A Reassessment of the Evidence that Accruals Quality is a Priced. Risk Factor

Transcription

1 A Reassessment of the Evidence that Accruals Quality is a Priced Risk Factor Kai Du June 2011 Abstract Without a theoretical consensus on how information risk a ects expected returns, the twopass methodology widely used to test whether accruals quality (AQ) is a priced risk factor can easily misinterpret mispricing of AQ as evidence of risk. Building on a simple model of asset pricing tests, I predict and con rm that the AQ factor premium estimated from a misspeci ed two-pass test is mechanically dependent on the correlation between AQ and AQ factor loading. As a result, existing evidence that AQ factor is priced is in fact driven by the mispricing of AQ characteristic. Consistent with the cross-sectional behavior of mispricing, the return regularity on AQ is stronger for rms with greater information uncertainty and imperfect investor competition. In addition, managers seem to strategically exploit market misvaluation by reporting more one-time items when rms with more volatile discretionary accruals earn a higher premium. Yale University School of Management. kai.du@yale.edu. This paper is partially based on my rst year paper advised by Jacob Thomas. I thank an anonymous reviewer, James Choi, Roger Ibbotson, Dasol Kim, Kalin Kolev, Dong Lou, Shyam Sunder, Frank Zhang, workshop participants at Yale SOM, and especially Jacob Thomas, for valuable discussions and comments. All errors are mine.

2 A Reassessment of the Evidence that Accruals Quality is a Priced Risk Factor 1 Introduction The relationship between information risk and asset prices is a subject of both theoretical and empirical interests. Even though theorists have yet to reach a consensus on whether and how information a ects expected returns (e.g., Easley and O Hara 2004; Lambert et al. 2007; Hughes et al. 2007), empirical studies have proposed various proxies of information risk 1 and examined their capital market consequences. One of the proxies is nancial reporting quality, and in particular accruals quality. An emerging literature studies whether accruals quality (AQ) constitutes a form of priced information risk (e.g., Francis et al. 2005; Core et al. 2009). Recent advances in this literature nd that the AQ factor is associated with signi cant premium in a two-pass asset pricing test, and conclude that AQ is a priced risk factor (e.g., Kim and Qi 2010; Ogneva 2010). However, without a well-articulated theory of how accruals quality a ects expected returns, results from a standard asset pricing test are susceptible to misinterpretation. Essentially, the pricing of accruals quality represents a form of return predictability based on AQ, 2 and any return predictability could be due to risk or mispricing (Daniel, Hirshleifer, and Subrahmanyam 2001). Therefore, an appropriate interpretation of asset pricing tests has to distinguish between pricing of covariance risk and mispricing of characteristics. Daniel and Titman 1997 propose the characteristic versus covariance test to check whether factor loading has explanatory power incremental to the corresponding characteristic. However, the power of the characteristic versus covariance test is hard to quantify, and it does not o er crosssectional or time-series predictions. A more powerful test would be based on the properties 1 Popular proxies include the probability of information-based trading (PIN) (e.g., Easley et al. 2002; Mohanram and Rajgopal 2009; Duarte and Young 2009), bid-ask spreads (e.g., Huang and Stoll 1997; Armstrong et al. 2011), return synchronicity (e.g., Morck et al. 2000; Durnev et al. 2003), and earnings quality (see Francis et al. (2008) for a review). 2 AQ is typically measured as of scal year end, and is linked to monthly returns of the 12-month period starting from the four month after the scal year end. Therefore, any nding of pricing is also a form of return predictability based on AQ. 1

3 of the factor premium estimated from a potentially misspeci ed pricing test. In this paper, I introduce a simple model of misspeci ed asset pricing tests, in which the return-generating process is characterized by the mispricing of accruals quality, but an econometrician believes in the pricing of AQ factor. The econometrician unsuspectingly estimates a factor model augmented by an AQ factor using the two-pass methodology, and obtains an estimate of the risk premium on AQ factor. I show that such estimate is mechanically dependent on the correlation between AQ and AQ factor loading. When such correlation is high which is often the case due to the way AQ factor is constructed the econometrician is likely to misinterpret the mispricing of AQ characteristic as risk. On the other hand, if the return-generating process is indeed determined by the risk factor model used by the econometrician, the estimate of AQ factor premium should not vary with the correlation between AQ characteristic and factor loading. Based on di erent properties of AQ factor premium estimated under the two competing hypotheses, this model prescribes a test to disentangle between risk and mispricing e ects. Consistent with the mispricing hypothesis, I nd that AQ factor premium is more signi cant in periods when AQ is highly correlated with AQ factor loading. On average, a 0.01 increase in the correlation between AQ and AQ factor loading in ates the t-statistic of AQ factor premium by This nding quanti es the severity of the misinterpretation problem that can plague any asset pricing test on accruals quality. Researchers unaware of the misspeci- cation issue of underlying asset pricing models are prone to recognizing accruals quality as a risk factor when in fact it is a rami cation of mispricing. I also provide collaborative evidence of mispricing by studying the cross-sectional behavior of the return predictability based on AQ. If a return predictability represents investor misvaluation as a result of ine cient processing of information or cognitive biases, it should be stronger when there are considerable impediments to corrective trades. In particular, behavioral asset pricing research suggests that an important determinant of the magnitude of misvaluation is information environment (e.g., Hirshleifer 2001; Zhang 2006). In contrast, there is no risk-based theory to justify a role of information environment in the pricing of covariance risk. Tests based on portfolios sorted on AQ and information environment proxies indicate that the return regularity on AQ is stronger in the presence of great information uncertainty and imperfect investor competition. This is consistent with the cross-sectional 2

4 behavior of of mispricing. Unlike other mispriced characteristics such as past returns (e.g., Jegadeesh and Titman 2001) and fundamental/price ratios (e.g., Daniel, Hirshleifer, and Subrahmanyam 2001), accruals quality re ects the discretion of corporate managers, who are incentivized by shortterm equity price, or want to raise more funds by issuing equity. If the market irrationally attaches a return or market-to-book premium to low quality of accruals (as evidenced by the positive premium), managers may want to exploit such irrationality by timing the market. In particular, they may want to engage in more discretionary reporting at times when the reward to such activities is large. This paper provides preliminary evidence of this prediction. Managers seem to report more one-time items when rms with more volatile discretionary accruals earn a higher return premium or market-to-book premium. Finally, the mispricing of accruals quality may not be separate from other forms of mispricing. In fact, there is suggestive evidence that the mispricing of accruals quality might be related to the accruals anomaly, and that the accruals quality factor might re ect a more general market sentiment. The rest of the paper is organized as follows. Section 2 reviews the literature, introduces a simple model of misspeci ed asset pricing tests, and develops testable predictions. Section 3 describes the measurement of main variables and the sample. Section 4 replicates asset pricing tests of previous studies, and shows that the results are in fact driven by mispricing, through the characteristic versus covariance test and a test motivated by the model. Section 5 discusses the role of information environment on the mispricing of accruals quality. Section 6 discusses managerial opportunism in nancial reporting to exploit the mispricing of accruals quality. Section 7 conducts robustness tests and explores the links between the mispricing of accruals quality and other forms of mispricing. Section 8 concludes. 2 Prior literature, motivating model, and predictions 2.1 Prior literature This study is related to three lines of research: studies on the pricing of accruals quality; the information risk literature; and the accruals anomaly literature. 3

5 First, this study joins the ongoing discussion of whether accruals quality is a priced risk factor. Researchers disagree on the appropriate methods as well as the interpretation of results. The concept of accruals quality is popularized by Francis et al. (2005), who nd signi cant loading of rm returns on an AQ factor and conclude that AQ is priced. However, Core, Guay, and Verdi (2008) point out that the test of Francis et al. does not address whether AQ factor is priced. Based on a two-pass asset pricing test, Core et al. nd an insigni cant premium on AQ factor, and conclude that there is no evidence that AQ is priced. Also using the two-pass methodology, several recent studies nevertheless nd the AQ factor is priced. In particular, Kim and Qi (2010) nd that after excluding low-priced stocks, AQ factor is signi cantly priced; Ogneva (2010) nds that after controlling for cash ow shocks, AQ factor is signi cantly priced. In addition, with di erent research questions, Aboody et al. (2005) provide weak evidence that the earnings quality factor is priced; Kravet and Shevlin (2010) nd that after restatement announcements, rms cost of capital increase as their factor loadings on a discretionary information risk factor increases. Even though researchers agree that a signi cant premium in a two-pass test is a not a su cent condition for pricing (e.g., Core et al. 2008; Ogneva 2010), those who indeed nd a signi cant premium have not proceeded to conduct a formal risk versus mispricing test (e.g., Kim and Qi 2010; Ogneva 2010). This paper takes a further step to examine whether the signi cant premium found in some studies are indeed evidence of risk pricing. Second, this study can be contextualized in the broad literature on information risk. The relation between accruals quality and asset prices is pivotal to understanding the role of accounting information in capital markets. Any nding of the market pricing of accruals quality could be alluded to information risk, which has long been the subject of both theoretical (e.g., Easley and O Hara 2004; Lambert et al. 2007; Hughes et al. 2007) and empirical interests (e.g., Easley et al. 2002). Theoretical studies of information risk is far from reaching a consensus. Easley and O Hara (2004) argue that investors demand a premium to hold stocks with greater private information, and rms can in uence their cost of capital by choosing features of information environment such as accounting treatments. However, Lambert et al. (2007) show that the information risk modeled by Easley and O Hara (2004) can be diversi ed away in the presence of a large number of investors. Earnings quality can reduce cost of capital, they argue, but only through its association with a lower beta. 4

6 Hughes et al. (2007) show that for large economies, private information about systematic factors a ects (market-wide) factor risk premiums, but has no e ect on rm betas. More recent studies examine the relationship between information quality and cost of capital in a multi- rm setting (e.g., Armstrong et al. 2009; Gao and Verrecchia 2011). Despite the lack of theoretical consensus, empirical studies have suggested a number of information risk measures. Several studies explicitly use earnings quality as a proxy for information risk (see Francis et al. (2008) for a review). Other studies use market microstructure based proxies such as probability of information-based trading (PIN) (e.g., Easley et al. 2002; Mohanram and Rajgopal 2009; Duarte and Young 2009), bid-ask spreads (e.g., Huang and Stoll 1997; Armstrong et al. 2011), return synchronicity (e.g., Morck et al. 2000; Durnev et al. 2003). The ndings on the relationship between information and asset prices are divided on whether and how information a ects expected returns. In particular, Easley et al. (2002) nd that PIN a ects asset prices incremental to Fama-French factors; Mohanram and Rajgopal (2009) show that the results of Easley et al. (2002) are not robust to alternative speci cations and time periods; Duarte and Young (2009) show that PIN a ects expected returns not because of information asymmetry but because of other liquidity e ects; Armstrong et al. (2011) nd that information asymmetry a ects cost of capital only when markets are not perfectly competitive. In general, the current state of this line of research suggests that information does not a ect expected returns in a way similar to standard risk factors. Third, by examining the nature of the return predictability associated with accruals quality (the standard deviation of discretionary accruals), this study also relates to research on the accruals anomaly (return predictability on the level of total accruals). Whether accruals anomaly is due to risk or mispricing is an issue of controversy. While some studies dissect the accruals anomaly from risk-based perspectives (e.g., Kahn 2008; Wu et al. 2008), others show that it is in fact driven by mispricing (e.g., Hirshleifer et al. 2010). In particular, Kahn (2008) nd that a four-factor model with cash ow news and discount rate news factors explains most of the cross-section variations in expected returns. Interpreting accruals as working capital investment, Wu et al. (2008) provide evidence that capital investment is an important driver of the accrual anomaly. Hirshleifer et al. (2010) cast doubt on the rational risk explanation of accruals anomaly and provide evidence that investors misvalue 5

7 the accruals characteristic. Indeed, separating risk from mispricing has also been a central issue for other accounting-based anomalies (e.g., Bernard and Thomas 1989; see Richardson et al. (2010) for a review of recent research). 2.2 A simple model of misspeci ed asset pricing tests The two-pass methodology developed by Black et al. (1972) and Fama and MacBeth (1973) has been used in recent studies to test the market pricing of accruals quality (e.g., Core et al. 2009; Kim and Qi 2010; Ogneva 2010) and market microstructure-based proxies for information risk (e.g., Mohanram and Rajgopal 2009; Duarte and Young 2009). A twopass asset pricing test of AQ is implemented in two steps. In the rst step, factor loadings are estimated in a time series regression for each testing portfolio, using a standard factor model augmented by an accruals quality factor (AQF). In the second step, factor loadings are used to estimate factor premia in cross-sectional regressions for each date, R i Rf = b i;f + 2 b i;aqf + " i (2.1) where b i;f d i;f is the vector of estimated loadings on standard risk factors; b i;aqf \ i;aqf is the estimated loading on AQF for portfolio i. In most studies, researchers use the Fama- French (1993) three factors as standard risk factors, i.e., b i;f = [b i;mkt ; b i;smb ; b i;hml ; ] 0, or further include momentum and liquidity factors. A signi cant premium on AQF (c 2 ) indicates that AQ factor is a priced risk factor. Even though the two-pass methodology is standard in asset pricing tests, it is also known to lead to spurious inferences (e.g., Daniel and Titman 1997; Kan and Zhang 1999; Lewellen et al. 2010). In particular, Daniel and Titman (1997) argue that a two-pass test is unable to distinguish between risk factor and characteristic models due to a multicollinearity problem. Kan and Zhang (1999) argue that a two-pass test tend to over-reject the null when a useless, purely noisy factor is included. Lewellen et al. (2010) show that seemingly strong explanatory power of asset pricing models can be misleading. Indeed, without a well-articulated theory of the proposed factor structure, nding signi cant premium alone is unlikely to justify a risk-based explanation. This concern is particularly relevant in the case of accruals quality. In the following, I illustrate why an econometrician having the wrong prior could accept 6

8 AQF as a priced risk factor when in fact AQF captures mispricing. Suppose stock returns are generated by the following the H-Mispriced Characteristic model, or H-Characteristic, R it = i + i;f F t + " it (H-Mispriced Characteristic) where i, the expected return for for rm i, is determined by i = i;f +AQ i, where AQ i is the mean accruals quality characteristic that has no bearing on covariance risk; F t is the vector of priced risk factors, and i;f is rm i s loading on F t ; " it is an i. i. d. error. For algebraic simplicity, in the following discussion F t is assumed to be a univariate factor; the insights are similar for a multivariate F t. This model entertains the possibility that expected returns are determined by both risk and misvaluation (e.g., Hirshleifer 2001). Speci cally, the AQ i component of expected return re ects the mispricing of accruals quality. 3 However, an econometrician believes in an alternative model, the H-Risk Factor model, or H-Risk, R it = i + i;f F t + i;aqf AQF t + " it (H-Risk Factor) where the expected return i is determined by i = i;f + 2 i;aqf, where AQF t is the accruals quality factor constructed based on AQ (the details on how AQF is constructed will be described in Section 3). In the rst pass of an asset pricing test designed to test H-Risk, the econometrician estimate i;aqf by regressing excess returns on F t and AQF t. Let us assume that b i;aqf is positively correlated with AQ in the cross-section, corr(aq; b AQF ) > 0 (2.2) This assumption is motivated by the observation that rms with similar AQ are likely to be mispriced at the same time, which induces a relationship between the factor structure and AQ characteristic. This is also con rmed in the data: Panel B of Table 1 shows that b AQF monotonically increases from the lowest AQ decile to for the highest AQ decile; in addition, Ecker et al. (2006) report that the loading on the AQ factor is correlated with drivers of earnings quality. We can show that in the second-pass, the risk premium on AQF 3 The assumption that AQ is the only mispriced characteristic is for presentational simplicity. In reality, other characteristics such as size, B/M may also play a role in determining expected returns. 7

9 is given by the following proposition. Proposition 1. In the second-pass cross-sectional regression, the econometrician would get an OLS estimate of c 2 which is characterized by the following property, plim c 2 = ( 1 + F ) s var(aqf ) cov(f; AQF ) + var(aq) var(b AQF ) corr(aq; b AQF ) (2.3) Proof: See Appendix. Because ( 1 + F ) var(aqf ) cov(f;aqf ) only depends on the statistical properties of factors F t and AQF t, equation (2.3) shows that c 2 is almost linearly dependent on the correlation between b i;aqf and AQ. In contrast, if H-Risk is the true data-generating process, i.e., AQ is a priced risk factor, the same econometrician would get an unbiased estimate of the true 2. 4 This model motivates a new test of mispricing versus risk. While the characteristic versus covariance test developed by Daniel and Titman (1997) primarily relies on detecting patterns in portfolio returns or intercepts from the rst-pass time-series regressions, equation (2.3) predicts a quantitative, testable relationship based on the second-pass cross-sectional regression results. 2.3 Disentangling competing hypotheses It is now clear that nding a signi cant risk premium on AQF is not a su cient condition for AQF to be a priced risk factor. To disentangle between the risk factor model and the mispriced characteristic model, I will conduct the following tests. 4 It is also possible that the true data-generating process is a more generalized, mixed model in the form of R it = i + i;f F t + i;aqf AQF t + " it (H-Mixed) where i = i;f + 2 i;aqf + AQ i, i.e., expected returns re ect both covariance risk and misperceptions of rms prospects based on AQ. This scenario has theoretical underpinnings suggested by Hirshleifer (2001) and Daniel, Hirshleifer, and Subrahmanyam (2001). Of course, H-Mixed is only a linearly separable form of many possibilities of how risk and mispricing coexist. If H-Mixed is true, the econometrician, still having the conviction that H-Risk is true, will get an in ated estimate of 2, s plim c 2 = 2 + ( 1 + F var(aqf ) ) cov(f; AQF ) + var(aq) var(b AQF ) corr(aq; b AQF ) In this case, c 2 is still related to corr(aq; b AQF ), and again the econometrician will likely accept H-Risk. 8

10 2.3.1 Characteristics versus covariances test To separate the e ects of characteristic mispricing from risk pricing, Daniel and Titman (1997) examine whether factor loading still has a discernible e ect on average returns after controlling for characteristics. This test is known as the characteristics versus covariances test, and has been used to distinguish between risk and mispricing explanations of size and value e ects (Davis et al. 2000; Daniel, Titman and Wei 2001), momentum strategy (Grundy and Martin 2001), and the accruals anomaly (Hirshleifer et al. 2010). This test involves forming two sets of testing portfolios: (i) Characteristic-balanced portfolios with similar characteristics but signi cantly di erent loadings; (ii) factor-balanced portfolios with similar factor loadings but signi cantly di erent characteristics. If H-Characteristic (H-Factor) is the correct model, the expected return of any characteristic-balanced (factor-balanced) portfolio should be zero Is AQF premium attributable to corr(aq; b AQF )? The drawback of the characteristics versus covariances test is that it relies primarily on detecting patterns in portfolio returns or intercepts, and does not o er cross-sectional or time-series predictions. A more powerful test could be developed based on the the properties of the factor premium estimated from a potentially misspeci ed pricing test, which is characterized by equation (2.3), plim c 2 = ( 1 + F ) var(aqf ) cov(f;aqf ) + q var(aq) var(b AQF ) corr(aq; b AQF ). This equation stipulates that if H-Characteristic is the true underlying model, c 2 should be linearly dependent on corr(aq; b AQF ). Instead, if H-Risk is true, c 2 should be unrelated to corr(aq; b AQF ). To test this prediction, I compare the time series of c 2 generated in monthly cross-sectional regressions with the time series of corr(aq; b AQF ), the cross-sectional correlation calculated for each month. If there is signi cant association between c 2 and corr(aq; b AQF ), it would be imperative to conclude that the signi cant risk premium estimate c 2 is driven by the correlation between the mispriced characteristic and factor loading. 9

11 2.3.3 The role of information environment Whether the magnitude of the return predictability based on AQ varies with features of information environment could shed light on the nature of such regularity. If the return predictability on AQ re ects risk, higher expected returns on lower accruals quality rms represent a fair compensation for the covariance risk, and such regularity would persist regardless of information environment. On the other hand, if such return predictability is due to mispricing, the abnormal returns earned on a hedge portfolio would be most pronounced in an opaque information environment, and insigni cant in a transparent information environment. This is because an opaque information environment ampli es the mispricing e ects of any mistaken-belief model by interacting with cognitive biases and posing considerable impediments to arbitrage and corrective trades (e.g., Hirshleifer 2001). In contrast, a transparent information environment facilitates the dissemination and impounding of accounting information into stock price, making it di cult for informationally advantaged investors to utilize their private information and make a pro t on accounting-based anomalies. Empirical studies con rm that several forms of return predictability not explained by standard risk factors are ampli ed in less transparent information environment. For examples, Zhang (2006) documents stronger stock price continuations such as underreaction to analyst forecast revision and the momentum e ect when information uncertainty is greater; Baker and Wurgler (2006) show that investor sentiment has larger e ects on assets whose valuations are highly subjective and di cult to arbitrage; Armstrong et al. (2011) show that information asymmetry has a positive relation with rms cost of capital in excess to standard risk factors only when market (investor) competition is imperfect. Based on this line of arguments, I hypothesize that if H-Characteristic is true, there should be considerable variations in the magnitude of mispricing across di erent levels of information uncertainty and investor competition. In particular, the return predictability based on accruals quality should be stronger when information uncertainty is high, and when investor competition is low. This is because both high information uncertainty and low investor competition contribute to the opacity of the information environment, which exacerbates misvaluation. On the other hand, if H-Risk is true, the return predictability on 10

12 AQ should not vary with proxies of information environment. The following table summarizes the predictions and provides an outline of the results. Hypothesis/ Predictions H-Risk: AQ is a priced risk factor. H-Characteristic: AQ is a mispriced characteristic. Table 3A; Fig 1A Portfolio returns increase with b AQF. There is no signi cant relation between b AQF and portfolio returns after controlling for AQ. Table 3B; Fig 1B Table 3C A factor model augmented with AQF should capture all variations in returns; i.e., regression intercepts should be jointly zero. The intercepts from a factor model augmented by AQF should be zero for characteristic-balanced portfolios. The intercepts from a AQF-augmented factor model should decrease with b AQF. The intercepts from a factor model augmented by AQF should be negative for characteristic-balanced portfolios. Table 4 When both AQ and b AQF are included in a cross-sectional regression, the power of b AQF should not be subsumed by AQ. Table 5; Fig 2 Risk premium on AQF from a two-pass test should not vary with corr(aq; b AQF ). When both AQ and b AQF are included in a cross-sectional regression, the power of b AQF should be subsumed by AQ. Risk premium on AQF from a two-pass test should increase with corr(aq; b AQF ). Table 6 Table 7 The predicting power of AQ does not vary with information uncertainty. The predicting power of AQ does not vary with investor competition. The predicting power of AQ increases with information uncertainty. The predicting power of AQ decreases with investor competition. 3 Measurement and sample 3.1 Accruals quality Following Francis et al. (2005) and subsequent studies, I measure accruals quality as the standard deviation of rm level residuals from McNichols (2002) modi cation of the Dechow 11

13 and Dichev (2002) model, T CA j;t = 0;j + 1;j CF O j;t 1 + 2;j CF O j;t + 3;j CF O j;t+1 + 4;j Rev j;t + 5;j P P E j;t + j;t (3.1) where, T CA j;t = CA j;t CL j;t Cash j;t + ST DEBT j;t is the total current accruals for rm j in year t, CF O j;t = NIBE j;t T A j;t is the cash ow from operations, NIBE j;t is the net income before extraordinary items (Compustat item IB), T A j;t = T CA j;t DEP N j;t is the total accruals, CA j;t is the change in current assets (ACT), CL j;t is the change in current liabilities (LCT), Cash j;t is the change in cash (CHE), ST DEBT j;t is the change in short-term debt (DLC), DEP N j;t is depreciation and amortization expense (DP), Rev j;t is the change in revenue (SALE), P P E j;t is the gross value of property, plant, and equipment (PPEGT). All variables are scaled by average total assets (AT). Equation (3.1) is estimated in the cross-section of each of 48 Fama-French (1997) industries for each scal year, requiring at least 20 rms. Accruals quality for rm j in year t is the standard deviation of rm level residuals over the ve-year period from t 4 to t, AQ j;t = ( j ) t, requiring at least three years of data. AQ captures the quality of mapping between accruals and economic fundamentals, and therefore re ects the excessive discretion or aggressiveness in nancial reporting. A higher AQ indicates a lower quality of accruals. For each rm-year, AQ, size (market value of equity), and B/M (book value of equity/market value of equity) are measured as of the scal year end, and matched to 12 consecutive monthly returns starting with the fourth month after scal year end, when - nancial information has already been disseminated through earnings announcements and SEC lings. 3.2 The accruals quality factor Consistent with prior studies (e.g., Core et al. 2008), I construct AQ factor mimicking portfolio as a zero-investment hedge portfolio based on AQ. In particular, at the beginning of each month, rms are ranked into ve quintiles based on AQ. Firm returns in each quintile are then equal-weighted to get a quintile return. The AQ factor mimicking portfolio buys the top two AQ quintiles and sells the bottom two AQ quintiles, with equal weights on quintiles. This portfolio is meant to mimic the risk factor related to accruals quality. The returns to 12

14 the AQ factor mimicking portfolio is called the AQ factor (AQF), to be distinguished from AQ. Panel A of Table 1 presents the mean returns and correlations of AQF, the Fama-French (1993) three factors (MKTRF, SMB, and HML), the momentum factor (UMD), and the Pastor and Stambaugh (2003) liquidity factor (LIQ), based on monthly factor returns from 1975 to The mean monthly return of AQF is 0.14% and the mean monthly returns of MKTRF, SMB, HML, UMD, and LIQ are 0.62%, 0.33%, 0.38%, 0.65%, and 0.56%, respectively. AQF is positively correlated with MKTRF and SMB, and is negatively correlated with HML and LIQ (by Spearman correlation). Panel A of Figure 3 plots the annual average returns of AQF and the long and short portfolios based on which AQF is formed. The pro le of factor returns is generally in accordance with Core et al. (2009) and Kim and Qi (2010). Even though the high correlation between AQF and SMB (0.619) implies a multicollinearity problem, such concern is mitigated by the large panel of data used in asset pricing tests, especially when individual rms are used as testing portfolios. Nevertheless, as a robustness check, I also construct an alternative AQF by controlling for size, and show that the results are qualitatively the same. 3.3 Sample and descriptive statistics The sample starts from all rms with available data on Compustat annual tape and CRSP. To be included in the sample, a rm is required to have at least seven years of accounting data. AQ is estimated for 142,800 rm-year observations with scal year ending between 1975 and While analyst forecast data from I/B/E/S and institutional holding data from CDA/Spectrum are also used in certain tests, requirements of data availability on these datasets are not imposed on the main sample. Panel B of Table 1 presents the descriptive statistics of sample rms, grouped into ten deciles based on AQ. AQ measure ranges from to across the ten AQ deciles, exhibiting substantial variation. AQ is negatively correlated with rm size, age, and profitability (ROA, EPS) measures. For example, rms in the lowest AQ decile have 23.7 years of history on CRSP, more than twice as long as rms in the highest AQ decile (10.1 years). The inverse of analyst coverage (1/COV), volatility of cash ow (CFVOL), and stock volatility (SIGMA) increase with AQ, indicating that information uncertainty is greater for rms with 13

15 high AQ (low quality). The probability of informed trading (PIN) is also higher for high AQ rms. Firms that are excluded because there is insu cient data to estimate AQ (decile NA) tend to be smaller and younger than overall average, with a mean size comparable to that of the eighth AQ decile. 4 Asset pricing tests 4.1 Two-pass asset pricing test In this section I conduct a two-pass asset pricing test using factor models augmented with the accruals quality factor (AQF). Take, for example, the Fama-French (1993) three-factor model augmented with AQF. In the rst stage, I estimate factor loadings from a time-series regression for each testing portfolio, which could be an individual rm, one of the 25 size- B/M portfolios, one of the 100 AQ portfolios, or one of the 64 size-b/m-aq portfolios. In the second stage, estimated factor loadings (betas) are used as independent variables in the following cross-sectional regression for each month, R i;t R f;t = b i;mkt + 2 b i;smb + 3 b i;hml + 4 b i;aqf + " i;t (4.1) A necessary condition for AQF to be a priced risk factor is a signi cant coe cient on b AQF. If AQF is indeed a risk factor, the estimated coe cient can be interpreted as the risk premium associated with AQF. However, if it is mispricing that drives the results, a signi cant coe cient represents no more than the return predictability due to misvaluation. Table 2 reports the time-series means and Fama-MacBeth (1973) t-statistics for the coe cients of the second pass cross-sectional regressions using individual rms as testing portfolios. 5 I choose individual rms as the main set of testing portfolios, because portfolios based on characteristic sorts could exacerbate the characteristic versus covariance concern (Daniel and Titman 1997). Five models are tested: the CAPM augmented with AQF, the Fama-French three-factor model (FF3), the Fama-French three-factor model augmented 5 An alternative method of conducting the second pass is through a single cross-sectional regression of mean excess returns, as in Core et al. (2009). Because the independent variables do not vary over time, the Fama- MacBeth procedure is equivalent to a single cross-sectional regression on time-series averages with standard errors corrected for cross-sectional correlation (Cochrane 2001). 14

16 with AQF (FF3+AQF), the Fama-French three-factor model augmented with UMD and AQF (FF4+AQF), the Fama-French three-factor model augmented with UMD, LIQ and AQF (FF5+AQF). The main objective is to test whether AQF carries a signi cant premium. Panel A presents results based on the full sample. The coe cient on b AQF is insigni cant in all four models with AQF. In all ve models, the risk premium on market beta (b MKT ) is positive and signi cant; the coe cient on b SMB is positive and signi cant in a six-factor model that includes UMD, LIQ, and AQF. The results are similar to those of prior studies, such as Core et al. (2009) and Kim and Qi (2010). I also conduct asset pricing tests based on a restricted sample after excluding all lowpriced stock returns (de ned as returns with two adjacent prices less than $5), whose realized returns may be noisy. The results are reported in Panel B. The coe cient on b AQF becomes signi cant in all speci cations on the restricted sample. For example, in a six-factor model with UMD, LIQ, and AQF (FF5+AQF), the AQF premium is 0.33% (t=2.15). The choice of testing portfolio can be crucial for inducing variations in returns and alleviating the errors-in-variable problem. Therefore, I also conduct two-pass tests on three alternative sets of testing portfolios: (i) 25 size-b/m portfolios; (ii) 100 AQ portfolios; and (iii) 64 size-b/m-aq portfolios. To get the 25 size-b/m portfolios, at the beginning of each month, I sort rms into ve size quintiles and (independently) ve B/M quintiles, and take the intersections as the 25 portfolios. To the get 100 AQ portfolios, at the beginning of each month, I sort rms into 100 AQ percentile groups. To get the 64 size-b/m-aq portfolios, at the beginning of each month, I sort rms into four size, four B/M, and four AQ quartiles, and take the intersections as 64 portfolios. Portfolio returns are monthly value-weighted returns. The results for the three sets of alternative testing portfolios are reported in Table A.1. There is evidence of signi cant positive AQF premium for the 25 size-b/m testing portfolios and the 64 size-b/m-aq portfolios, but not the 100 AQ portfolios. Results on the restricted sample are generally stronger. This is consistent with the ndings of Kim and Qi (2010). While prior studies interpret a signi cant premium as evidence that AQF is a priced risk factor (e.g., Kim and Qi 2010; Ogneva 2010), such results are also consistent with the mispricing of AQ. Because AQ is measured at the previous scal year end, which is at least four months earlier than stock returns, the mispricing of AQ could be a result of investor underreaction to new information contained in AQ. In order to disentangle between H-Risk 15

17 and H-Characteristic, I conduct the characteristic versus covariance test and a test motivated by the simple model. 4.2 Characteristic versus covariance test Portfolio tests Characteristic versus covariance tests are conducted by portfolio sorts and cross-sectional regressions. The rst portfolio test involves portfolios sorted by size, AQ and the loading on the AQ factor, or b AQF. To obtain b AQF for sorting purpose (to be distinguished from the whole-period b AQF used in the asset pricing test), for each rm-month, the FF3+AQF four-factor model is estimated over a rolling window from month -60 to month -1 relative to the portfolio formation date, requiring a minimum of 24 months. The mean b AQF for each AQ decile is reported in Panel B of Table 1. There is a high positive correlation between AQ and b AQF, which justi es e orts to distinguish characteristic e ects from factor loading e ects. For each month, rms are sorted into three size tertiles and three AQ tertiles independently. Within each of the nine size-aq intersections, rms are sorted into b AQF quintiles. If H-Risk is true, the portfolio returns should increase with b AQF ; in contrast, if H-Characteristic is true, the portfolio returns should not exhibit any pattern with b AQF. The mean excess returns of 45 size-aq-b AQF portfolios are reported in Panel A of Table 3 and Panel A of Figure 1. The results reveal no positive relation between b AQF and returns. If anything, the pattern seems to be the opposite: The average return for the b AQF quintiles monotonically decreases as b AQF increases (1.022%, 0.966%, 0.913%, 0.869%, and 0.695%). Under H-Risk, the intercepts from a FF3+AQF model should be zero and exhibit no pattern with respect to b AQF rank; under H-Characteristic, the intercepts should be positive for low b AQF quintiles, and negative for high b AQF quintiles, to compensate for the tted return accounted by positive premium multiplied by b AQF. The results in Panel B of Table 3 and Panel B of Figure 1 are inconsistent with the prediction of H-Risk but consistent with H-Characteristic. In particular, 13 (15) out of 45 intercepts are signi cant at the 0.01 (0.05) level, rejecting H-Risk; seven out of nine intercepts of the lowest b AQF quintile are positive, and all nine are higher than the intercepts of the highest b AQF quintile, ve of which are 16

18 negative. The average intercept monotonically decreases from 0.146% to % along b AQF ranks, providing more support to H-Characteristic. A formal test involves forming characteristic-balanced portfolios with similar characteristics but substantially di erent factor loadings. I form nine portfolios by buying the top two b AQF quintiles and shorting the bottom two b AQF quintiles within each size-aq group. Panel C of Table 3 reports the mean excess returns and regression results of the nine characteristicbalanced portfolios. Eight out of nine mean excess returns are negative (with two signi cant at the 0.01 level), inconsistent with H-Risk, which predicts that mean returns are positive to re ect the positive loading. The portfolio intercepts obtained from a FF3+AQF model represent the returns of a hypothetical factor-balanced portfolio (Daniel, Titman, and Wei 2011), and should be zero under H-Risk. However, Panel C shows that eight out of nine intercepts are negative, with two signi cant at the 0.01 level. The Gibbons, Ross, and Shanken (1989) F-test rejects the hypothesis that the intercepts are jointly zero at the 0.01 level. Finally, a portfolio formed by equally weighting the nine characteristic-balanced portfolios has a negative mean excess return (-0.212%) and a negative intercept. Overall, the results based on portfolios sorts are consistent with the predictions of H-Characteristic instead of H-Risk Cross-sectional regressions If it is indeed the mispricing of AQ rather than pricing of AQF that drives stock returns, the explanatory power of b AQF should be subsumed by AQ in a cross-sectional regression that includes both AQ and b AQF. Cross-sectional regressions provide the exibility of including more control variables than portfolio sorts. In Table 4, I conduct Fama-MacBeth (1973) regressions of monthly returns on AQ, b AQF, and control variables including loadings on Fama-French three factors and past returns. The coe cient of b AQF is insigni cant from 0 after controlling for AQ, which has a positive coe cient of 2.40 (t=1.90). This result is robust to the inclusion of FF3 factor loadings (estimated over the same rolling window as b AQF ), returns from last month (R 1 ), and the buy-and-hold returns from month -12 to month -2 (R 12: 2 ). 17

19 4.3 Is AQF premium attributable to corr(aq; b AQF )? The AQF premium (or c 2 following the notation from the motivating model) should have no relation with corr(aq; b AQF ) under H-Risk, but a positive relation under H-Characteristic, which predicts that varition of c 2 across di erent samples is mainly driven by corr(aq; b AQF ). To x ideas, assume that an econometrician who believes in H-Risk will estimate the FF3+AQF model. As each month constitutes a di erent cross-section of rms and is associated with a unique c 2 and corr(aq; b AQF ), we can test the prediction on the time series of c 2 and corr(aq; b AQF ). Panel A of Table 5 presents the summary statistics of AQF premium (c 2 ) estimated from monthly cross-sectional regressions, and corr(aq; b AQF ) based on Pearson and Spearman correlations. To examine the positive risk premium found in the literature, we focus on positive AQF premium. The median AQF premium is 1.303%, and its t-statistic has a median value of The Pearson (Spearman) correlation between AQ and b AQF is high, ranging from to (0.164 to 0.383). Figure 3 plots the time series of corr(aq; b AQF ) against the t-statistic of the AQF premium (t(c 2 )) for the period of Consistent with the prediction of H-Characteristic, there is considerable comovement between the two, suggesting that corr(aq; b AQF ) is the determinant of the varying signi cance of c 2. Panel B of Table 5 formally tests this prediction in a time-series regression. Both Pearman and Spearman correlations are highly signi cant in explaining the variations of c 2 and t(c 2 ). For example, an increase of Pearson corr(aq; b AQF ) by 0.01 in ates c 2 by as much as (t=4.30), and in ates t(c 2 ) by as much as (t=2.76), on average. These results collaborate the evidence of the characteristic versus covariance test, and quantify the importance of the role of AQ characteristic in driving the results which are misinterpreted as evidence of risk. 5 Information environment and the mispricing of accruals quality In this section, I test whether information environment plays a role in the cross-sectional variations of the return regularity associated with AQ. 18

20 5.1 Information uncertainty Following Zhang (2006), I use the following proxies for information uncertainty: inverse of rm size (1/MV), the inverse of rm age (1/AGE), the inverse of analyst coverage (1/COV), stock volatility (SIGMA), and cash ow volatility (CFVOL). Firm age is the number years since the rm was rst covered by CRSP. Analyst coverage is the number of analysts making an one-year-ahead annual EPS forecast. the Stock volatility is the standard deviation of weekly market excess return over the year ending at the portfolio formation date, where weekly returns are measured from Thursday to Wednesday. Cash ow volatility is calculated as the standard deviation of cash ow from operations in the past ve years, requiring a minimum of three years. Because higher information uncertainty prevents e cient information sharing among investors, I also include PIN and the illiquidity component of PIN (PSOS) calculated by Durate and Young (2009) as measures of information uncertainty. A higher value of any of these proxies indicates higher information uncertainty. Panel A of Table 6 presents the mean returns of 20 portfolios sorted by 1/MV and AQ. At the beginning of each month, rms are sorted into ve AQ quintiles; within each AQ quintile, rms are sorted into four quartiles based on 1/MV. For each 1/MV quartile, I construct a hedge portfolio (AQ5-AQ1) which buys AQ5 and shorts AQ1, to capture the abnormal returns that can be earned by exploiting the mispricing of AQ. The mean return of AQ5-AQ1 increases from an insigni cant -0.07% for the lowest information uncertainty quartile to 2.80% (t=13.59) for the highest information uncertainty quartile. To control for the e ects of standard risk factors, Panel B presents the intercepts from the Fama-French three-factor model (FF3), FF3 augmented by UMD (FF4), and FF3 augmented by UMD and LIQ (FF5). The intercepts of the four hedge portfolios invariably exhibit a monotonic, positive relation with 1/MV. Panel C conducts the same analysis using alternative information uncertainty proxies. 6 Portfolios sorted on SIGMA, CFVOL, PIN, and PSOS exhibit the same monotonic pattern as portfolios sorted by 1/MV. In all models and across di erent measures of information uncertainty, the hedge portfolio in the highest information uncertainty quartile (U4) always earns a higher return or alpha than the hedge portfolio in the lowest information uncertainty quartile (U1). This implies that the return predictability is stronger 6 To enhance the power of sorts, I require data availability only for the sorting variable. Therefore, samples across di erent sorts may not be directly comparable. 19

21 when information uncertainty is greater, consistent with the prediction of H-Characteristic but inconsistent with H-Risk, which prescribes no role for information uncertainty. 5.2 Investor competition I focus on measures of institutional investors as proxies for investor competition, because institutional investors are arguably more sophisticated and informed, and they are more likely to compete for information and exploit mispricing. 7 Based on the CDA/Spectrum Institutional Holdings database available from Thomson Reuters, I develop three measures of investor competition. The rst measure is the number of institutional investors (N_INST). The second measure is the inverse of the Her ndahl index of institutional investor holdings (1/HERF_INST), where HERF_INST = P N_INST i=1 h 2 i, h i is the fraction of a rm s total institutional holding accounted by institutional investor i. Because the Her ndahl index measures the level of concentration, the inverse of this index measures the number of e ective competitors among all institutional investors. The third measure is the percentage of institutional holding (PCT_INST). A rm with higher institutional holding will likely face more erce competition for information. Therefore, all three measures supposedly have a positive relation with investor competition for information. Table 7 presents the mean returns and regression intercepts of portfolios sorted by AQ and investor competition measures. Panel A reports the mean returns of 20 portfolios sorted by AQ and N_INST, and four hedge portfolios (AQ5-AQ1). The hedge portfolio return monotonically decreases from 1.35% (t=2.52) to an insigni cant -0.30% as investor competition increases, generating a signi cant spread of -1.65% (t=-2.84). The FF3, FF4, and FF5 regression intercepts are reported in Panel B. The intercepts of the four hedge portfolios exhibit the same monotonic trend as mean returns. Panel C replicates the portfolio tests on on 1/HERF_INST and PCT_INST. The hedge portfolio in the lowest competition quartile (C1) always earns a higher return or alpha than the hedge portfolio in the highest competition quartile (C4). This supports the claim that the return predictability in the form of priced AQ risk is actually due to mispricing, which is considerably weaker when the competition for information among sophisticated investors gets ercer. 7 This measurement choice is similar to Akins et al. (2011), who nd that there is a smaller e ect of information asymmetry and information quality on cost of capital when there are more competition among informed investors. 20

22 6 Do managers cater to market sentiment for accruals volatility? Firms with a higher AQ (volatility of discretionary accruals) are associated with a return or valuation premium, as evidenced by a positive AQF premium and a higher MTB (to be calculated below). Since such regularity represents investor irrationality and cognitive biases, rm managers, who are arguably more sophisticated, could exploit such irrationality by engaging in opportunistic nancial reporting. In other words, rms may cater to the sentiment of the market for high accruals volatility. In behavioral corporate nance, the idea of catering or corporate opportunism in the presence of irrational capital markets has been explored by several studies. For example, Baker and Wurgler (2002) nd that rms are more likely to issue equity when market valuation is high, in an attempt to exploit temporary misvaluation; Baker and Wurgler (2004) nd that rms are also more likely to pay dividends when prevailing investor demand for dividend payers is high. In accounting, there are a few studies on the opportunism in - nancial reporting in response to investor irrationality. For example, Du (2009) introduces a multi-period model in which rms exploit the behavioral biases of investors by shifting earnings over time and manipulating market expectations; Rajgopal et al. (2007) nd that managers in ate earnings when investors react optimistically to positive earnings surprises relative to negative ones. In this paper, I conduct an exploratory analysis on the corporate opportunism in response to market sentiment for accruals quality (or rather, market sentiment for accruals volatility). In particular, if rm managers have incentives to boost short-term rm valuation 8, they may want to in ate accruals volatility by engaging in more disrectionary reporting at times when the reward to such activities is high. To test this prediction, we need to develop measures of market-wide discretionary reporting and market sentiment for accruals volatility. Market-level discretionary reporting is measured by aggregate one-time items, de ned as the sum of one-time items (special items after tax plus extraordinary items) for all rms in the main sample with available AQ measure, 8 This could either because managers receive equity-based compensation (e.g., Burns and Kedia 2006), or because they want to raise more funds through seasoned equity issuances (e.g., Baker and Wurgler 2002). 21

23 scaled by aggregate total assets for sample rms. For market sentiment, I propose two measures. The rst measure is the accruals quality factor (AQF), which re ects the return premium earned by rms with higher AQ, or more volatile discretionary accruals. Panel A of Figure 3 plots AQF and the long and short positions based on which it is formed. The second measure of sentiment is MTB_DIFF, the di erence in market-to-book (MTB) ratios between high AQ rms and low AQ rms. In each scal year, all rms are sorted into AQ quintiles. Within each quintile, the MTB (book assets minus book equity plus market equity all divided by book assets) of individual rms are value-weighted to get the quintile MTB. MTB_DIFF is the average MTB of the top two AQ quintiles minus the average MTB of the bottom two AQ quintiles. From the perspective of market participants, MTB_DIFF is a simpler and more salient measure than AQF. Panel C and Panel D of Figure 3 plot aggregate one-time items against the two measures of market sentiment, AQF and MTB_DIFF, respectively. Apparently, there is a positive association between the magnitude of aggregate one-time items and market sentiment. In particular, aggregate one-time items and MTB_DIFF behave like mirror image for each other. This provides preliminary evidence that rm managers strategically time discretionary reporting to exploit the mispricing of AQ. 7 Robustness tests and connections to other forms of mispricing 7.1 Robustness tests Construction of the accruals quality factor As shown in Panel B of Table 1, the accruals quality factor (AQF) is correlated with SMB. To mitigate multicollinearity concerns, I replicate the main analysis using an alternative AQF that captures the net e ect of AQ on returns after controlling for size. In each month, rms are sorted into 100 percentile groups on size, and rms within each size group are further sorted into ve AQ quintiles. A hedge portfolio is formed for each size group by buying the top two AQ quintiles and shorting the bottom two AQ quintiles. The alternative AQF is the average return of the 100 hedge portfolios. This procedure reduces the correlation between 22

24 AQF and SMB from 0.62 to Robustness checks using the alternative AQF nd no substantial deviation from the results using the primary AQF. The results are also robust to an alternative AQF constructed by a more extreme hedging strategy: buying the top AQ quintile and shorting the bottom AQ quintile, instead of buying the top two AQ quintiles and shorting the bottom two AQ quintiles Construction of characteristic-balanced portfolios In the characteristic versus covariance test, I triple-sort stocks by size, AQ, and b AQF. As a robustness check, the rst sorting variable, size, is replaced by B/M. The conclusion still obtains. I also construct an alternative set of nine characteristic-balanced portfolios by buying the top AQ quintile and shorting the bottom AQ quintile within each size-aq (B/M-AQ) group, and show that the conclusions still hold Weighting schemes Following prior studies (e.g., Core et al. 2009), AQF is based on equal-weighted stock returns within each AQ quintile, while the testing portfolios in the two-pass asset pricing test and the characteristic versus covariance test are based on value-weighted returns. As a robustness check, the AQF is formed by value-weighting, and (or) the testing portfolios are formed by equal-weighting. The alternative weighting schemes do not qualitatively change the main results Estimation windows Several variables are based on rolling-window estimation: AQ is the standard deviation of previous ve years of rm-level regression residuals in McNichols (2002) modi cation of the Dechow and Dichev (2002) model; the sorting variable b AQF used in the characteristic versus covariance test is estimated over the previous 60 months; cash ow volatility (CFVOL) is estimated as the standard deviation of previous ve years of cash ows; stock volatility (SIGMA) is measured by the standard deviation of weekly returns over the past year. In 9 It is impossible to entirely circumvent the size e ect in constructing AQF. According to Chen et al. (1986), it has been facetiously noted that size may be the best theory we now have of expected returns. (p. 394) 23

25 robustness checks, the estimation windows for AQ, b AQF, and CFVOL are changed to four or six years, and the estimation window for SIGMA is changed to six months or two years. None of the alternative measurement windows has a qualitative impact on the ndings. 7.2 Connections to other forms of mispricing The accruals anomaly It is possible that the return predictability based on AQ (the standard deviation of discretionary accruals) is related to the accruals anomaly (return predictability on the level of total accruals, e.g., Sloan 1996). I test this possibility by including total accruals scaled by total assets (TACC) as a control in the Fama-MacBeth cross-sectional regressions of returns on risk and mispricing proxies. The results are reported in models 7-11 of Table 4. There is some evidence that the inclusion of total accruals reduces the power of AQ, but AQ is still signi cant when I control for past returns. As before, b AQF continues to be insigni cant in all models. Even though the power of AQ is partially subsumed by total accruals, the relationship between the two could be more nuanced for two reasons. First, the lower explanatory power of accruals quality after controlling for total accruals might be due to the measurement error in accruals quality estimates. Second, there is no monotonic relation between AQ measure and total accruals (Panel B of Table 1). Potential links between the mispricing of accruals quality and the accruals anomaly could alleviate the interpretative burden of the mispricing hypothesis of accruals quality: While a behavioral explanation for the mispricing of accruals quality has to be intricate, such explanation for the accruals anomaly could simply hinge on investors naive xation on level of earnings, which is a salient measure of rm performance A more general market sentiment The accruals quality factor, if interpreted as the time-varying sentiment for accruals volatility, might be an aspect of a more general market sentiment. As shown in Panel B of Figure 3, MTB_DIFF exhibits considerable comovement with the Baker and Wurgler 24

26 (2006) composite sentiment index, which is a summary statistic 10 of popular sentiment measures, including the closed-end fund discount, NYSE share turnover, the number and average rst-day returns on IPOs, the equity share in new issues, and the dividend premium. The comovement with other market-level proxies of mispricing provides additional support to the mispricing hypothesis. I caution against using links between the pricing e ect of AQ and macroeconomic conditions as evidence of fundamental risk (e.g., Kim and Qi 2010). Simple time series of macroeconomic variables (e.g., NBER business cycle dates) are likely to be correlated with market sentiment, which by design are related to the pricing e ect of characteristics such as AQ. 8 Concluding remarks Accruals quality is not a priced risk factor; instead, the return regularity misinterpreted as evidence of pricing represents the mispricing of accruals quality. This paper shows, both theoretically and empirically, that when the mispricing hypothesis is true but an econometrician conducts a two-pass test as if the risk hypothesis were true, she will invariably get an estimate of the AQ factor premium that is linearly dependent on the correlation between AQ and AQ factor loading. In addition, the return regularity is stronger in the presence of greater information uncertainty and imperfect investor competition, consistent with the cross-sectional behavior of mispricing. What is more, managers seem to cater to such mispricing by timing discretionary nancial reporting. This study is a skeptical appraisal of the growing literature that applies the two-pass cross-sectional test to address whether accruals (earnings) quality is a priced risk factor. Accruals quality is just one of the plethora of earnings quality measures proposed in the literature (see Dechow et al. (2010) for a review). It is likely that capital markets research in the future will bring other measures to the scrutiny of asset pricing tests. This paper cautions against making inferences based solely on such tests, especially when the underlying model has little theoretical underpinning. In particular, in interpreting the ndings from 10 The composite sentiment index is based on rst principal component of six (standardized) sentiment proxies over , where each of the proxies has rst been orthogonalized with respect to a set of macroeconomic conditions. 25

27 such tests, it is imperative to beware of the spurious signi cance problem addressed in this paper, and other known caveats to the two-pass methodology. A battery of tests can be performed before a researcher reaches the conclusion that some proxy of information risk is priced or mispriced. The mispricing of accruals quality may not be a new anomaly that can give rise to a pro table trading strategy incremental to those based on known mispricing proxies. In fact, there is preliminary evidence that the mispricing of accruals quality might partially represent the accruals anomaly and a broader concept of market sentiment. Researchers could draw on related studies for corroborative evidence that accruals quality is mispriced. This study does not attempt to identify the investor heuristics and cognitive biases that underlie the mispricing of accruals quality. A possible mechanism in the spirit of Daniel, Hirshleifer, and Subrahmanyam (2001) is that, some investors are overcon dent about their ability to project future pro tability of a rm based on its accruals quality, while more sophisticated investors exploit the pricing errors introduced by the overcon dent investors, but do not eliminate all mispricing due to risk aversion. Future research could investigate how the relation between accruals quality and future fundamentals are misperceived by investors, and how (and to what extent) such valuation errors are corrected in the long run. 26

28 Appendix Proof of Proposition 1. In the rst stage, the econometrician estimates factor betas from rm-speci c time-series regressions. Based on the true data-generating process given by H-Mispricing, we have plim b i;f = i;f (8.1) and plim b i;aqf = cov(f; AQF ) var(aqf ) i;f (8.2) or equivalently, Therefore, plim b i;f = var(aqf ) cov(f; AQF ) plim b i;aqf (8.3) cov(b F ; b AQF ) = var(aqf ) cov(f; AQF ) var(b AQF ) (8.4) In the second stage, the econometrician conducts a cross-sectional regression, and obtains the following estimates of risk premium, plim c 2 = cov( R; b AQF ) var(b AQF ) = ( 1 + F ) cov(b F ; b AQF ) var(b AQF ) var(aqf ) + cov(aq; b AQF ) var(b AQF ) = ( 1 + F cov(f;aqf ) ) var(b AQF ) + cov(aq; b AQF ) var(b AQF ) var(b AQF ) s = ( 1 + F var(aqf ) ) cov(f; AQF ) + var(aq) var(b AQF ) corr(aq; b AQF ) (8.5) This completes the proof of Proposition 1. 27

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32 Figure 1- Characteristic versus Covariance Tests Based on 45 Size-AQ- model intercepts of the 45 size-aq- sorted portfolios (see Table 3). The nine size-aq groups are labeled by a pair of size rank (S, M, B) and AQ rank (H, M, L). A low (high) AQ value indicates high (low) accruals quality, and is therefore labeled as H ( L ). The five AQ quintiles are labeled by the rank of AQ loading,. Size is the market value of equity; AQ is the accruals quality measure (the standard deviation of the past five years firm-level residuals from McNichols [2002] modification of the Dechow and Dichev [2002] model). Size and AQ are matched to 12 consecutive monthly returns starting from the fourth month after the fiscal year end. is the factor loading on AQF, estimated over the previous 60 months for each firm-month. At the beginning of each month, firms are sorted into 3 size tertiles and 3 AQ tertiles independently; within each of the 9 size-aq intersections, firms are sorted into quintiles. Portfolio returns are the value-weighted returns of individual firms within each group. Panel A reports the mean excess returns of 45 Size-AQ- portfolios. Panel B reports the intercepts of a time-series regression using the Fama-French three-factor model augmented with AQF, for each portfolio,,,,, Portfolios This figure provides a graphical representation of the mean excess returns and factor Panel A: Mean Excesss Returns AQF load 1 AQF load 2 AQF load 3 AQF load 4 AQF load S/H S/M S/L M/H M/M M/L B/H B/M B/L Panel B: FF4+AQF Alphas AQF load 1 AQF load S/H S/M S/L M/H M/M M/L B/H B/M B/L AQF load 3 AQF load 4 AQF load