 5 Models used to estimate cost of capital often make assumptions on firms' future earnings growth rates to calculate the cost of capital (e.g., Claus & Thomas, 2001; Gebhardt, et al., 2001; Baginski & Wahlen, 2003). 6 A more detailed discussion of the VAR model is presented in Section 3.1. 7 We are making the implicit assumption that the expected return is an overall measure of risk. Our findings should be interpreted with caution in that the expected return estimates could have measurement errors.

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which contributes to higher (lower) abnormal returns for low (high) accrual firms.8 The regression analysis shows that changes in expected earnings growth have a positive association with abnormal stock returns whereas changes in expected returns have a negative relationship with abnormal stock returns. These findings are consistent with the Campbell (1991) model that unexpected returns are functions of return news and cash flow news. Also, regression results indicate that the abnormal stock returns associated with the accrual anomaly are primarily explained by changes in earnings growth and to a lesser extent by changes in expected return. We also undertake an analysis of covariance to investigate whether it is changes in expectations about future earnings growth (proxy for cash flow news) or about future returns that drives abnormal returns. We find that cash flow news plays a larger role in driving abnormal returns than return news. This finding is consistent with Vuolteenaho (2002), who shows that stock returns are more heavily driven by cash flow news than by return news. The current study makes several contributions to the accrual anomaly literature. First, this study extends extant literature that explores market anomalies under the Campbell (1991) framework. Prior research (Khan, 2008) investigated the accrual anomaly using the VAR (vector autoregressive) model, an approach that has been shown to have serious limitations. The current study applies the Easton (2004) model to facilitate the adoption of the Campbell (1991) model to study the accrual anomaly. Second, we find that high accrual firms have a higher current cost of capital than low accrual firms, which suggests that the market perceives high accrual firms as more risky than low accrual firms. This finding contradicts prior research (Ng, 2005; Khan, 2008) that infers that low accrual firms have attributes of financial distress and are thus more risky. While Ng (2005) and Khan (2008) examine firm attributes such as Altman's Z score and sales growth to infer risk, this study directly estimates the average cost of capital for firms with extreme accruals. Third, this study finds that investors systematically underestimate future earnings growth for firms with low accruals and overestimate future earnings growth for firms with high accruals. The results are consistent with conjectures that the market tends to overestimate the persistence of accruals (Sloan, 1996) and that accruals are related to information about future growth that investors fail to fully understand (Fairfield, et al., 2003a,b; Cohen & Lys, 2006; Dechow, et al., 2008). Section 2 reviews prior research and discusses the research question. Section 3 presents the research methodology. Section 4 describes the sample and the test results. Section 5 contains sensitivity analyses. Section 6 concludes the paper. 2. Review of prior research and discussion of research question 2.1. Review of prior accrual anomaly literature Prior research has documented that a simple trading strategy that buys firms with low accruals to total asset ratios (ACC) and shorts firms with high ACC can yield significantly positive abnormal returns (Sloan, 1996). The extant literature provides various explanations for the accrual anomaly. The debate is centered on whether the accrual anomaly arises due to underlying risk factors or market inefficiency in processing information related to accruals. One group of researchers argues that the accrual anomaly does not constitute a violation of the efficient market hypothesis because the abnormal returns are due to

8 We use past reported accruals as the starting point to measure observed revisions in investors' expectations, which convey the market's over/underreaction to historical accounting information. By sorting firms according to their reported accruals at prior year end, one can observe consistent patterns in the changes in investors' expectations. Studies on the accrual anomaly often classify observations according to past reported accruals.

underlying unaccounted or mis-measured risk. For example, Ng (2005) and Khan (2008) provide evidence that firms with low ACC have higher financial distress risk than firms with high ACC and infer that at least a portion of the abnormal returns compensate for the distress risk associated with accruals. Kraft, et al. (2006) and Beaver, et al. (2007) document that the abnormal returns found in accrual anomaly research are sensitive to the inclusion of delisting firm years and to a small number of outlier firm years. Their findings indicate that the accrual anomaly may be due to measurement errors in calculating risk-adjusted returns. In contrast, another group of researchers argues that the accrual anomaly is caused by a systematic bias in investors' expectations about firms' future prospects. Sloan (1996) contends that investors naively fixate on earnings as a whole and fail to realize that the accrual component of earnings is less persistent than the cash flow component of earnings. He suggests that the observed abnormal returns reflect price corrections when the accruals reverse in subsequent periods. Xie (2001) finds that lower returns and lower persistence associated with accruals are mainly due to firms with high discretionary accruals, which suggests that the accrual anomaly could be induced by earnings management. Pincus, et al. (2007) confirm findings in Xie (2001) by showing that the abnormal returns associated with the accrual anomaly are driven by discretionary as opposed to non-discretionary accruals in countries for which they document the accrual anomaly (Australia, Canada, the U. K., and the U. S.). Other literature (Fairfield, et al., 2003a,b; Cohen & Lys, 2006; Dechow, et al., 2008) documents evidence on a growth related explanation for the accrual anomaly. Managers tend to be overconfident about firms' growth opportunities and expand their operations by increasing both their accruals and long-term operating assets. Diminishing marginal returns to new investments and agency-related overinvestment problems may be factors that lead to the negative association between accruals and subsequent earnings and stock returns. A lack of available arbitrage opportunities could also help explain the accrual anomaly. Mashruwala, Rajgopal, and Shevlin (2006) find that firms with extreme accruals tend to have high idiosyncratic risk and low trading volume, which pose a barrier to arbitrage activities on the accrual anomaly. Their findings present a plausible explanation for the persistence of the accrual anomaly after it becomes known to the public. 2.2. The Campbell (1991) model and discussion of research question Recent studies (Cohen, Polk, & Vuolteenaho, 2003; Campbell & Vuolteenaho, 2004; Khan, 2008) implement the Campbell (1991) model to explore the causes of market anomalies. Campbell (1991) decomposes realized asset returns (rt + 1) into three components, namely current expected returns (Etrt + 1), change in expectations about future returns (return news, Nr,t + 1), and change in expectations about future cash flows (cash flow news, Ncf,t + 1).9 ∞

i

∞

i

rt + 1 ≈Et ½rt + 1  + ðEt + 1 −Et Þ ∑ ρ Δdt + 1 + i −ðEt + 1 −Et Þ ∑ ρ rt + 1 + j i=0

j=1

= Et ½rt + 1  + Ncf;t + 1 −Nr;t + 1 ð1Þ where the variable rt + 1 ≡ log realized returns, ρ ≡ a constant discount factor determined by the average dividend yield, Et[ ] ≡ the expectation in period t, (Et + 1 − Et)[ ] ≡ the change in expectation from period t to period t + 1, and Δd ≡ log dividend growth. Ignoring an error term, the above decomposition model accounts for realized asset returns. 9 The Campbell model follows from the dividend-growth model of Campbell and Shiller (1988). Campbell and Shiller (1988) derive the dividend-growth model by taking a first-order Taylor approximation of the definition of log return as rt + 1 = log (Pt + 1 + Dt + 1) − log(Pt), where P and D represent stock price and dividends, respectively.

R.Z. Xu, M.J. Lacina / Advances in Accounting, incorporating Advances in International Accounting 25 (2009) 190–199

Moving the expected returns Et[rt + 1] to the left hand side of the above equation, the model represents unexpected returns (or abnormal returns) as a function of changes in expectations of future cash flows and future returns: rt + 1 −Et ½rt + 1  = Ncf;t + 1 −Nr;t + 1

ð2Þ

An increase in expected future cash flows (positive cash flow news Ncf,t + 1) leads to positive unexpected returns, while an increase in expected future returns (positive return news Nr,t + 1) leads to negative unexpected returns. The above interpretation can be easily understood in the framework of the dividend discount model for firm value.10 The Campbell (1991) return decomposition model provides a framework to explore the causes for abnormal returns associated with the accrual anomaly. Eq. (1) conveys that the positive abnormal returns for low ACC firms may be due to one or more of the following factors: (1) low ACC firms are riskier and thus have higher expected returns Et[rt + 1] than high ACC firms, but the estimated measure of subsequent abnormal returns does not fully adjust for the higher risk associated with low ACC firms, (2) the market makes upward revisions in its expectations of low ACC firms' future cash flows, and (3) the market makes downward revisions in its expectations of low ACC firms' future returns (i.e., downward revisions in their discount rates). If the first factor holds, we would expect to find low ACC firms to have higher current period expected returns than high ACC firms. Further, the second and/or third factor holding is consistent with an error in expectations explanation, where investors change their expectations of future cash flows and/or returns. Evidence of significant changes in market expected future cash flows (proxied by earnings in this paper) or future returns for the ACC portfolios would indicate that investors have bias in their initial perceptions of the firms' prospects and adjust their assessments in a subsequent period as new information is revealed.

Vuolteenaho (2004) do not hold when the three state variables11 used in their study are substituted with other highly correlated variables or when updated data are used. As an extreme example, the Campbell and Vuolteenaho (2004) approach yields results on Treasury bond returns that are opposite to theory and common knowledge. Since the future cash flows of Treasury bonds are fixed, unexpected returns for Treasury bonds should be driven solely by return news. Yet, the VAR approach concludes that Treasury bonds' cash flow news contributes more to unexpected returns than does return news. 3.2. Easton (2004) Easton (2004) has developed a model that simultaneously estimates the expected returns and earnings growth rates that are implied by stock price and analysts' earnings forecasts. Since this model does not make estimates from residuals, it is likely not as sensitive to modeling errors from missing variables as the VAR approach. The Easton (2004) model is derived from the Ohlson and Juettner-Nauroth (2005) model, which has certain advantages over the residual income model (Preinreich, 1938; Ohlson,1995; and others). As suggested by Easton (2004), the key element of the Ohlson and Juettner-Nauroth (2005) model, future earnings, is readily available from the analysts' forecasts. In contrast, the residual income model needs both future earnings and future book values. Future book values are estimated with the clean surplus relation,12 and this assumption does not hold for most firms (Ohlson, 2005). The Easton (2004) model solves for expected returns r and the growth rate of abnormal earnings g for a portfolio of firms with the following regression equation: ceps2;j = P0;j = γ0 + γ1 ðeps1;j = P0;j Þ + ε0;j

3.1. Vector autoregressive (VAR) model ceps2 A number of studies (Campbell, 1991; Vuolteenaho, 2002; Campbell & Vuolteenaho, 2004; Hecht & Vuolteenaho, 2006; Khan, 2008) attempt to estimate return news and cash flow news with a first-order vector autoregressive (VAR) model. The VAR model is usually set up as: zt

+ 1

= Γzt + ut

ð3Þ

+ 1

where zt is a vector of variables at time t with stock returns as the first element and state variables related to stock returns such as the price-toearnings ratio as the other elements; and Γ is a matrix of constant parameters. The VAR model first estimates return news (i.e., the term Nr,t + 1 in Eq. (2)) and then backs out cash flow news (i.e., the term Ncf,t + 1 in Eq. (2)) as the sum of unexpected returns and return news (see Eq. (2)). A serious limitation with the VAR approach is that the estimated cash flow news, which is treated as a residual of the estimation model, could be a catchall for modeling errors. In fact, the results obtained with the VAR approach are found to be sensitive to the specifications of its state variables. Chen and Zhao (2006) show that the findings of Campbell and 10

In the dividend discount model, stock price is equal to the sum of discounted ∞

Dividendt

+ i . If expected future dividends increase, ð1 + rÞi price P will increase, leading to positive returns. On the other hand, given a fixed stream of expected future dividends, an increase in expected future returns (i.e., discount rate) will lower P, leading to negative returns. 11 The state variables in Campbell and Vuolteenaho (2004) are the term spread (difference between long-term and short-term bond yields), the price-to-earnings (PE) ratio, and the value spread (log book-to-market ratio of value stocks minus that of growth stocks).

future dividends; i.e., Pt = ∑

i=1

ð4Þ

where J P0 eps1

3. Discussion of research methodology

193

γ0

γ1

Firm j; Stock price at period 0; Expected earnings (per share) for Period 1 (the following period); eps2 +r ⁎ dps1, Expected cum-dividend earnings for Period 2,13 where dps1 is dividends (per share) for Period 1;14 r(r −g), where r is the expected equity return; g =agrt + 1/ agrt − 1, the perpetual growth rate of agr; and agrt =epst + 1 + r⁎dpst − (1 +r)epst, which is cum-dividend earnings less ‘normal’ earnings; and g + 1.

Eq. (4) is a random coefficient regression, where the two unknowns r and g are embedded in the coefficients γ0 and γ1 (see Appendix B for details of the Easton model).15 The value of the coefficient γ1 is used to solve for g. Further, the value of g in unison with the coefficient γ0 determines the value of r. One problem with the implementation of the Easton model is that the calculation of ceps2 requires an estimate of r whereas ceps2 is used to estimate r. Therefore, an iterative procedure is used to overcome the circularity. The procedure calculates an initial value of ceps2 by assuming 12 The clean surplus relation is the assumption that the book value of equity changes due to earnings and dividends only, i.e. ending book value = beginning book value + current period earnings – current period dividends. 13 Cum-dividend earnings are calculated as current year reported earnings plus the product of the firm's expected return and its prior year dividend payment. 14 The one year ahead dividends (per share) are assumed to equal the dividends (per share) declared during Period 0, which is the year prior to the year of the first analyst forecast (Period 1). We also estimate the Period 1 dividend as dividend declared in Period 0 adjusted by the firm's dividend growth rate from Period - 1 to Period 0, and get similar results. Specifically, the dividend growth rate is calculated as gd = (dps0 – dps−1)/dps−1 and the Period 1 dividend = dps0⁎(1 + gd). 15 In the random coefficient regression, the error term ε0,j comes from the firmspecific random components of γ0 and γ1.

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Table 1 Summary statistics.

ME BV ACC ceps2P eps1P

Table 2 Portfolio buy-hold returns based on one variable.

Mean

Standard deviation

Quartile 1

Median

Quartile 3

N

ACC quintile

1

2

3

4

5

Q1–Q5

3,385 1,123 − 0.03 0.07 0.05

13,299 3586 0.07 0.08 0.09

159 71 − 0.07 0.05 0.04

488 202 − 0.04 0.08 0.06

1718 736 0.00 0.10 0.08

22,477 22,477 22,477 22,477 22,477

Ret12 SAR12

0.218 0.046

0.198 0.034

0.177 0.019

0.176 0.019

0.121 − 0.027

0.096⁎⁎ 0.074⁎

Notes: 1. ME is the firm's market value of equity at fiscal year end (in millions). 2. BV is the firm's book value of equity at fiscal year end (in millions). 3. ACC is prior year total accruals over average total assets. Accruals are computed using the balance sheet method as in Sloan (1996); i.e., accruals=(Δcurrent assets−Δcash)− (Δcurrent liabilities−Δshort term debt−Δincome taxes payable)−depreciation expense. 4. ceps2P is the forecasted two year ahead cum-dividend earnings over market value of equity at end of March. Forecasted two year ahead cum-dividend earnings is the analyst forecast of two year ahead earnings plus the product of expected return and prior period dividends. 5. eps1P is the forecasted one year ahead earnings over market value of equity at end of March.

a rate of 0.12 for r, which is roughly the historical market return. With the calculated ceps2, the regression model is run to obtain an initial estimate of r and g. Then a revised value of ceps2 is calculated with the newly estimated r, and the regression model is estimated again with the revised ceps2. The procedure is repeated until the revision in the estimate of ceps2 leads to little change in the estimates of r and g.16 In the current study, the iterative procedure is conducted using portfolios of firms sorted by ACC (the ratio of accruals17 to average total assets). At the end of March18 of each sample year, firms are sorted into quintiles by prior year end ACC. The expected returns r and earnings growth rates g are estimated for each extreme ACC quintile19 at both the time of portfolio formation and one year after portfolio formation. We measure cash flow news and return news as changes in the expected earnings growth rates (Δg) and changes in the expected returns (Δr) for the same accrual level portfolio between portfolio formation and one year after portfolio formation. Since the expected return measure r is an intertemporal constant under the Easton model, the change in r from the base period to one year later measures the ex post change in the risk of a stock and not the base period risk. Similarly, the estimated r at the time of portfolio formation is the current expected return that we use to test the risk-based explanation for the accrual anomaly. 4. Sample and results 4.1. Sample and descriptive statistics The sample consists of the intersection of the COMPUSTAT, CRSP and I/B/E/S databases. Median analysts' earnings forecasts for two years are gathered from the I/B/E/S consensus file released near the end of March to be confident that the actual financial statement information for the prior year (Period 0) has been disclosed.20 Thus, the first (Period 1) I/B/ 16 In most cases, it takes no more than two iterations for the regression model to converge. The regression results are not sensitive to the starting value of r. 17 Accruals are computed using the balance sheet method as in Sloan (1996); i.e., accruals= (Δcurrent assets− Δcash)− (Δcurrent liabilities− Δshort term debt− Δincome taxes payable)–depreciation expense. 18 This paper uses only firms with December fiscal year-ends. Most firms with December fiscal year ends have released their annual financial reports by the end of March. Therefore, forming portfolios at the end of March increases confidence that the empirical tests are conducted with publicly available accounting information. 19 This study focuses on extreme ACC portfolios because the abnormal returns associated with the accrual anomaly are produced by trading strategies that hold firms with low accruals and short firms with high accruals (Sloan, 1996; Xie, 2001; etc.). 20 The empirical test results are robust to using mean analysts' earning forecasts. As in prior studies (Easton, 2004), the current study does not adjust for potential biases in analysts' earning forecasts. Therefore, the test results may be affected by biases in the data.

Notes: 1. ⁎⁎ and ⁎ represent two-tailed t-test significance at the 0.05 and 0.10 level, respectively. 2. Quintiles are in ascending order, with a higher quintile meaning higher accruals. 3. Ret12 refers to cumulative 12 month returns for the ACC quintile portfolio from April, year t to March, year t + 1. 4. SAR12 refers to cumulative 12 month size-adjusted returns for the ACC quintile portfolio from April, year t to March, year t + 1. 5. ACC is prior year total accruals over average total assets. Accruals are computed using the balance sheet method as in Sloan (1996); i.e., accruals= (Δcurrent assets − Δcash)− (Δcurrent liabilities − Δshort term debt − Δincome taxes payable) − depreciation expense.

E/S forecast is the forecast that applies to the year of the consensus file (e.g., consensus file from March and forecast for the same year ending December 31) and the second (Period 2) I/B/E/S forecast is the forecast that applies to the following year. The financial statement items used to estimate ACC and other accounting related variables are retrieved from COMPUSTAT. The sample period is from 1982 to 2004. The sample starts in 1982 because 1982 is the first year in which there is a sufficient number of firms with analyst coverage on I/B/E/S. The sample ends in 2004 because calculation of portfolio returns requires two years of stock return data after each fiscal year ends. As in Easton (2004), firms with non-December fiscal year ends and firms with negative book values are deleted from the sample.21 The final sample has 22,477 firm-year observations. The sample summary statistics are reported in Table 1. The sample firms tend to be larger than average COMPUSTAT firms due to the requirement of I/B/E/S analysts' forecasts. The sample average market value of equity and book value of equity are $3,385 million and $1,123 million, respectively, which are about twice the corresponding averages for COMPUSTAT firms. The mean ACC is −0.03, which is consistent with statistics documented in prior research (Sloan, 1996). Table 2 documents the accrual anomaly by showing the abnormal returns for five accrual level quintiles. The table presents the twelvemonth cumulative equal-weighted returns (Ret) and cumulative equal-weighted size-adjusted returns (SAR) from April of the current year to March of the following year. The SARs are calculated using size decile assignments from CRSP. A hedge strategy that holds the low ACC quintile and shorts the high ACC quintile yields a twelve-month return of 9.6% and a twelve-month SAR of 7.4%. 4.2. Empirical test results Table 3 presents the expected returns (r) and earnings growth rates (g) estimated with the Easton (2004) model. We estimate the portfolio r and g for the extreme ACC quintiles at the end of March when the portfolios are formed (i.e., r0 and g0) and one year after these portfolios are formed (i.e., r1 and g1). The estimated r0 is 11.9% for the portfolio of firms with low accruals and 14.7% for firms with high accruals. These values are consistent with previously documented expected returns in Easton (2004). The estimated g0 values are −20.8% and −0.3% for the low and high accrual portfolios, respectively, and a two-tailed t-test shows that the difference is significant at the five percent level. The negative growth values likely stem from expected future mean reversion in abnormal earnings (the earnings measure in the Easton (2004) model).

21 Only December fiscal year end firms are kept in the sample to ensure that the expected returns and earnings growth rates are estimated at the same time with similar information sets for each portfolio of firms.

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Table 3 Analysis of expected returns and earnings growth rates simultaneously estimated by Easton model.

ACC Q1 ACC Q5 Q1–Q5

r0

r1

Δr

g0

g1

Δg

r0CAPM

r1CAPM

r0FF

r1FF

0.119 0.147 − 0.027⁎⁎

0.124 0.148 − 0.024⁎⁎

0.005 0.001 0.004

− 0.208 − 0.003 − 0.205⁎⁎

− 0.139 − 0.054 − 0.085⁎

0.069⁎ − 0.050⁎ 0.120⁎⁎

0.114 0.118 − 0.003

0.110 0.115 − 0.005

0.134 0.132 0.002

0.133 0.126 0.006

Notes: 1. ⁎⁎ and ⁎ denote two-tailed t-test significance at the 0.05 and 0.10 level, respectively. 2. ACC is prior year total accruals over average total assets. Accruals are computed using the balance sheet method as in Sloan (1996); i.e., accruals= (Δcurrent assets − Δcash)− (Δcurrent liabilities − Δshort term debt− Δincome taxes payable) − depreciation expense. 3. Quintiles are sorted by prior year end ACC in ascending order, with a higher ACC quintile meaning higher accruals. 4. r0 is expected equity return estimated at time of portfolio formation; r1 is expected equity return for the same group of firms estimated one year after portfolio formation; Δr is change in expected equity return for the same portfolio of firms during the year after portfolio formation. 5. g0 is earnings growth rate (i.e., growth rate of abnormal earnings) estimated at time of portfolio formation; g1 is earnings growth rate for the same group of firms estimated one year after portfolio formation; Δg is change in earnings growth rate for the same portfolio of firms over the year following portfolio formation. 6. The subscript CAPM refers to the capital asset pricing model; FF refers to the Fama-French three-factor model.

Some researchers (Fama & French, 1993; Fama & French, 1996; Ng, 2005; Khan, 2008) interpret the abnormal returns associated with market anomalies as compensation for risk. Further, Ng (2005) and Khan (2008) examine firm attributes related to financial distress to infer the risk for firms with extreme ACC. Their arguments suggest that firms with low accruals are more risky and thus should have higher expected returns than firms with high accruals. As shown in Table 2, firms in the low ACC quintile have an average SAR (size-adjusted abnormal return) of 4.6%, much higher than the SAR of −2.7% for firms in the high ACC quintile. However, the pattern of estimated expected returns for the extreme ACC quintiles presented in Table 3 does not support the riskbased explanation for the accrual anomaly. Firms in the low ACC quintile have expected returns of 11.9% and 12.4% at portfolio formation and one year after portfolio formation, respectively. These are lower than the expected returns of 14.7% and 14.8% for firms in the high ACC quintile. The differences in expected returns between the low and high ACC quintiles are significant at the 5% level for both the current year and the following year. To provide more insight on the issue of expected returns, this study estimates expected returns based on the CAPM model (r0CAPM and r1CAPM) and the Fama-French three factor model (Fama & French, 1993) (r0FF and r1FF). The CAPM and Fama-French three factor expected returns are similar for firms in the low and the high ACC quintiles and there is no significant difference in expected returns between the quintiles.22 These alternative measures of expected returns provide little evidence that firms with low ACC have higher expected returns than firms with high ACC. Table 3 also reports the difference between expected returns estimated for the same group of firms at the portfolio formation date and one year after formation (Δr) and the difference between future earnings growth rates estimated for the same group of firms at the portfolio formation date and one year after formation (Δg). The measures Δr and Δg serve as proxies for revisions in investors' expectations of future returns and future earnings growth over the year following portfolio formation. The estimated Δr (Δg) is 0.5% and 0.1% (6.9% and −5.0%) for firms in the low and the high ACC quintiles, respectively. The difference in Δr (Δg) between the low and the high quintiles is not significant (significant at the five percent level). The revisions in investors' expectations follow different patterns for firms with low ACC and for firms with high ACC. For firms with low ACC, there is a slight increase of 0.5% in expected returns and a significant increase of 6.9% in the expected earnings growth rate during the year 22 The Easton measure of expected return is directly estimated by the Easton (2004) model for a portfolio of firms. On the other hand, the CAPM and Fama-French measures of average expected return are the arithmetic means of firm-specific expected returns estimated by the CAPM and Fama-French three factor model, respectively. Since firmspecific measurement errors offset each other when expected return is estimated for a portfolio of firms, we argue that the expected return estimated by the Easton (2004) model directly for the portfolio may be more reliable than the average expected return measures estimated by the CAPM and the Fama-French three factor model.

after portfolio formation. For firms with high ACC, the expected return basically remains the same, while the expected earnings growth rate decreases by 5.0% during the year. These findings are consistent with the errors in investors' perceptions about firm performance explanation for market anomalies (Sloan, 1996; Skinner & Sloan, 2002; Fairfield, et al., 2003a; Cohen & Lys, 2006; Dechow, et al., 2008). The results suggest that investors initially underestimate future earnings growth rates of firms with low ACC and overestimate future earnings growth rates of firms with high ACC. When more information is subsequently revealed on these firms' expected performance, investors reassess the firms' future operating performance and revise their expectations accordingly.23 Eq. (2) (the Campbell model) shows that unexpected returns increase with cash flow news and decrease with return news. In Eq. (5), size-adjusted return SAR is regressed on the change in the expected earnings growth rate Δg (proxy for cash flow news) and the change in expected returns Δr (proxy for return news). The regression model also includes the variable r0 (the portfolio expected return at portfolio formation) to account for differences in risk between high and low accrual firms potentially unaccounted for by the size-adjusted returns. SAR12 = a0 + a1 Δg + a2 Δr + a3 r0 + ε

ð5Þ

Since there are 23 sample years and two extreme ACC portfolios for each year, the regression models are estimated with 46 observations. The results in Table 4, Panel A report that Δg and Δr estimated with the Easton (2004) model are both significantly associated with SAR at the one percent significance level based on two-tailed tests,24 with signs as predicted by the Campbell model (i.e., positive sign for Δg and negative sign for Δr). The regression results confirm the validity of estimated Δg and Δr as proxies for cash flow news and return news. Eqs. (6) and (7) are used to investigate whether the accrual anomaly can be explained by cash flow news and return news. If abnormal returns are functions of cash flow news and return news as suggested by the Campbell (1991) model, the accounting ratio ACC may no longer be a significant factor in explaining unexpected returns in a regression that controls for cash flow news and return news. SAR12 = a0 + a1 Portfolio + a2 r0 + ε SAR12 = a0 + a1 Portfolio + a2 Δg + a3 Δr + a4 Δr0 + ε

ð6Þ ð7Þ

where Portfolio is a dummy variable, equal to 1 for the highest ACC quintile and 0 for the lowest ACC quintile. In Eq. (6), SAR is regressed on Portfolio to examine the association of ACC with size-adjusted abnormal returns. Eq. (7) tests whether ACC has any incremental

23 The results could be at least partially driven by earnings management. Specifically, investors initially mis-estimate earnings growth by over-estimating the persistence of accruals that result from earnings management. 24 All p-values reported in this study are two-tailed.

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Table 4 Regression analysis of accrual anomaly using simultaneously estimated cash flow news and return news. Panel A: Using SAR as dependent variable SAR12 = a0 + a1 Δg + a2 Δr + a3 r0 + ε SAR12 = a0 + a1 Portfolio + a2 r0 + ε SAR12 = a0 + a1 Portfolio + a2 Δg + a3 Δr + a4 Δr0 + ε Model

Intercept

5 6 7

0.009 (0.46) 0.046 (b 0.01) 0.029 (0.11)

Portfolio − 0.019 (b 0.01) − 0.011 (0.13)

Δg

Δr

r0

R2

N

0.362 (b 0.01)

− 1.136 (b0.01)

0.302 (b 0.01)

− 0.965 (b0.01)

0.003 (0.83) 0.008 (0.37) 0.002 (0.92)

0.31 0.19 0.35

46 46 46

Panel B: Using unexpected return as dependent variable UnexpRet12 = a0 + a1 Δg + a2 Δr + ε UnexpRet12 = a0 + a1 Portfolio + ε UnexpRet12 = a0 + a1 Portfolio + a2 Δg + a3 Δr + ε Model

Intercept

8 9 10

0.037 (0.32) 0.099 (0.11) 0.032 (0.56)

Portfolio − 0.031 (0.11) 0.002 (0.90)

Δg

Δr

R2

N

1.197 (b 0.01)

− 4.467 (b 0.01)

1.211 (b 0.01)

− 4.508 (b 0.01)

0.33 0.05 0.33

46 46 46

Notes: 1. SAR12 is portfolio cumulative 12 month size-adjusted return from April of current year to March of next year. 2. UnexpRet 12 is portfolio cumulative 12 month unexpected return from April of current year to March of next year. Unexpected return is portfolio mean raw return minus expected return estimated by the Easton model (r 0 ). 3. ACC is prior year total accruals over average total assets. Accruals are computed using the balance sheet method as in Sloan (1996); i.e., accruals = (Δcurrent assets − Δcash) − (Δcurrent liabilities − Δshort term debt − Δincome taxes payable) − depreciation expense. 4. Portfolio is equal to 0 for the lowest ACC quintile, and 1 for the highest ACC quintile. 5. Δg is change in earnings growth rate from portfolio formation time to one year after portfolio formation. It serves as a proxy for cash flow news. 6. Δr is change in expected equity return from portfolio formation time to one year after portfolio formation. It serves as a proxy for expected return news. 7. r0 is the portfolio expected return at the time of portfolio formation. 8. N is number of observations used in the regression. The regressions analyze the abnormal returns for the top and bottom quintiles. As a result, each year has two observations. 9. Estimated coefficients are listed next to the p-values, which are based on two-tailed tests.

association with abnormal returns after controlling for cash flow news and return news, Δg and Δr. The results in Panel A of Table 4 show that the variable Portfolio is negatively associated with SAR at the one percent level in Eq. (6), indicating that the portfolio of firms with high ACC has lower abnormal returns than the portfolio of firms with low ACC. However, the results from the Eq. (7) regression show that after controlling for earnings news (proxy for cash flow news) and return news, Δg and Δr, the coefficient on Portfolio is negative but no longer statistically significant at conventional levels. On the other hand, the coefficients on Δg and Δr remain significant at the one percent level with signs consistent with the Campbell (1991) model. Therefore, earnings news and return news strongly influence abnormal returns. Of course, measurement error could contribute to insignificance for the level of accruals, as the coefficient on the variable Portfolio has a p-value of 0.13. Nevertheless, it appears that the level of accruals has a weaker influence on future abnormal returns when earnings news and return news are considered. As a robustness test, this study computes an alternative measure of riskadjusted unexpected returns, UnexpRet, by subtracting the ACC quintile expected return estimated by the Easton model (r0) from the mean raw return of the ACC quintile. The regression analysis is repeated using UnexpRet as the dependent variable in the regression models.25 Namely, UnexpRet12 = a0 + a1 Δg + a2 Δr + ε

ð8Þ

UnexpRet12 = a0 + a1 Portfolio + ε

ð9Þ

UnexpRet12 = a0 + a1 Portfolio + a2 Δg + a3 Δr + ε

ð10Þ

25 The variable r0 is not included as an independent variable in Eqs. (8)–(10) because r0 is subtracted in determining the dependent variable, UnexpRet.

The additional regression analysis produces qualitatively similar results. Panel B of Table 4 shows that in an estimation of Eq. (8), the variable Δg (Δr) is positively (negatively) associated with UnexpRet, the proxy for unexpected returns, at a one percent significance level. In regression Eq. (9), the dummy variable Portfolio is negatively related to UnexpRet but is not significant at conventional levels (p-value= 0.11). In regression Eq. (10), when the model controls for earnings news and return news, Δg and Δr, Portfolio shows no relationship with unexpected returns (p-value = 0.90). However, Δg and Δr are still significant at the 1% level. The study also conducts an ANCOVA analysis to assess the comparative roles of cash flow news and return news in determining abnormal returns, controlling for the expected return at the time of portfolio formation. As shown in Table 5, the measure Δg explains a variance of 0.065 in SAR, over one and a half times the variance of 0.041 explained by Δr. The result indicates that earnings news (the proxy for cash flow news) plays a more important role than return news in producing the abnormal returns. The result is consistent with Vuolteenaho (2002), who finds that firm-level stock returns are mainly driven by cash flow news. 5. Sensitivity analyses We also conduct robustness tests to address concerns about potential estimation errors with the Easton (2004) model and the computation of accruals.26 Additionally, we undertake a regression analysis to examine the individual roles that cash flow news and return news play in explaining the accrual anomaly.27 26 27

We thank the anonymous referees for noting the need for these robustness tests. We thank the Associate Editor for suggesting additional tests to examine this issue.

R.Z. Xu, M.J. Lacina / Advances in Accounting, incorporating Advances in International Accounting 25 (2009) 190–199 Table 5 Analysis of the relative effects of cash flow news and return news on unexpected returns SAR12 = a0 + a1 Δg + a2 Δr + a3 r0 + ε. Variables

Variance

SAR Δg Δr r0

0.315 0.065 0.041 0.006

Notes: 1. SAR12 is portfolio cumulative 12 month size-adjusted return from April of the current year to March of the following year. 2. ACC is prior year total accruals over average total assets. Accruals are computed using the balance sheet method as in Sloan (1996); i.e., accruals = (Δcurrent assets − Δcash)− (Δcurrent liabilities − Δshort term debt − Δincome taxes payable) − depreciation expense. 3. Δg serves as proxy for cash flow news and is calculated as change in future earnings growth rate for the same portfolio of firms from portfolio formation date to one year after portfolio formation. 4. Δr serves as proxy for return news and is calculated as change in expected equity return for the same portfolio of firms from portfolio formation date to one year after portfolio formation. 5. r0 is the portfolio expected return at the time of portfolio formation.

5.1. Comparison of analyst earnings forecast errors for high and low accrual firms

197

Table 6 Comparison of analyst earnings forecast errors for firms with high accruals and firms with low accruals.

Raw analyst earnings forecast errors Standardized analyst earnings forecast errors

ACC Q5 ACC Q1 Difference ACC Q5 ACC Q1 Difference

One-year ahead

Two-year ahead

0.358 0.328 0.030 0.271 0.199 0.072

0.809 0.753 0.056 0.527 0.523 0.004

Notes: 1. ACC is prior year total accruals deflated by prior year average total assets. Accruals are computed using the balance sheet method as in Sloan (1996); i.e., accruals = (Δcurrent assets− Δcash)− (Δcurrent liabilities − Δshort term debt− Δincome taxes payable) − depreciation expense. 2. Quintiles are sorted by prior year end ACC in ascending order, with a higher quintile meaning higher accruals. 3. Raw errors in analyst earnings forecasts are forecasted earnings minus actual earnings for the same period reported in IBES. 4. Standardized earnings forecast errors are measured by deflating the raw forecast errors with the absolute value of actual earnings.

low accrual portfolios of firms reduces concerns about estimation errors with the Easton (2004) model. 5.2. Alternative measure of accruals from cash flow statement data

An important input to the Easton (2004) model in computing the expected return and expected earnings growth rate is analyst one- and two-year ahead earnings forecasts. Since the tests in the current study largely involve comparison of expected returns and earnings growth rates derived by the Easton (2004) model for extreme ACC quintiles, it is important to investigate the quality of the analyst earnings forecasts between high and low accrual firms. If there is a systematic difference in the quality of earnings forecasts between firms with high accruals and firms with low accruals, our test results could be a spurious manifestation of the discrepancy in analyst earnings forecast quality.28 We compute the raw errors in analyst earnings forecasts as forecasted earnings minus actual earnings for the same period reported in IBES. To make the forecast errors more comparable across firms of different levels of earnings, we also compute standardized earnings forecast errors by deflating the raw forecast errors with the absolute value of actual earnings. As presented in Table 6, the mean raw (standardized) earnings forecast errors for one-year ahead earnings are 0.358 and 0.328 (0.271 and 0.199) for firms in the high and low accrual quintiles, respectively.29 The positive forecast errors indicate that analysts tend to make over-optimistic earnings forecasts. However, the difference in the means of raw (standardized) forecast errors between high and low accrual portfolios is 0.030 (0.072), which is insignificant at conventional levels. Similarly, the mean raw (standardized) earnings forecast errors for two-year ahead earnings are 0.809 and 0.753 (0.527 and 0.523) for firms in the high and low accrual quintiles, respectively. The difference in the raw (standardized) means of two-year ahead earnings forecast errors between high and low accrual portfolios is also insignificant at conventional levels. The similarity in the analyst forecast errors between high and

28 The cash flow news and return news are estimated as the changes in expected earnings growth rates and expected returns during the one-year period from portfolio formation. As a result, errors in analyst earnings forecasts are expected to largely cancel out when we take the difference in analyst forecast errors for the same portfolio of firms between the beginning and the end of the one-year period. On the other hand, when we compare high accrual firms with low accrual firms, the difference in analyst forecast errors between the two groups of firms may be critical to the analysis. 29 We drop the top and bottom 1% of standardized earnings forecast error observations in calculating the mean standardized earnings forecast errors.

Our empirical tests are conducted using a measure of accruals derived from balance sheet data. Hribar and Collins (2002) find that accruals derived from changes in balance sheet data items are contaminated with measurement errors due to mergers and acquisitions and discontinued operations. The measurement errors could lead to biased results if the measurement errors vary systematically across accrual portfolios. To address the concern, we calculate an alternative measure of accruals using cash flow statement data for the period of 1988–2004. The cash flow based accruals are computed as earnings before extraordinary items and discontinued operations minus operating cash flow from continuing operations as reported on the statement of cash flows. With the new measure of accruals, we sort our sample into quintiles and redo the empirical tests. Untabulated data show that the results are qualitatively similar to those obtained using the balance sheet based accruals. 5.3. Individual roles of cash flow news and return news Table 4 indicates that the variable Portfolio is insignificant when cash flow news (Δg) (proxied by earnings news) and return news (Δr) are included as independent variables. However, Table 3 shows that Δg is significantly lower for the high accrual portfolio than for the low accrual portfolio whereas there is no significant difference in Δr between the two portfolios. Therefore, the Table 3 results indicate that Δg would play a larger part than Δr in eliminating significance in the variable Portfolio and hence helping to explain the accrual anomaly. To verify the roles of Δg and Δr in helping to explain the accrual anomaly, we add these variables to regression Eq. (6) one at a time.30 Recall that the variable Portfolio is significant at the 1% level when neither Δg nor Δr are included as independent variables (see Table 4, Panel A). Untabulated results show that the variable Portfolio becomes marginally significant (p-value= 0.09) when Δg is added to Eq. (6) and that Portfolio remains highly significant (p-value = 0.02) when Δr is added. As before, both Δg and Δr are significant at the one percent level. These tests show that cash flow news plays a major role in explaining the

30 We acknowledge that these regression specifications have only one of the two news variables (cash flow news and return news) in the models, and thus are not consistent with Campbell (1991). Readers may need to exercise caution in interpreting the results from these regressions.

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abnormal returns from the accrual anomaly. On the other hand, much of the association between return news and abnormal returns appears to be unrelated to the accrual anomaly although return news appears to play a small part in explaining abnormal returns stemming from the accrual anomaly. 6. Conclusions This study examines the accrual anomaly using the framework of Campbell (1991). Campbell (1991) illustrates that realized stock returns are the combined effect of expected returns and changes in investors' expectations about future cash flows and future returns. The current study uses the Easton (2004) model to estimate proxies for current expected returns and changes in expectations of both future cash flows (proxied by earnings) and future returns. Empirical results show that firms with high accruals have higher current expected returns than firms with low accruals, which contradicts the inferences in the extant literature that firms with low accruals are riskier. On the other hand, investors seem to be overly pessimistic with the future earnings growth of firms with low accruals and overly optimistic regarding the future earnings growth of firms with high accruals. This suggests that the mis-estimation of earnings growth leads to positive (negative) future abnormal returns for firms with low (high) accruals. Further, a regression analysis indicates that the abnormal returns associated with the accrual anomaly can be explained by cash flow news (proxied by earnings news) and return news, as predicted by the Campbell (1991) model. However, most of the explanatory power associated with the accrual anomaly stems from cash flow news. Additionally, an ANCOVA analysis shows that abnormal returns are driven mainly by cash flows news as opposed to return news. The findings from this research have implications on standard setting. The results suggest that disclosure is needed to help investors better assess firms' future performance in terms of earnings growth. Such information would especially benefit unsophisticated investors, given the findings in prior literature that small individual investors exhibit more biases in utilizing the information in financial reports (Bartov, Radhakrishnan, & Krinsky, 2000; Collins, Gong, & Hribar, 2003). This research documents a method to measure the changes in market expected future returns and future earnings growth for portfolios of firms. Researchers can apply this methodology in studies that require knowledge about investors' perceptions of firms' future prospects. A potential limitation of the study is that analysts' forecasts are used as a proxy for the market's expected future earnings in estimating the Easton (2004) model. To the extent the market expects earnings to differ from analysts' forecasts, the expected returns and expected earnings growth rates from the Easton (2004) model may contain noise. A related potential limitation of this paper is that Easton and Monahan (2005) document that all seven of the proxies for expected returns that they evaluate, including the Easton (2004) model proxy, are not reliably related to ex post realized returns. Easton and Monahan (2005) conclude that low-quality analysts' forecasts are partially responsible. However, we find no significant difference in analysts' earnings forecast errors between our high accrual portfolio and our low accrual portfolio. Moreover, Easton and Monahan (2005) find the expected return based on the Easton model to be associated with commonly recognized risk measures and Botosan and Plumlee (2005) show that expected returns estimated by the Easton model are reliably associated with risk. Further, Botosan and Plumlee (2005, 32– 33) extensively discuss problems with associating realized returns with estimates of expected returns. They comment “…it is not clear if the lack of correlation between the estimates and future realized returns heralds a problem with the estimates, future realized returns, or both.” According to Botosan and Plumlee (2005), Elton (1999) mentions that realized returns are less than risk-free returns for some periods extending ten years or more. Thus, Elton (1999, 1199) argues “realized returns are a very poor measure of expected returns.”

Appendix A. Derivation of stock return decomposition model using accounting earnings Vuolteenaho (2002) and Easton and Monahan (2005) demonstrate that the returns decomposition model can be derived using accounting earnings instead of dividend payments. The derivation starts with two identities. Bi;t + 1 + Di;t + 1 ≡ Bi;t +Ei;t + 1 ðMi;t + 1 + Di;t + 1 Þ = Mi;t ≡1+ Ri;t + 1

ðA1Þ ðA2Þ

The variable Bi,t + 1 represents the book value of equity for firm i at the end of period t + 1, Di,t + 1 is firm i's dividend in period t + 1, Ei,t + 1 is firm i's accounting earnings for period t + 1, Mi,t is the market value of equity at end of period t and Ri,t + 1 is stock return for period t + 1. Transforming the above two identities into new forms, we can get: −1

1≡ð1 + ROEi;t + 1 Þ ½ðBi;t + 1 + Di;t + 1 Þ = Bi;t  " # −1 Mi;t + 1 + Di;t + 1 1≡ð1 + Ri;t + 1 Þ Mi;t

ðA3Þ ðA4Þ

where ROE is earnings over book value of equity (Ei,t + 1/Bi,t). Dividing both sides of Eqs. (A3) and (A4) by Di,t, rearranging and taking logs yields the following: ðbi;t −di;t Þ = InðBi;t Þ−InðDi;t Þ = InðBi;t = Di;t Þ ðA5Þ ≡Inðexpðbi;t + 1 −di;t + 1 Þ + 1Þ + Δdi;t + 1 –roei;t + 1 ðmi;t −di;t Þ = InðMi;t Þ−InðDi;t Þ = InðMi;t = Di;t Þ ≡Inðexpðmi;t + 1 −di;t + 1 Þ + 1Þ + Δdi;t + 1 –ðri;t + 1 + f i;t + 1 Þ ðA6Þ The lower case letters in the above two equations represent natural logs, with m, b, d, Δd, r, f, and roe denoting natural log of market value of equity, book value of equity, dividend, dividend growth, excess of stock return over interest rate, one plus interest rate, and one plus accounting return on equity, respectively. After taking Taylor's expansions of In(exp (bi,t + 1 − di,t + 1) + 1) and In(exp(mi,t + 1 −di,t + 1) + 1) and doing some transformations, we get the following linear approximation of the natural log of the book-to-market ratio: τ−1

ðbi;t −mi;t Þ≈∑ρ

ri;t

τ−1 ðroei;t + τ −fi;t + 1 Þ + τ −∑ρ

ðA7Þ

where ρ is a number between 0 and 1, and is increasing in the price to dividend ratio.31 The Campbell return decomposition model can be obtained by taking the change in the expectations of Eq. (A7) from period t to t + 1: τ−1

τ−1

ri;t +1 ≈Et ½ri;t +1 +ΔEt +1 ½∑ρ ðroei;t + τ −fi;t +1 Þ−ΔEt +1 ½∑ρ = Et ½ri;t + 1  + cni;t + 1 −rni;t + 1

ri;t +τ  ðA8Þ

where Et[ ] denotes the expectation, ΔEt + 1 is equal to Et + 1[ ] − Et[ ], and cni,t + 1 and rni,t + 1 denote the cash flow news and return news, respectively. Appendix B. Derivation of Easton (2004) model The Easton (2004) model is derived from the Ohlson and Juettner-Nauroth (2005) model. The Ohlson and Juettner-Nauroth model specifies stock price as the capitalized one period ahead

31 Prior studies (Vuolteenaho, 2002; Easton & Monahan, 2005) estimate ρ to be a number slightly less than 1.

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earnings plus the stream of capitalized abnormal earnings beyond year one: P0;j =

eps1;j agr1;j + rj rj ðrj −Δagrj Þ

ðB1Þ

where eps1 r agr1

Δagr j

Expected earnings for the following year (Year 1); Expected equity return; eps2 + r ⁎ dps1 − (1 + r) ⁎ eps1, which is cum-dividend earnings (eps2 + r ⁎ dps1) minus normal accounting earnings ((1 + r) ⁎ eps1) for Year 2. It is regarded as expected abnormal growth in accounting earnings for Year 2. agrt + 1/agrt − 1, which is the perpetual growth rate of agr; and Firm j.

To estimate r and Δagr, Eq. (B1) is reorganized as: ceps2;j = P0;j = γ0 + γ1 ðeps1;j = P0;j Þ

ðB2Þ

where ceps2,j = eps2,j + r⁎dps1,j, γ0 = r(r − Δagrj), and γ1 = Δagrj + 1. The two unknowns in Eq. (2), γ0 and γ1, can be solved for with a linear regression of ceps2,j/P0,j on eps1,j/P0,j for a portfolio of firms. The regression equation based on Eq. (B2) is: ceps2;j = P0;j = γ0 + γ1 ðeps1;j = P0;j Þ + ε0;j

ðB3Þ

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