Accounting Anomalies and Information Uncertainty

Transcription

1 Accounting Anomalies and Information Uncertainty Jennifer Francis (Duke University) Ryan LaFond (University of Wisconsin) Per Olsson (Duke University) Katherine Schipper (Financial Accounting Standards Board) We examine whether rational investor responses to information uncertainty explain properties of and returns to accounting-based trading anomalies. We proxy for information uncertainty with two measures of earnings quality: the standard deviation of the residuals from a Dechow and Dichev [2002] model relating accruals to cash flows, and the absolute value of performanceadjusted abnormal accruals from a modified Jones [1991] model. Over , we find that accounting-based trading anomalies (post-earnings announcement drift, value-glamour, and accruals strategies) are correlated with earnings quality. Specifically, extreme anomaly portfolios have poorer earnings quality than non-extreme portfolios, and within the extreme anomaly portfolios, poor earnings quality securities are more prevalent and earn larger abnormal returns than good earnings quality securities. Consistent with greater resolution of uncertainty for poor earnings quality securities, the abnormal returns to poor quality securities converge to the abnormal returns to good quality securities as the post-portfolio formation period lengthens. Taken as a whole, these results indicate that information uncertainty plays an important role in explaining accounting anomalies. Draft: February 2003 This research was supported by the Fuqua School of Business, Duke University, and the University of Wisconsin. Analysts earnings forecasts are from Zacks Investment Research. The views expressed in this paper are those of the authors. Official positions of the Financial Accounting Standards Board are arrived at only after extensive due process and deliberation. We appreciate discussions with and comments from Alon Brav and David Robinson.

2 Accounting Anomalies and Information Uncertainty 1. Introduction This study investigates whether proxies for information uncertainty explain several welldocumented accounting-based trading anomalies. By information uncertainty, we mean the precision or quality of an investment signal; we characterize poor (good) quality signals as having high (low) information uncertainty. Accounting-based trading anomalies refer to systematic patterns in long term stock returns following an accounting signal which can be exploited to generate returns over and above the expected return as measured by the one-factor capital asset pricing model (CAPM) or its three-factor extension (Fama and French [1993]). We investigate three classes of accounting-based trading anomalies: post earnings announcement drift (based on both analysts forecasts and seasonal random walk forecasts), value-glamour strategies (book-to-market, cash flow-to-price, and earnings-to-price), and accruals strategies (total accruals and abnormal accruals). Our analysis is motivated by two literatures which relate to the role of information uncertainty in explaining asset prices. The first has its roots in Bayesian decision theory research, which shows that loss-minimizing investors rationally place less weight on noisier (i.e., more uncertain) information (e.g., DeGroot [1970]). As information uncertainty is resolved, investors update their beliefs and increase the weight placed on the initial signal. In the context of accounting information, this explanation predicts muted reactions to high uncertainty accounting signals (which would appear as under-reactions), followed by diminishing abnormal returns as uncertainty is resolved; both the initial under-reaction and the subsequent abnormal returns are measured relative to expected returns derived from conventional asset pricing models. As Brav and Heaton [2002] discuss, rational learning may explain the pattern of abnormal returns to trading anomalies but not their persistence. That is, why is the premium to information uncertainty not quickly arbitraged away by traders who do not care about this uncertainty? Evidence that such arbitrage may not be possible is provided by the second literature to which our study relates. Specifically, recent 1

3 analytical models (Easley and O Hara [2001]) and empirical studies (e.g., Easley, Hvidkjær and O Hara [2002]; Francis, LaFond, Olsson and Schipper [2002]; Botosan [1997]; and Botosan and Plumlee [2002]) report results consistent with capital market pricing of information risk, in the form of higher costs of capital for securities characterized by greater information uncertainty. In addition, both Easley et al. and Francis et al. find that information uncertainty effects are not subsumed by risk proxies included in traditional models of expected return (such as the CAPM beta, size, and book-to-market). If, as suggested by these studies, available models of expected returns do not capture firm-specific information uncertainty, and this risk is priced by investors, then measures of abnormal returns based on these models will be, on average, systematically associated with information uncertainty. Rational investor responses to information uncertainty offer a potential explanation for the persistent and significant abnormal returns to trading strategies that exploit extreme accounting signals. Specifically, rational learning predicts delayed price reactions in the form of significant abnormal returns to signals characterized by high information uncertainty, while research on information risk provides indirect evidence of the persistence of such returns by documenting the inability of investors to completely diversify such risk. In this paper, we provide evidence on three elements of this explanation for accounting anomalies. First, we test whether securities included in extreme accounting anomaly portfolios have higher information uncertainty than securities in non-extreme portfolios. Second, we examine whether a disproportionate amount of the abnormal returns to trading strategies which take positions in these extreme portfolios is concentrated in stocks with high information uncertainty. Third, we investigate whether, as uncertainty about the accounting signal is resolved, the magnitude of high information uncertainty securities abnormal returns declines, converging in magnitude to the abnormal returns of low information uncertainty securities. Our tests of these predictions use two proxies for information uncertainty identified by Francis et al. as being priced by investors. The first measure is the standard deviation of the firm s regression residuals obtained from rolling Dechow and Dichev [2002] regressions relating working capital accruals to past, current and future cash flows. This measure captures the mapping of earnings into cash flows: the 2

4 weaker the mapping, the poorer is the quality of earnings. The second measure, the absolute value of the performance-matched abnormal accruals obtained from industry-year estimations of the modified-jones [1991] model, identifies the portion of total accruals that cannot be explained by fundamentals as an inverse measure of earnings quality. For both measures, we assign greater information uncertainty to firms with lower earnings quality. However, we do not attempt to investigate the source(s) of information uncertainty, or to distinguish between intrinsic uncertainty that is inherent in firms business models and their operating environments, and management-induced uncertainty that is due to unintentional or intentional recognition and measurement errors. For the purposes of our investigations, only the existence and magnitude of information uncertainty matter, not its source. For each anomaly, we investigate whether the ranking of the accounting signal is correlated with its quality. Moving from the top portfolios of the ranked signal to the bottom portfolios, we document a U-shaped pattern in earnings quality: stocks in the extreme portfolios have significantly (at the.01 level) poorer average earnings quality than stocks in the non-extreme portfolios. In addition, within each extreme portfolio, the incidence of securities with poor earnings quality (Poor) is generally significantly (at the.01 level) greater than both chance and the incidence of securities with good earnings quality (Good). We interpret the U-shaped pattern as indicating a separation between the quality of the accounting signal (i.e., its information uncertainty) and the nature of the news carried by the signal. That is, information uncertainty is associated with extreme realizations of accounting-based investment signals, abstracting from the favorable or unfavorable information conveyed by the signal. The concentration of poor earnings quality firms in the extreme anomaly portfolios suggests that abnormal returns to trading strategies which take positions in securities in these extreme portfolios are associated with information uncertainty. Specifically, holding the anomaly portfolio constant, we expect long-minus-short positions in high information uncertainty securities to yield larger abnormal returns than similar positions in low information uncertainty stocks. Our results are generally consistent with this expectation. For example, for a post earnings announcement drift strategy based on analysts earnings forecasts, the average abnormal return is basis points (bp) per month for the Poor securities 3

5 versus bp for the Good securities; for the book-to-market strategy, the mean abnormal return is about 160 bp per month for Poor securities versus bp for Good securities; for a total accruals (Sloan [1996]) strategy, the monthly abnormal return is 102 bp for Poor securities and 50 bp for Good securities. The finding that Poor earnings quality securities generate larger abnormal returns than Good earnings quality securities is consistent across the anomalies and the measures of earnings quality. We note, however, that these results do not fully explain prior studies findings of significant abnormal returns to accounting-based trading strategies, because securities with the least information uncertainty (i.e., the Good earnings quality securities) are associated with non-zero anomaly-specific abnormal returns, albeit of significantly (at the.01 level) smaller magnitude than abnormal returns to portfolios with the most information uncertainty. Finally, we find that, over the 36 months following portfolio formation, abnormal returns to Poor earnings quality securities tend to converge to the magnitude of abnormal returns to Good quality stocks. The protracted period over which abnormal returns persist, but diminish, for Poor quality securities is consistent with the argument that investors require time to resolve the greater information uncertainty for these stocks. Specifically, as information uncertainty diminishes, so too does the abnormal return. We probe firm size and growth as alternative explanations for the results. Concerning firm size, we note that the fact that we draw similar inferences using three-factor abnormal returns as well as CAPM abnormal returns suggests that firm size (an explicit factor included in the three-factor model) is unlikely to explain the results. In sensitivity tests which repeat the analyses on size partitions (small, medium and large firms), we find no evidence that the results are concentrated in, or driven by, small firms. We also find no support for growth as an explanation for the results. Our main tests are conditional on the identification of specific accounting-based trading anomalies and the design of the trading strategies. We also conduct a more general investigation of the influence of information uncertainty on abnormal returns by testing the association between earnings quality and perfect foresight abnormal returns, as measured by the intercepts obtained from rolling fiveyear firm-specific CAPM and three-factor asset pricing regressions over These perfect- 4

6 foresight abnormal returns abstract from details of trading strategy implementation choices, and they are not exploitable. Similar to the results documented for the accounting anomalies, we find that both CAPM and three-factor abnormal returns exhibit a U-shaped relation with earnings quality: firms with the most extreme abnormal returns (positive or negative) have poorer average earnings quality than firms with moderate or no abnormal returns. Regressions of absolute abnormal returns on ranked values of the earnings quality metrics show that absolute abnormal returns increase by bp per month, or 10%- 14% per year, when moving from the best earnings quality decile to the poorest earnings quality decile (significant at the.01 level). These results suggest that information uncertainty, as proxied by earnings quality, is a pervasive determinant of abnormal returns. We interpret our findings as contributing to the debate over the existence and persistence of anomalous returns. Returns to accounting-based trading strategies are viewed as anomalous because market efficiency dictates that rational traders should be able to quickly trade away any abnormal returns to public accounting signals, unless it is risky and/or costly to do so (Friedman [1953]). A minimal interpretation of our results is that such trading is not riskless, and that information uncertainty limits arbitrage for accounting-based trading portfolios. Because some limit to arbitrage is necessary for mispricings to continue over extended periods of time in both rational and irrational models of capital markets (see, for example, Miller [1977] and Barberis and Thaler [2002]), our results therefore provide an explanation for the persistence of such anomalies, regardless of whether one believes they are driven by rational or irrational behaviors. A more ambitious interpretation of our results is that the existence of the apparent mispricing of the information in accounting signals also derives from information uncertainty. The rest of the paper is organized as follows. The next section relates our study to prior research both on the role of information uncertainty in asset pricing and on the profitability of accounting-based trading strategies; we also develop hypotheses linking properties of the accounting anomalies to predictable effects of information uncertainty. Section 3 describes our measures of information uncertainty. Section 4 reports the results of our main tests, and section 5 reports the extension examining 5

7 the relation between information uncertainty and perfect-foresight abnormal returns. Section 6 reports the results of sensitivity analyses and additional tests, and section 7 concludes. 2. Motivation and Hypotheses Our study links research on asset pricing to research documenting long-term abnormal returns to trading strategies based on accounting signals. In terms of the former, research has explored the effects of investor irrationality, rationality and rational expectations on asset pricing. The literature on irrationality posits behavioral explanations for the existence of abnormal returns (see Barberis and Thaler [2002] for an overview). In general, behavioral studies argue that one or more cognitive processing biases such as representativeness and conservatism lead to the observed under- and over-reaction patterns. 1 However, in direct out-of-sample tests, Chan, Frankel and Kothari [2002] find little support for explanations based on the representativeness bias. Research which models rational investor processing of incomplete information structures (for example, Merton [1987], Timmerman [1993], Kurtz [1994], Morris [1996], and Lewellen and Shanken [2002]) shows that uncertainty (or other imperfections, such as partial information) about the information structure can lead to the appearance of risk premiums or asset pricing anomalies. That is, faced with valuation parameter uncertainty, investors rationally price stocks in a way that leads to the appearance of deviations from market efficiency. Of particular relevance to our study is Brav and Heaton s [2002] structural uncertainty, or rational learning, model in which investors place less weight on investment signals that are characterized by greater information uncertainty. 2 As this uncertainty is resolved, investors increase their weights on the information in the original signal, resulting in subsequent movements in asset prices. The abnormal returns resulting from such price movements diminish as uncertainty is resolved. 1 Representativeness occurs when subjects over-weight recent pieces of evidence, ignoring base rate information. Conservatism is the opposite: subjects under-weight recent information, placing excessive weight on base rates. 2 Under-reaction may also be driven by investor irrationality. As Brav and Heaton demonstrate, it is not possible to separate a rational information uncertainty explanation from an irrational behavioral explanation. We make no attempt to do so either. 6

8 The unresolved issue in these incomplete information models is why an asset premium to information uncertainty is not arbitraged away. The extent to which arbitrage traders, such as hedge funds, face institutional and other constraints that preclude eliminating the effects of imperfections in information structures is an empirical issue. We note, however, that Easley and O Hara [2001] develop an analytical setting in which such arbitrage is not possible. In their multi-asset rational expectations setting, the private and public composition of information affects required returns. Because privately informed investors are better able to shift their portfolio weights to take advantage of new information, relatively more private information increases uninformed investors risk of holding the stock. This information risk is systematic, i.e., not diversifiable, so uninformed investors require higher returns (charge a higher cost of capital) as compensation. In equilibrium, required returns are affected by the extent of private information and the precision (quality) of public information; that is, there is a risk premium associated with information uncertainty. Several studies provide empirical support for such a premium to information uncertainty (Easley, Hvidkjær and O Hara [2002]; Francis, LaFond, Olsson and Schipper [2002]; Botosan [1997]; Botosan and Plumlee [2002]). 3 Both Francis et al. and Easley et al. document that the information risk effect is associated with traditional risk proxies (beta, size, and book-to-market), but it is not subsumed by them. Consequently, we expect a significant portion of the returns effects due to information uncertainty to be associated with abnormal returns, i.e., returns not explained by traditional asset pricing models. In summary, both research on rational learning and research demonstrating that information risk is priced in the capital markets predict an association between abnormal returns and information uncertainty. To maximize the power of our tests of this association, we focus on contexts where abnormal returns are linked to public information signals that have the appearance of being under-utilized 3 Easley, Hvidkjær and O Hara [2002] find that firms with more private information, as proxied by higher probabilities of informed trading (PIN) scores, have larger expected returns. Francis, LaFond, Olsson and Schipper [2002] show that firms with higher earnings quality (as proxied by strong mappings of accruals into fundamentals) enjoy a lower cost of capital for both debt and equity. Botosan [1997] and Botosan and Plumlee [2002] document a positive relation between costs of capital and disclosure scores (where the scores include an index developed for the quantity of information reported in annual reports, and analysts perceptions as expressed in AIMR scores). 7

9 by market participants. We emphasize these contextual features because they are consistent with both a rational learning explanation (which argues that investors rationally place less weight on poor quality investment signals, giving rise to abnormal returns over the period during which the information uncertainty is resolved) and with an information risk explanation (which argues that abnormal returns, measured against the CAPM or three-factor model, are systematically mis-measured for firms with high information risk, with the extent of mis-measurement positively associated with the magnitude of information risk). Accounting-based trading anomalies exhibit these features and, therefore, are prime candidates for examination. 4 We consider three classes of accounting anomalies: post earnings announcement drift (PEAD), accounting-based value-glamour strategies, and accruals strategies. Descriptions of each anomaly, as well as summaries of prior related research, are reported in the Appendix. Briefly, the accounting-based trading strategies take positions based on extreme realizations of the accounting signal, buying stocks with the most favorable signals and selling stocks with the least favorable signals. The abnormal return to the long-minus-short position measures the strategy s profitability. Prior studies document significant positive abnormal returns to the accounting strategies over periods from six months to 36 months following portfolio formation. We test three predictions related to information uncertainty as an explanation for these abnormal returns. The first is based on the information uncertainty properties of securities with the most extreme accounting signals. Specifically, because we expect investors to assign low weights to poor quality signals irrespective of the content of the signal, we hypothesize that both the long position and the short 4 We label the accounting anomalies as under-reactions to the current signal (e.g., the earnings surprise or the valueglamour ratio) based on prior research which argues that prices behave as if investors underutilize the information in the signal. This labeling should not be confused with behavioral finance theories which argue that some anomalies are due to overreactions to past patterns. For example, Lakonishok, Shleifer and Vishny [1994] show that firms with low earnings-price ratios have high past growth, and argue that investors overreact to this high past growth by naively extrapolating it into the future, causing price to become too high (and, therefore, the current earnings-price signal is low). Whether one views this scenario as investor over-reaction to the past growth pattern or as investor under-reaction to the current earnings-price signal, the prediction about the direction of the future price drift is the same. 8

10 position of accounting-based trading strategies are characterized by securities with high information uncertainty (Hypothesis 1). Our second hypothesis focuses on differences in the long-minus-short abnormal returns to securities in the extreme portfolios, depending on whether the securities are characterized by high versus low information uncertainty. To understand why we expect such differences, it is important to note that portfolios are formed based on signed magnitudes of accounting signals and, unless information uncertainty is perfectly correlated across securities, information uncertainty will not be hedged by taking offsetting positions in high (or low) information uncertainty stocks. 5 To the extent information uncertainty is idiosyncratic, not state dependent, the information uncertainty of the long position will not offset the information uncertainty of the short position. Hence, only in the limiting case of perfect correlation of information uncertainty will the long-minus-short abnormal return to high information uncertainty securities equal the abnormal return to low information uncertainty securities. Otherwise, when portfolio formation is based on signed magnitudes of accounting signals, we expect the long-minusshort abnormal return to high information uncertainty (poor quality) securities to exceed the abnormal return to low information uncertainty (good quality) securities (Hypothesis 2). Tests of Hypothesis 2 are necessarily joint tests that there is imperfect correlation of information uncertainty across securities and the prediction that abnormal returns to trading strategies based on extreme realizations of accounting signals are larger for signals with higher information uncertainty. Our third hypothesis links the magnitude of abnormal returns to the time period over which information uncertainty is resolved. In particular, we expect that as information uncertainty is resolved over time, the abnormal returns to poor quality signals will diminish, converging in magnitude to the abnormal returns to good quality signals (Hypothesis 3). 5 Easley and O Hara [2001] show that when information uncertainty is uncorrelated across securities, investors cannot diversify it. Further, even when information uncertainty is correlated across securities, investors can reduce, but never eliminate, it by diversification. They note that the correlation of information uncertainty across securities is an empirical question. 9

11 3. Information Uncertainty Our measures of information uncertainty are derived from the mapping of accruals into fundamentals, either cash flows or reported numbers that are presumed to reflect underlying economics. The approaches differ in terms of the underlying model, the data requirements (which affect sample size), and the extent of over-time variation in the resulting metrics. We use two approaches to mitigate concerns that the results are sensitive to the choice of metric and/or to the sample of firms with data available to calculate a given metric. The first metric is based on Dechow and Dichev s [2002] model which separates accruals based on their association with cash flows by regressing working capital accruals on cash from operations in the current period, prior period and future period. The unexplained portion of the variation in working capital accruals is an inverse measure of earnings quality; that is, a greater unexplained portion implies lower quality. We estimate equation (1) for each year t for each of the 48 Fama-French [1997] industry groups with at least 20 observations: 6 TCA CFO CFO CFO jt, jt, 1 jt, jt, + 1 = φ0 + φ1 + φ2 + φ3 +ν jt, jt, jt, jt, jt, Assets Assets Assets Assets (1) where TCA = firm j s total current accruals in year t, = ( CA CL Cash + STDEBT ); j, t jt, jt, jt, jt, Assets jt, = firm j s average total assets in year t and t-1; CFO = firm j s cash flow from operations in j,t year t, CFO j, t = NIBE j, t TA j, t ; TA j,t = firm j s total accruals in year t, measured as ( CA jt, CLjt, Cashjt, + STDEBT jt, DEPN jt, ); CA j, t = firm j s change in current assets (Compustat #4) between year t-1 and year t; CL j, t = firm j s change in current liabilities (Compustat #5) between year t-1 and year t; Cash j, t = firm j s change in cash (Compustat #1) between year t-1 and year t; STDEBT, j t = firm j s change in debt in current liabilities (Compustat #34) between year t-1 and 6 Consistent with the prior literature and throughout this section, we winsorize the extreme values of the distribution of each variable to the 1 and 99 percentiles. 10

12 year t; DEPN j, t = firm j s depreciation and amortization expense (Compustat #14) in year t; NIBE j, t = firm j s net income before extraordinary items (Compustat #18) in year t. These estimations yield firm- and year-specific residuals, which form the basis for the first information uncertainty metric, σ ˆ ). σ ˆ ) is the rolling five-year standard deviation of firm j s TA Asset ( ν j,t ( ν j,t residuals, with larger standard deviations indicating poorer earnings quality and, therefore, greater information uncertainty. The five-year requirement and the lead and lag terms in equation (1) mean that the sample used in tests based on σ ˆ ) is limited to firms with seven years of data. ( ν j,t The second metric is based on abnormal accruals estimated from the Jones [1991] model as modified by Dechow, Sloan and Sweeney [1995]. This metric measures earnings quality as the extent to which accruals are well captured by fitted values obtained by regressing total accruals on the change in revenues and property, plant and equipment: Rev PPE = + + +ε (2) jt, 1 j,t jt, κ1 κ2 κ3 jt, 1 Asset jt, 1 Asset jt, 1 Asset jt, 1 jt, where Asset = firm j s total assets (Compustat #6) at the beginning of year t, jt, 1 Rev jt, PPE j, t = firm j s change in revenues (Compustat #12) between year t-1 and year t, = firm j s gross value of property plant and equipment (Compustat #7) in year t. The industry- and year-specific parameter estimates obtained from equation (2) are used to estimate firm-specific normal accruals (as a percent of lagged total assets), NA 1 ( Rev jt, AR jt, ) PPE jt, = ˆ κ + ˆ κ2 + ˆ κ3, where AR jt, = firm j s change in accounts Asset Asset Asset jt, 1 jt, 1 jt, 1 jt, 1 receivable (Compustat #2) between year t-1 and year t. Abnormal accruals, AA jt,, in year t are the difference between total accruals and normal accruals, TA Asset jt, jt, 1 NA jt,. Based on results in Kothari, Leone and Wasley [2002], we adjust the abnormal accruals measures for firm performance, as proxied by return on assets. Our performance-matching procedure first partitions the sample of firms in each of the 11

13 48 Fama-French industries into deciles based on the firm s prior year return on assets (ROA) defined as net income before extraordinary items divided by beginning of year total assets. Performance-adjusted abnormal accruals are calculated as the difference between firm j s AA jt, and the median value of AA jt, for its industry ROA decile, where the median calculation excludes firm j. Because both large negative and large positive performance-adjusted abnormal accruals reflect a poor mapping of earnings into cash flows, we use the absolute value of this measure, AA jt,, as our second information uncertainty metric. We calculate each metric for all firms with available data for each fiscal year We begin the sample in 1981 for two reasons. First, the requirement of seven years of data to calculate σ (νˆ ) means that 1981 is the first year for which we can include NASDAQ firms (in addition to NYSE and AMEX firms). Second, tests of post earnings announcement drift use analyst earnings forecast data. Zacks, our source for these data, is reasonably complete beginning in the early 1980s. To ensure that the earnings quality measures are available to the market, we use lagged earnings quality scores in our tests. Specifically, we assume that the earnings quality metrics are available to the market at the beginning of the fourth month following fiscal year end. Table 1, Panel A reports the number of observations in each sample year, As expected, sample sizes are smaller for σ (νˆ ) than for AA. The number of firms in the σ (νˆ ) sample ranges from about 2,200 to about 2,900 per year, with an average of 2,534 firms per year and a pooled size of 50,682 observations. For the AA sample, the number of firms ranges between about 3,000 and about 5,200 per year, with an average of 4,009 per year and a pooled size of 80,177 observations. Panel B reports descriptive information about each earnings quality metric for the pooled samples. To ensure that our results are not driven by outliers, we eliminate earnings quality metrics in the extreme 1% of the distribution; our results are not sensitive to the use or choice of outlier rules. The mean (median) value of σ (νˆ ) is.0553 (.0453), compared to.0766 (.0509) for AA. The standard deviations,.0379 for σ (νˆ ) and.0787 for AA, indicate substantial variation in earnings quality across 12

14 firms. Consistent with the longer time period needed to estimate σ (νˆ ), unreported tests show that σ (νˆ ) has less over-time variation than AA. As shown in Panel C, both Pearson and Spearman correlations between σ (νˆ ) and AA are reliably different from zero (at the.01 level). Their magnitude of suggests that the two metrics capture different constructs. 4. Empirical Tests and Results In this section, we investigate whether properties of accounting anomalies are associated with information uncertainty. We replicate prior studies tests of post earnings announcement drift, valueglamour anomalies, and the accruals anomalies for all firms with the necessary data for the period , and for the samples of firms with earnings quality metrics (section 4.1), to ascertain whether the strategies yield similar results for these securities. Section 4.2 reports tests of Hypotheses 1-3, and section 4.3 summarizes the main results. 4.1 Abnormal returns to accounting anomalies, For each accounting anomaly, we identify all observations with the necessary data to determine both the accounting signal and the subsequent return to a portfolio strategy that exploits this signal. We evaluate abnormal returns by taking long positions in the stocks ranked in the top two deciles of the distribution of the accounting signal and short positions in the stocks ranked in the bottom two deciles. 7 Appendix A discusses the construction of the accounting signals and the formation of accounting signal portfolios. Because all signals are publicly available before or at the date the portfolio is formed, the abnormal returns correspond to an implementable trading strategy. For all abnormal returns tests, we use calendar-time portfolio regressions (described next) to assess the magnitude and statistical significance of the abnormal returns. 8 7 While the differences in abnormal returns become more pronounced if we use the top and bottom decile, inferences remain unchanged. Similarly, inferences are not affected by using the top three and bottom three deciles. 8 There is a methodological debate about the best way to evaluate abnormal returns over long intervals. Kothari and Warner [1997] show that commonly used methods, such as buy-and-hold abnormal returns, are mis-specified. Fama [1998] argues that calendar-time abnormal monthly returns are strongly preferred because: (i) the portfolio variance automatically accounts for cross-correlations of abnormal returns; (ii) relative to buy-and-hold abnormal returns, 13

15 Each month m, we calculate the average abnormal return to the p = long (L) and short (S) portfolios. For the CAPM-based abnormal return, the average abnormal return equals the intercept from regressing the excess return for the p th portfolio on the excess market return for month m: CAPM CAPM pm, Fm, αp βp m εpm, R R = + RMRF + (3a) where R p,m is the return to portfolio p in month m, R F,m is the monthly risk-free rate, and RMRF m is the monthly excess market return. The three-factor abnormal return to portfolio p equals the intercept from regressing the mean excess return for the p th portfolio on the excess market return, the monthly return of a factor-mimicking portfolio for size (SMB m ), and the monthly return of a factor- mimicking portfolio for book-to-market (HML m ), where SMB and HML are formed as in Fama and French [1993, 1996]: 3f 3f pm, Fm, α p p m p m p m ε pm, R R = + b RMRF + s SMB + h HML + (3b) Finally, the CAPM and three-factor abnormal returns to the long-minus-short (LS) positions are the estimated intercepts from equations (3c) and (3d), respectively: CAPM CAPM R L RS ) m = α LS + β LS RMRFm + LS, m ( ε (3c) L S m 3 f LS ( R R ) = α + b RMRF + s SMB + h HML + ε (3d) LS m LS m LS m 3 f LS, m Table 2 shows the average monthly abnormal returns for each anomaly over (i.e., over the m=240 months comprising this interval). The columns labeled Unrestricted Sample show abnormal returns unconditional on the firm having data on the earnings quality metrics. We report the results for the Unrestricted Sample to ensure that we find the same empirical regularities as found in prior research. (Because prior studies differ in terms of time period examined as well as portfolio formation and estimation procedures, we do not seek to replicate a particular prior study s results.) The columns labeled average monthly abnormal returns are less susceptible to problems with the model of expected return; and (iii) the distribution of monthly returns is well-approximated by a normal distribution, allowing for classical statistical inference, whereas longer horizon returns are skewed, requiring special statistical corrections. While Loughran and Ritter [2000] argue that calendar-time abnormal monthly returns have low power, Mitchell and Stafford [2000] show that monthly calendar-time regressions have sufficient power to detect economically interesting abnormal returns, and have more power than statistically-corrected buy-and-hold returns. Based on the extant evidence, we use calendar-time portfolio regressions based on monthly returns because this procedure is more robust to methodological concerns than alternative procedures. 14

16 σ (νˆ ) Sample and AA Sample show abnormal returns for the observations where we also have data on the noted earnings quality metric (Restricted Samples). Predictably, all of the trading strategies show negative abnormal returns to the short positions and positive abnormal returns to the long positions. Both CAPM and three-factor abnormal returns to the long-minus-short strategy are significantly positive (at the.01 level), and three-factor abnormal returns are smaller in absolute value than CAPM abnormal returns. In general, the profitability of the trading strategies for the Restricted Samples is smaller than the profitability for the Unrestricted Sample. Hereafter, results for an anomaly or strategy (we use these phrases interchangeably) refer to the abnormal return of the long-minus-short position unless explicitly noted. Turning first to the post earnings announcement drift anomalies (Panel A), we document abnormal returns to the analyst specification of bp per month or 8-9% on a yearly basis, for the Unrestricted Sample. Abnormal returns for the seasonal random walk (SRW) specification are bp per month, or 11-12% annualized. For the Restricted Samples, CAPM and three-factor abnormal returns are, respectively, bp and bp for the analyst specification versus bp and bp for the SRW-specification. These returns are roughly similar to those documented in prior studies. For example, Bernard and Thomas [1990, Table 2] report an 8.6% four-quarter cumulative abnormal return for the period , and in the 1990 s, Johnson and Schwartz [2000] find that the four-quarter cumulative abnormal return declined to about 5.7%. Abarbanell and Bernard [1992] report significant abnormal returns in two quarters using an analyst specification, with the combined abnormal return being about 6%. Abnormal returns to the value-glamour anomalies (Panel B) are highest for the book-to-market specification, where, for the Unrestricted Sample, we document CAPM abnormal returns of 159 bp per month (19.1% per year) and three-factor abnormal returns of 96 bp per month (11.5% per year). 9 For the Restricted Samples, the one-factor and three-factor returns are bp and bp, respectively. 9 Our finding of significant three-factor-based abnormal returns to the book-to-market strategy is consistent with prior research which documents significant abnormal returns to extreme book-to-market portfolios even when a three-factor model (which includes a book-to-market factor) is used as the benchmark for expected returns (e.g., Fama and French [1993, 1997], Mitchell and Stafford [2000]). 15

17 The cash flow-to-price and earnings-to-price specifications show CAPM abnormal returns for the Unrestricted Sample ranging between bp per month (11.8%-13.6% per year) and three-factor abnormal returns of bp per month (7.1%-7.6% per year). For the Restricted Samples, CAPM abnormal returns range between bp, and three-factor abnormal returns between bp. These returns are similar to the annualized value-glamour abnormal returns (CAPM) reported by Lakonishok, Schleifer and Vishny [1994] for the period : 7.6% for earnings-price (5.4% size-adjusted); 11% for cash flow-to-price (8.8% size-adjusted); and 10.5% for book-to-market (7.8% size-adjusted). 10 Finally, for the accruals anomalies (Panel C), the Unrestricted Sample shows abnormal returns of bp per month for the total accruals strategy, and similar results for the abnormal accruals strategy. The accrual-based abnormal returns calculated for the Restricted Sample are similar to those for the Unrestricted Sample (the range is bp per month). On an annualized basis, the abnormal return to both the total accruals and abnormal accruals strategies (for both the Restricted and Unrestricted Samples) is about 9-10%, and is similar to the 10.4% return documented by Sloan [1996] for the total accruals strategy and to the 11% documented by Xie [2001] for the abnormal accruals strategy Tests of Hypotheses 1-3 Our analysis of whether information uncertainty is associated with accounting anomalies begins by examining whether information uncertainty is concentrated in the extreme deciles of the ranked distribution of the signal underlying each accounting anomaly (Hypothesis 1). Specifically, each month we calculate the mean value of the earnings quality metrics for securities within each anomaly decile as well as the difference between extreme and non-extreme deciles. Table 3 reports the over-time average of the 240 mean values of σ (νˆ ) and AA by anomaly decile, and Figures 1a and 1b illustrate these data for SRW-PEAD and cash flow-to-price. In all cases, 10 There are numerous differences in how studies implement value-glamour strategies. For example, similar to Lakonishok, Schleifer and Vishny [1994], we exclude observations where the accounting signal (earnings, cash flows, book value of equity) is negative; it is not always clear how other studies treat these observations. As another example, our dynamic portfolio formation technique updates the accounting signals as of the fourth month following each firm s fiscal year end; other studies update only at a particular calendar month (Lakonishok et al. update in April; Fama and French [1992] update in June). 16

18 we document a U-shaped pattern: stocks in the extreme anomaly deciles have poorer earnings quality than stocks in the moderate deciles. The rightmost columns of Table 3 report comparisons of the mean earnings quality of deciles 1, 2, 9 and 10 (the extreme portfolios) with the mean earnings quality of deciles 3-8 (the moderate portfolios). To control for cross-sectional dependence across observations in a given month, the statistical significance of this difference is based on the standard error of the time series of 240 monthly differences. In all cases, the difference in earnings quality is significantly positive, with t- statistics exceeding 18. The U-shaped relation between AA and signed abnormal accruals, AA, is expected, given that extreme values of signed abnormal accruals are also likely to be extreme values of AA. The issue is whether the constructs underlying the two measures are distinct or overlapping. In unreported tests, we find that the pairwise correlations between our proxies for information uncertainty, σ ( ˆ ν ) and AA, and the accruals signals that form the basis for the total accruals and abnormal accruals anomalies are reliably different from zero and small in magnitude: no correlation exceeds.10. Given this result, we conclude that our measure of earnings quality does not map directly into the accrual signals. To assess the sensitivity of the t-statistics in Table 3 results to time-series dependence, the rightmost column of Table 3 reports the number of months (out of 240) where a single-period crosssectional t-test shows that the mean earnings quality of the extreme portfolios is significantly poorer (as indicated by a t-statistic exceeding 1.96) than that of the moderate portfolios. In all but one combination of anomaly and earnings quality metric, we find that at least 80% of the months have significant t- statistics; 11 in 11 of the 14 combinations considered, there are 238 or more months (over 99%) with t- statistics in excess of To examine whether the greater information uncertainty in the extreme deciles is pervasive across the securities in these portfolios, we begin by ranking observations from smallest to largest based on each 11 The exception is the analyst-based PEAD strategy using AA where we find significant t-statistics in 147 of 240 months (61.2%). In unreported tests, we find that the number of months where this difference is positive (but not necessarily statistically significant) is

19 earnings quality metric: the Good portfolio (deciles 1 and 2) contains the best earnings quality stocks, while the Poor portfolio (deciles 9 and 10) contains the worst earnings quality stocks. We then examine the frequency of Good versus Poor earnings quality securities within each of the extreme anomaly portfolios. That is, we form the following matrix for each anomaly: Good Earnings Quality Poor Earnings Quality Short position Short/Good Short/Poor Long position Long/Good Long/Poor Long-minus-Short Long-Short/Good Long-Short/Poor Because we rank on earnings quality independent of the trading strategy that is, we do not rank on earnings quality within each of the long and short positions the cell counts of the matrix are not forced to be equal, as would be the case if we ranked on earnings quality within each of the positions. 12 Table 4 reports summary information about the mean number and percentage of securities in each of the long and short positions classified as Good and Poor earnings quality. If earnings quality is randomly distributed across the anomaly deciles, 20% of all securities within each quintile will be Good earnings quality and 20% will be Poor earnings quality. Table 4 reports results of tests of the prediction that within the extreme anomaly quintiles, the incidence of Poor earnings quality securities is greater than the incidence of Good earnings quality securities; in unreported tests, we also test whether the incidence of Poor (Good) quality securities is generally greater (less) than the expected frequency of 20%. Similar to Table 3, statistical significance is based on the time series of 240 monthly differences. The results (both reported and unreported) are generally consistent with predictions, although there are exceptions. In terms of the PEAD strategies, the results show that the extreme portfolios of the SRW-PEAD anomaly contain an average of 14-18% Good earnings quality securities (depending on the earnings quality metric), compared to a mean of 23-27% Poor earnings quality securities, differences 12 While the unbalanced design leads to greater within-cell cross-sectional variation in earnings quality, which increases the power of our tests, it also leads to small cell sizes (and, therefore low power) when the partitioning variable (in this case, the earnings quality metric) is correlated with the anomaly. The unbalanced design results in average sample sizes of at least 33, except for the ranking of AA for the abnormal accruals strategies where we observe means of 10 and 13 observations of Good earnings quality firms in the short and long positions, respectively. In subsequent tests, we assess the sensitivity of our results to a balanced design, where we rank securities on earnings quality within each position. 18

20 significant at the.01 level or better. Similarly, the short position of the analyst-pead anomaly contains 15-18% Good quality firms and 25-27% Poor quality firms; differences significant at the.01 level. Contrary to our prediction, the analyst-pead anomaly results for extreme positive earnings surprises indicate significantly (at the.01 level) more Good earnings quality firms in the extreme portfolios (22-23% Good earnings quality securities versus 19-20% Poor earnings quality securities). Within the extreme value-glamour portfolios, Poor earnings quality securities are usually disproportionately represented, and Good earnings quality securities are usually underrepresented, consistent with our prediction; differences are highly significant. Two exceptions occur for the AA sample. First, Poor earnings quality securities comprise 18% of the largest earnings-to-price ratio portfolios, significantly (at the.01 level) less than the fraction of Good quality securities (22%). Second, firms with the highest book-to-market ratios have a larger than predicted proportion of good earnings quality firms (21%) and a smaller than predicted proportion of Poor earnings quality firms (16%), difference significant at the.01 level. Finally, there is no difference in proportions (about 22%) between Good and Poor quality firms for the largest earnings-to-price ratios for the σ ( ˆ ν ) sample. As noted earlier, the frequency of Good versus Poor earnings quality securities is related by construction to the accruals strategies when AA is used as the earnings quality metric, so the high (low) frequency of Poor (Good) earnings quality securities in the extreme portfolios of the total accruals and abnormal accruals anomalies is not surprising (Panel C). The poorest earnings quality securities dominate both the long and the short positions of the total accruals anomaly and the abnormal accruals anomaly: 42-48% of the securities comprising the extreme portfolios of these anomalies are classified as having Poor earnings quality, compared to only 1-7% Good earnings quality (differences significant at the.01 level). That is, regardless of the sign of the accruals signal, large values of accruals are associated with poor earnings quality (and, therefore, greater information uncertainty). On the whole, we believe the results in Tables 3 and 4 provide strong and consistent evidence that information uncertainty is concentrated in extreme portfolios formed on the basis of signed realizations of 19