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 performance-adjusted abnormal accruals from a modified Jones [1991] model. Over 1982-2001, 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 * Corresponding author: Fuqua School of Business, Duke University, Durham, NC 27708. Email address, jfrancis@duke.edu. 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.

Accounting Anomalies and Information Uncertainty 1. Introduction

This study investigates whether proxies for information uncertainty explain several well-

documented 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

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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

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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 107-120 basis points (bp) per month for the Poor securities

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versus 16-21 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 53-93 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 five-

year firm-specific CAPM and three-factor asset pricing regressions over 1982-2001. These perfect-

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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 82-118 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

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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.

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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).

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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 value-glamour 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.

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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-minus-

short 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.

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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

, , 1 , ,0 1 2 3 ,

, , ,

j t j t j t j tj t

j t j t j t j t

TCA CFO CFO CFOAssets Assets Assets Assets

1

,φ φ φ φ−= + + + +ν+

,

(1)

where TCA = firm j’s total current accruals in year t, ; tj , , , ,( )j t j t j t j tCA CL Cash STDEBT= ∆ − ∆ − ∆ + ∆

,j tAssets

j tCA∆ −

= firm j’s average total assets in year t and t-1; CFO = firm j’s cash flow from operations in

year t, CFO ; TA = firm j’s total accruals in year t, measured as

;

tj ,

, tjCA ,

tjtjtj TANIBE ,,, −=

, , ,j t j tCL Cash STD∆ − ∆ + ∆

tj ,

EBT ,( )j t j tDEPN− ∆ = firm j’s change in current assets

(Compustat #4) between year t-1 and year t; tjCL ,∆ = firm j’s change in current liabilities (Compustat

#5) between year t-1 and year t; = firm j’s change in cash (Compustat #1) between year t-1 and

year t; = firm j’s change in debt in current liabilities (Compustat #34) between year t-1 and

tjCash ,∆

tjSTDEBT ,∆

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.

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year t; = firm j’s depreciation and amortization expense (Compustat #14) in year t; =

firm j’s net income before extraordinary items (Compustat #18) in year t.

tjDEPN , tjNIBE ,

,

j t

j t

TAAsset

,j tAsset −

,j tRev∆

tjPPE ,

, 11

Asset

These estimations yield firm- and year-specific residuals, which form the basis for the first

information uncertainty metric, )ˆ( ,tjνσ . )ˆ( ,tjνσ is the rolling five-year standard deviation of firm j’s

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 )ˆ( ,tjνσ is limited to firms with seven years of data.

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:

,1 2 3

1 , 1 , 1 , 1

1 j,t j tj t

j t j t j t

Rev PPEAsset Asset Asset

κ κ κ− − − −

∆= + + (2) ,

,ε+

where = firm j’s total assets (Compustat #6) at the beginning of year t, 1

= 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),

, ,2 3

, 1 , 1 , 1

( )ˆ ˆ ˆj t j t j t

j tj t j t j t

Rev AR PPENA

Asset Assetκ κ κ

− −

∆ − ∆= + + , where ,j tAR∆ = firm j’s change in accounts

receivable (Compustat #2) between year t-1 and year t. Abnormal accruals, , in year t are the

difference between total accruals and normal accruals,

,j tAA

,

, 1

j t

j t

TA,j tNA

Asset −

− . 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

,

−

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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 and the median value of

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,

,j tAA ,j tAA

,j tAA , as our second information uncertainty metric.

ˆ(νσ

We calculate each metric for all firms with available data for each fiscal year 1981-2000. We

begin the sample in 1981 for two reasons. First, the requirement of seven years of data to calculate )

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, 1981-2000. As

expected, sample sizes are smaller for )ˆ(νσ than for |AA|. The number of firms in the )ˆ(νσ 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 )ˆ(νσ is .0553 (.0453), compared to .0766 (.0509) for |AA|. The standard

deviations, .0379 for )ˆ(νσ and .0787 for |AA|, indicate substantial variation in earnings quality across

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firms. Consistent with the longer time period needed to estimate )ˆ(νσ , unreported tests show that )ˆ(νσ

has less over-time variation than |AA|. As shown in Panel C, both Pearson and Spearman correlations

between )ˆ(νσ and |AA| are reliably different from zero (at the .01 level). Their magnitude of 0.33-0.34

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, value-

glamour anomalies, and the accruals anomalies for all firms with the necessary data for the period 1982-

2001, 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, 1982-2001

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,

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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

p m F m p p m p mR R RMRFα β ε− = + + (3a)

where Rp,m is the return to portfolio p in month m, RF,m is the monthly risk-free rate, and RMRFm 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 (SMBm), and the monthly return of a factor- mimicking portfolio for

book-to-market (HMLm), where SMB and HML are formed as in Fama and French [1993, 1996]:

3 3, , ,

f fp m F m p p m p m p m p mR R b RMRF s SMB h HMLα ε− = + + + + (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:

CAPMmLSmLS

CAPMLSmSL RMRFRR ,)( εβα ++=− (3c)

f

mLSmLSmLSmLSf

LSmSL HMLhSMBsRMRFbRR 3,

3)( εα ++++=− (3d)

Table 2 shows the average monthly abnormal returns for each anomaly over 1982-2001 (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

“ )ˆ(νσ 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 69-75 bp per month or 8-9% on a yearly basis, for the

Unrestricted Sample. Abnormal returns for the seasonal random walk (SRW) specification are 96-102 bp

per month, or 11-12% annualized. For the Restricted Samples, CAPM and three-factor abnormal returns

are, respectively, 57-76 bp and 49-68 bp for the analyst specification versus 73-96 bp and 69-90 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 1974-1986, 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 102-138 bp and 58-83 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

The cash flow-to-price and earnings-to-price specifications show CAPM abnormal returns for the

Unrestricted Sample ranging between 98-113 bp per month (11.8%-13.6% per year) and three-factor

abnormal returns of 59-63 bp per month (7.1%-7.6% per year). For the Restricted Samples, CAPM

abnormal returns range between 59-109 bp, and three-factor abnormal returns between 31-62 bp. These

returns are similar to the annualized value-glamour abnormal returns (CAPM) reported by Lakonishok,

Schleifer and Vishny [1994] for the period 1968-1990: 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

77-80 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 63-81 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.

4.2. 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 )ˆ(νσ 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

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

ˆ(

. 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 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 cross-

sectional 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 1.96.

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 214.

17

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

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 ˆ( )σ 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

accounting signals (Hypothesis 1). That is, regardless of whether the accounting signal is adverse or

favorable, extreme values of the signal are associated with poor information quality.

Our tests of Hypothesis 2 examine the abnormal returns to securities classified as Good versus

Poor earnings quality in each long, short, and long-minus-short position. We predict that positions in

Poor earnings quality securities generate larger (in magnitude) returns than positions in Good quality

securities. Table 5 shows the mean CAPM and three-factor abnormal returns to Good and Poor earnings

quality securities in each of the long, short and long-minus-short positions of each anomaly; these

abnormal returns are based on calendar-time portfolio regressions (similar to Table 2, equations 3a-d)

estimated separately for Good and Poor earnings quality securities. We also examine the difference in

long-minus-short abnormal returns between Poor and Good earnings quality securities (PG), as captured

by the intercepts in equations (3e-f):

, , ,( ) ( )Poor Good CAPM CAPML S m L S m LS PG LS PG m LS PG mR R R R RMRFα β ε− − − = + + ,

,

(3e)

3 3, , , , ,( ) ( )Poor Good f f

L S m L S m LS PG LS PG m LS PG m LS PG m LS PG mR R R R b RMRF s SMB h HMLα ε− − − = + + + + (3f)

For the PEAD strategies (Panel A) we find the long-minus-short position to the analyst-

specification earns 10-38 bp per month (depending on the earnings quality metric and the model of

expected returns) for the Good earnings quality portfolio, while the Poor earnings quality portfolio earns

93-128 bp per month; the 56-114 bp per month difference is significant at the .03 level or better (one-

sided). The SRW specification earns 49-63 bp per month for the Good earnings quality portfolio

(depending on the earnings quality metric), compared to 74-126 bp per month for the Poor earnings

quality portfolio. Differences for the |AA| sample of 63 bp (CAPM) and 75 bp (three-factor) are

significant at the .01 level. Differences for the ˆ( )σ ν sample, of 25 bp (both CAPM and three-factor), are

not reliably different from zero at conventional significance levels.

For the value-glamour strategies (panel B), abnormal returns to the book-to-market strategy are

101-176 bp for Poor earnings quality versus 5-108 bp for Good earnings quality. The difference of 66-

115 bp per month is significant at the .01 level. For the cash flow-to-price and earnings-price

20

specifications, monthly abnormal return differences are about 51-86 bp, and results are significant at the

.01 level when earnings quality is measured by |AA|. Abnormal return differences are less pronounced,

both in terms of magnitude and statistical significance, when earnings quality is measured by ˆ( )σ ν (the

three-factor earnings-price anomaly difference is insignificantly different from zero; the other differences

range from 28 to 38 bp, with associated p-values of .05-.12).

Results for the total accruals anomaly (Panel C) show larger abnormal returns to Poor earnings

quality securities than to Good earnings quality securities; differences are 58-85 bp per month, significant

at the .03 level or better. Results for the abnormal accruals strategy indicate no statistically reliable

differences between the returns to Good and Poor quality securities, although the point estimates of

differences range between 5 and 81 bp per month.

To assess whether the results for the abnormal accruals strategy are due to large standard

deviations in abnormal returns, because of small sizes for the Good earnings quality cells (see Table 4,

Panel C), we repeat the analyses in Table 5 using a balanced design. The balanced design ranks

observations within each anomaly decile based on earnings quality and forces 10% of the securities in

each anomaly decile into each earnings quality decile. While this approach ensures that no cell has too

few observations to meaningfully estimate the abnormal return, it may also induce cross-sectional

differences in earnings quality where none exist; this biases against finding differences between the

abnormal returns to Good and Poor earnings quality securities.

Results of the balanced design, reported in Table 6, are similar to the results reported in Table 5.

We continue to find, for the PEAD, value-glamour and total accruals anomalies, that within the extreme

portfolios Poor earnings quality stocks tend to earn larger long-minus-short abnormal returns than Good

earnings quality stocks, and results continue to be stronger for the |AA| sample. The balanced design has

little effect on the results for the abnormal accruals anomaly, except to reduce the point estimates of the

difference in abnormal returns between Poor and Good securities.

Overall, we believe the results in Tables 5 and 6 are broadly consistent with second hypothesis,

which posits a positive relation between information uncertainty and returns to accounting anomalies.

21

Results are not sensitive to the use of CAPM versus three-factor returns as the benchmark, but some

results are stronger when earnings quality is measured by absolute abnormal accruals.

Information uncertainty also implies over-time patterns in abnormal returns. Specifically, the

difference in abnormal returns between Poor and Good securities should diminish over time as the

information uncertainty about Poor quality stocks is resolved (Hypothesis 3). This prediction is related to

Freeman and Tse’s [1989] finding, in the context of post earnings announcement drift, of price reactions

to subsequent news that directionally confirms the initial earnings signal. In contrast to Freeman and Tse,

we do not specify how information uncertainty is resolved; rather, we posit cross-sectional differences in

over-time abnormal returns behavior because uncertainty is resolved to different extents for Poor versus

Good quality securities.

Figure 2 illustrates this hypothesis (and preliminarily indicates its empirical validity) for the

book-to-market strategy, using the CAPM as the model of expected returns and the |AA| measure of

earnings quality. The Y-axis represents the monthly abnormal return to the long-minus-short position and

the X-axis represents the period (month) after the portfolio is formed (recall that the portfolio is formed in

month 0 when the signal is first known). The graph shows how the monthly abnormal return to a

portfolio evolves over time, as one moves further and further away from the portfolio formation date.

The abnormal returns to Poor securities (top line in Figure 2) trend downward much more sharply than

the abnormal returns to Good securities (bottom line). The trend line for Poor securities converges to the

trend line for Good securities about 21 months after portfolio formation.

To formally test Hypothesis 3, we first calculate abnormal returns to the Good and Poor quality

securities for the long-minus-short position of each anomaly over h periods beyond the portfolio

formation date. We denote the CAPM-based abnormal returns to Poor and Good securities in each

position as and , respectively; three-factor abnormal returns are denoted

and . The subscript h indexes each non-overlapping period, measured relative

to the date the portfolio is formed; for the post earnings announcement drift strategies, we set h=1,2,…,12

, (CAPMLS h Poorα

) 3,

fLS hα

) ), (CAPMLS h Goodα

)3, (f

LS h Poorα (Good

22

quarters, and for the value-glamour and accruals strategies, we set h=1,2,…,36 months. For example, for

the PEAD strategies, is the mean monthly CAPM abnormal return to Poor securities in the

third quarter (months 7-9) following the portfolio formation quarter.

, 3 (CAPMLS h Poorα =

, ( )fLS h Good

, ,( ) (CAPMLS h Goodα−

)

)

)

Relative to Poor earnings quality securities, there is less information uncertainty to be resolved

for Good earnings quality stocks; therefore, we expect the abnormal returns to Good securities,

or , to decline slightly, or to remain constant, as h increases.13 In contrast,

we expect the abnormal returns to Poor securities, or , to decline as h

increases. That is, we expect abnormal returns to Poor securities to diminish as the portfolio formation

date becomes more distant, so that Poor securities’ abnormal returns converge to Good securities’

abnormal returns. We predict that the difference between Poor and Good quality securities’ abnormal

returns, or , declines as h increases. Results of

tests of these predictions are reported in Table 7, where we report coefficient estimates and t-statistics

associated with regressions of anomaly abnormal returns to Poor securities, Good securities, and the

difference, Poor-Good, on h.

, ( )CAPMLS h Goodα

CAPMLS h

3α

or

, ( )CAPMLS h Poorα

3, ( ) (f

LS hor Gα−

3, (f

LS h Poorα

)Poα 3,

fLS h Po oodα

Although the statistical power of this test is limited by the small number of observations (12

observations for PEAD and 36 for the other anomalies), the results are generally consistent with

Hypothesis 3. In particular, for the analyst-based PEAD strategy, the results show that the abnormal

returns difference between Poor and Good earnings quality securities decreases over time at a rate of

between 6 and 16 bp per quarter, significant at the .06 level or better. This diminishing difference is due

to a reliably negative trend for Poor earnings quality securities’ abnormal returns, whereas there is no

detectable trend in Good earnings quality securities’ abnormal returns. Results for the SRW specification

of PEAD are inconclusive: while the point estimates indicate that the Poor minus Good difference

diminishes over time, the effect is not significant at conventional levels.

13 Results in Tables 5 and 6 show that that the abnormal returns to Good quality securities, while significantly smaller in magnitude than the abnormal returns to Poor quality securities, are still generally reliably different from zero.

23

Results for the book-to-market, cash flow-to-price and earnings-price anomalies (Panel B) are

consistent with Hypothesis 3. While abnormal returns to both Good and Poor quality securities tend to

decrease, in all cases the abnormal returns to Poor quality securities decrease more sharply; t-statistics for

the coefficient from regressing the Poor – Good difference on h range from -3.55 to -13.22. Finally,

results for the accruals anomalies (Panel C) are consistent with Hypothesis 3, except for the |AA| sample

in the abnormal accruals strategy. In the total accruals strategy, Good securities’ abnormal returns are

either flat or increasing and Poor securities returns are decreasing at about 2 bp per month; the difference

is decreasing at 2-3 bp per month (significant at the .01 level). For the abnormal accruals strategy, the

Good - Poor difference shows a significant (at the .01 level) decrease over time for the ˆ( )σ ν sample,

whereas there is no evidence of convergence for the |AA| sample.

4.3. Summary of results

Overall, the results in Tables 3-7 suggest an association between information uncertainty and

returns to accounting-based trading strategies. Consistent with Hypothesis 1, we find that the extreme

portfolios formed on signed magnitudes of accounting signals are characterized by significantly worse

average earnings quality and, in most cases, a disproportionate percentage of poor earnings quality

securities. Consistent with Hypothesis 2, we find that within a given anomaly portfolio, poor earnings

quality securities generally generate significantly larger abnormal returns than good earnings quality

securities; these results are stronger and more consistent when we measure earnings quality based on

absolute abnormal accruals. Finally, consistent with greater resolution of information uncertainty for

poor quality securities (Hypothesis 3), we find a declining difference between Poor and Good abnormal

returns, as the magnitude of the abnormal returns to Poor securities converges to that of Good securities.

5. Extension: Perfect Foresight Measure of Abnormal Returns

Our tests so far have conditioned on specific accounting-based trading strategies, because we

believe that information uncertainty should have the greatest consequences for returns to these strategies.

In this section, we conduct unconditional tests to investigate whether earnings quality is associated with

24

firm-specific abnormal returns estimated from the CAPM and the three-factor model. We term the

abnormal returns implied by the intercepts from these models perfect foresight abnormal returns because

information about the sign and magnitude of the intercepts is known only with hindsight. This analysis

permits investigation of the effects of information uncertainty on a larger sample of firms than is available

for any of the implementable trading strategies considered in section 4, and abstracts from any effects that

arise from the selection and implementation of specific accounting-based trading strategies.

We estimate CAPM and three-factor returns regressions, where the intercept in each regression

constitutes the measure of abnormal return for firm j in month m:

CAPMmjmj

CAPMjmFmj RMRFRR ,,, εβα ++=− (4a)

3, , , , . ,

3,

f fj m F m j m j m m j m m j m m j mR R b RMRF s SMB h HMLα ε− = + + + + (4b)

Equations (4a) and (4b) are estimated every month, January 1982 to December 2001, on a firm-

specific basis.14 We use rolling 60-month windows (so, for example, the January 1982 regression uses

returns data from 1977 and onwards), and we require a minimum of 24 monthly returns. The estimations

are performed for all firms with available data on at least one of the earnings quality metrics. Estimation

of equations (4a) and (4b) produces firm-specific estimates of monthly abnormal returns (monthly alphas)

for each of the 240 months in the sample period. Table 8, panel A reports summary information on the

distributions of the monthly alphas for each earnings quality sample. For the ˆ( )σ ν sample, the mean

(median) CAPM monthly abnormal return is -33bp (-15 bp), compared to -34 bp (-22 bp) for the three-

factor regression. For the |AA| sample, the abnormal returns are more negative: the mean (median) value

of is –64 bp (-35 bp), compared to -52 bp (-33 bp) for CAPMα 3 fα .

To determine whether extreme abnormal returns are associated with greater information

uncertainty, we rank firms each month into deciles based on their abnormal return estimate. Decile one

(ten) contains firms with the most negative (positive) values of (or CAPMα 3 fα ). For each decile, we

14 Firm-specific estimations of the CAPM or three-factor pricing regression are inherently noisy. This noise should, if anything, bias against finding associations between perfect foresight abnormal returns and information uncertainty.

25

calculate the mean value of each earnings quality metric. If information uncertainty is higher for firms

with extreme abnormal returns, we expect to observe the same U-shaped relation in the earnings quality

measures across the and CAPMα 3 fα deciles as observed across the anomaly deciles (documented in

Table 3). That is, we expect the most extreme abnormal returns deciles to show the poorest earnings

quality (high values of ˆ( )σ ν and |AA|) and we expect moderate abnormal returns deciles to show better

earnings quality (low values ˆ)(σ ν and |AA|). The results, tabulated in Panel B of Table 8, and graphed in

Figure 3, show a U-shaped relation between abnormal returns and earnings quality. The two rightmost

columns of Panel B show the difference between the mean earnings quality of the extreme deciles (1,2,9,

and 10) and the moderate deciles (3-8). In all cases, the difference in earnings quality is significantly

positive, with t-statistics exceeding 47.

CAPMm

mj ,

CAPMm +

fmb3+

EQ

j3,ζ+

b

EQ

CAPM 3 fα

Panel C, Table 8 provides a regression-based test of the effect of information uncertainty on the

magnitude of abnormal return. Specifically, we regress the absolute value of firm j’s estimated alpha in

month m on its earnings quality signal, { }ˆ( ),EQ AAσ ν∈ , for month m:

(5a) CAPMmjmj

CAPMmj a ,,, || ζα +=

(5b) f

mf

mfmj a33

, ||α =

Estimation of equation (5a) or (5b) produces m=240 monthly estimates of and . Panel C reports the

mean of these 240 parameter estimates; t-statistics are based on the standard errors of the time series. The

results show that

ma mb

α and are positively related to each of the earnings quality metrics, with t-

statistics exceeding 68. Panel C also reports the results of decile rank regressions, where we substitute the

decile rank of earnings quality for the raw earnings quality score in equations (5a-b). The coefficient

estimate on the decile rank of earnings quality represents the average difference in absolute abnormal

returns for firms in adjacent earnings quality deciles. Depending on the underlying model (CAPM or

three-factor), this difference is between 8.1 and 11.8 bp per month (significant at the .01 level). For firms

26

in the worst versus the best earnings quality deciles (i.e., D10 versus D1), these estimates correspond to

differences in absolute abnormal returns of 81-118 bp per month, or about 10%-14% per year.

In unreported tests, we repeat the tests in Table 8 on the roughly 15% of the sample estimates of

(or CAPMα 3 fα ) that are reliably different from zero at the 10% level, i.e., firms that have statistically

significant abnormal returns. The results are similar or stronger than those reported in Table 8.

Overall, the results indicate that perfect foresight abnormal returns, as estimated from firm-

specific CAPM and three-factor regressions, are associated with information uncertainty. Firms with the

extreme abnormal returns (positive or negative) have systematically poorer earnings quality than firms

with moderate or no abnormal returns. These results, which are not conditional on the choice and

implementation of accounting-based trading strategies, indicate that information uncertainty is a pervasive

determinant of abnormal returns in the general cross-section of firms.

6. Additional Tests

We perform numerous sensitivity checks on the results. Because none of these tests has a

qualitative effect on the results, we summarize, but do not tabulate, the findings from each analysis.

Briefly, we obtain similar results using other measures of earnings quality, including the absolute value of

firm-specific Dechow-Dichev regression residuals, non-performance matched abnormal accruals, and

matched and non-matched abnormal current accruals.

We also explore the relation between our measures of information uncertainty and firm size,

known to be inversely associated both with ˆ( )σ ν (Dechow and Dichev [2002]) and with returns to some

of the accounting-based trading strategies (e.g., Bernard and Thomas [1989]). Concerning prior studies’

finding that smaller firms have larger anomalous returns, we note that we obtain similar inferences if we

use abnormal returns based on the three-factor model, which includes a size-mimicking factor (SMB) as a

control variable. Second, our requirement of seven years of data to estimate ˆ( )σ ν effectively eliminates

young (small) firms from the sample used in tests based on this metric. Finally, and as check on these

27

arguments, we repeat our tests after partitioning the sample into thirds based on firm size (our results are

not sensitive to using total assets, sales revenues or market value of equity as the proxy for firm size). We

find no evidence that results are driven by small firms. Specifically, the U-shaped pattern in information

uncertainty measures across anomaly deciles is observed (with similar statistical significance) for small,

medium and large firms for all anomalies. In addition, differences in long-minus-short abnormal returns

between the Good and Poor securities of the extreme anomaly deciles are not confined, nor are they

necessarily the largest for, small firms.

It is also unlikely that our measures of information uncertainty proxy for growth. If they did, we

would observe linear, not U-shaped, patterns in the information uncertainty measures across portfolios

ranked on the value-glamour variables (such as book-to-market, which is often used as a proxy for

growth). Further, the pairwise correlations between our proxies for information uncertainty and proxies

for growth, other than value-glamour ratios (such as five-year compounded annual growth in sales

revenues or in book values of equity) are small (Pearson correlations are less than 0.01 in magnitude, not

reported). Such small correlations are inconsistent with the view that information uncertainty is a

manifestation of prior studies’ finding of larger drifts in stock prices for stocks with high past growth

(Lakonishok, Shleifer and Vishny [1994]).

As an additional test, we probe a possible link between our finding of high concentrations of

information uncertainty in the extreme anomaly portfolios and Bartov, Radhakrishnan and Krinksy’s

[2000] finding that firms with high levels of institutional holdings (their proxy for investor sophistication)

exhibit smaller post earnings announcement drift than firms with low levels of institutional holdings.

Specifically, while they find that institutional holdings are negatively correlated with PEAD abnormal

returns, further tests of the construct validity of institutional holdings as measure of investor

sophistication yield mixed results. One interpretation of their results is that it is not investor

sophistication per se that affects the profitability of the drift strategy, but rather some other factor which is

negatively associated with institutional holdings and positively associated with PEAD. Given our finding

that information uncertainty is positively associated with PEAD, we investigate whether information

28

uncertainty is also negatively related to institutional holdings. From Spectrum, we collect annual data on

the percent of outstanding shares held by institutions and the number of institutions that own stock in our

sample firms. We find that both measures of institutional holdings are negatively correlated with our

earnings quality metrics, with correlations ranging from -0.13 to -0.41 (significant at the .01 level).

In summary, our results are not driven by the choice or specification of the proxy variables for

information uncertainty, nor are the results driven by these proxies capturing firm size or growth effects.

In addition, as documented in the tables, our results are not sensitive to using the CAPM or the three-

factor model as the benchmark for expected returns.

7. Summary and Conclusions

A substantial body of work in accounting and finance documents long-term abnormal returns

following publicly-available accounting signals. Research characterizes these returns as anomalous

because implementable trading strategies can be developed to exploit these signals. While there is debate

about the proper risk adjustment for evaluating the profitability of such strategies, all of the strategies we

investigate (post earnings announcement drift, value-glamour, and accruals strategies) yield significant

abnormal returns as measured against the CAPM or the three-factor model. We link these abnormal

returns to predictions derived from structural uncertainty models (Brav and Heaton [2002]) and rational

expectations models (Easley and O’Hara [2001]). We argue that both types of models are consistent with

predictions that properties of and returns to accounting anomalies can be explained, partially or wholly,

by information uncertainty. We proxy for information uncertainty by the degree to which earnings map

into fundamentals; weak mappings imply poor quality earnings (high information uncertainty), while

strong mappings imply good earnings quality (low information uncertainty).

Examination of the characteristics of accounting anomaly portfolios shows that the extreme

portfolios of the ranked accounting signals have significantly worse average earnings quality, and a

significantly greater incidence of securities with poor earnings quality, than do non-extreme portfolios.

Conditioning on earnings quality, we find that abnormal returns to trading strategies that take positions in

29

these extreme anomaly portfolios are significantly larger for poor earnings quality securities than for good

earnings quality securities. That is, within the portfolios shown to generate significant abnormal trading

returns, a substantial portion of the abnormal return is concentrated in stocks with high information

uncertainty.

We further predict that the abnormal returns associated with accounting signals that are extreme

in magnitude and poor in quality should diminish over time, as the uncertainty about the information

signal is resolved. Holding the anomaly portfolio constant and increasing the time past the formation of

the portfolio, we expect the abnormal returns to high information uncertainty securities to approach those

of low information uncertainty securities. Consistent with this hypothesis, we find that the abnormal

returns to poor quality securities diminish, usually converging in magnitude to those of good quality

securities over the 36 months following the formation of the portfolios.

Finally, we examine the association between information uncertainty and perfect foresight

abnormal returns, as measured by firm-specific intercepts (alphas) estimated from CAPM and three-factor

pricing regressions. These tests allow us to draw inferences about a broader cross-section of firms,

unconditional on the effects of both specific choices of trading strategies and specific implementation

choices. Similar to the accounting anomaly portfolios, we observe a U-shaped relation between the

alphas and our proxies for information uncertainty: stocks with the most negative and most positive

alphas have significantly poorer average earnings quality than stocks with non-extreme alphas. Further,

regressions of the absolute value of alpha on earnings quality shows that securities with poor quality

earnings have significantly larger absolute alphas than do firms with good earnings quality.

Taken as a whole, the results indicate that abnormal returns are systematically associated with

measures of the quality of the firm’s accounting information—that is, with information uncertainty. A

minimal interpretation of our main result – that exploitation of accounting signals requires taking

positions in securities with high information uncertainty – is that accounting anomalies do not represent

riskless arbitrage opportunities despite yielding predictable abnormal returns. Together with prior

researchers’ finding that investors price information uncertainty, these results provide a rational

30

explanation for why accounting anomalies persist. Specifically, the high information uncertainty of the

securities in these positions poses a limit to arbitrage.

Our results also suggest a rational explanation for the existence of abnormal returns to accounting

signals, namely, that investors place lower weights on investment signals of lower quality, and revise

those weights as uncertainty about the signal is resolved. Because it is not possible to distinguish

between this rational explanation and competing irrational explanations, we do not draw conclusions

about whether investors’ rational responses to information uncertainty or their irrational cognitive biases

offer a more convincing explanation for the existence of accounting anomalies. We are not aware,

however, of any behavioral explanation for our results; that is, we know of no reason why a cognitive bias

that is consistent with under-reaction (such as conservatism) would also vary cross-sectionally with

information uncertainty. Moreover, recent work by Chan, Frankel and Kothari [2002] finds no support

for the view that cognitive biases explain accounting anomalies.

31

Appendix: Overview of Accounting Anomalies, Construction of Accounting Signals and Implementation of Accounting-Based Trading Strategies

In this section, we describe, and review prior findings about, the accounting anomalies that we

investigate in our study.15 Following each description, we detail the calculation of the accounting

signal(s) that forms the basis for the strategy and we summarize the procedures used to implement the

calendar-time-portfolio regressions used to assess the statistical significance of the abnormal returns to

the trading strategy.

A.1. Post earnings announcement drift (PEAD)

PEAD is arguably the most well-documented and most robust of the anomalies, showing

consistent evidence of abnormal returns across time periods, samples (although the effects are strongest

for small firms), and measures of earnings surprise. Bernard and Thomas [1989; 1990] and Bernard,

Thomas and Wahlen [1996] also show that PEAD is robust to a battery of risk adjustments. Several

papers interpret PEAD as a failure by the market to fully appreciate the implications of current earnings

for future earnings (e.g., Abarbanell and Bernard [1992], Chan, Jegadeesh, and Lakonishok [1996]). Ball

and Bartov [1996] show that while stock prices reflect the positive and negative autoregressive terms in

the earnings series, investors appear to underestimate the magnitudes of these serial correlations. In a

general discussion of earnings-based anomalies, Ball [1992] concludes that PEAD is due to some

combination of information-processing costs and market inefficiency.

Taking positions based on post earnings announcement drift requires information about the

earnings announcement date and the earnings surprise in firm j’s quarter q earnings announcement. We

use Compustat earnings announcement dates, and we calculate earnings surprises using Zacks analysts’

earnings forecasts as well as a seasonal random walk (SRW) specification. The analyst-based measure

15 Research also suggests overlaps among some of the accounting anomalies. For example, Fama and French [1996] show that a combination of book-to-market and size anomalies overlaps with the cash flow-to-price and earnings- price anomalies. Desai, Rajgopal and Venkatachalam [2002] show that the accruals anomaly overlaps with a cash flow-to-price strategy. Raedy [2000] concludes that the cash flow-to-price anomaly subsumes the earnings-to-price anomaly. Kraft [2000] finds overlap between PEAD and several other anomalies. Our research design treats the accounting-based strategies as distinct, and investigates the extent to which each of them is separately associated with information uncertainty.

32

equals the difference between firm j’s reported earnings per share before extraordinary items (Compustat

#19) for quarter q and the consensus median analyst forecast of firm j’s quarter q earnings, divided by

firm j’s share price 20 days prior to the earnings announcement. The consensus median forecast is the

median forecast for the quarter made by all analysts following firm j; in forming the consensus, we use

only the last forecast made by each analyst prior to the earnings announcement. The seasonal change in

earnings per share is the difference between firm j’s reported earnings before extraordinary items

(Compustat # 8) for quarter q and firm j’s four-quarter ago reported earnings, divided by the number of

shares used to calculate earnings per share (Compustat #15). The SRW-measure of earnings surprise is

the seasonal change in earnings per share divided by share price 20 days prior to the earnings

announcement.

Each calendar quarter, we rank firms into deciles based on the analyst- or SRW measure of the

earnings surprise. We take long positions in the 20% of stocks with the most positive earnings surprises

and short positions in the 20% of stocks with the most negative surprises. Firms enter the portfolio on the

first day of the calendar quarter following the earnings announcement, and are held for six months. For

example, if a firm announces its quarterly earnings on May 25, it enters a portfolio on July 1. We choose

six months as our holding period to ensure that it includes two subsequent quarterly earnings

announcements.16 The return to the p’th portfolio in month m, Rp,m, is the mean of the equally-weighted

returns across the j=1,…,J securities comprising portfolio { }, ,p Long Short Long Short∈ − .

A.2. Value-Glamour Strategies

Research on the returns characteristics of value versus glamour stocks has shown superior returns

to investing in stocks with high book-to-market ratios, high cash flow-to-price ratios and high earnings-

price ratios, relative to stocks with low values of these ratios (see Fama and French [1993] and

Lakonishok, Shleifer and Vishny [1994] for overviews). While there is a debate as to whether the returns

16 Studies of PEAD show significant returns over two to four quarters after the earnings announcement date (e.g., Bernard and Thomas [1989; 1990], Abarbanell and Bernard [1992]). All such studies that we are aware of show economically and statistically significant effects over two quarters.

33

to value-glamour signals are due to risk or mispricing (e.g., Fama [1998], Loughran and Ritter [2000]),

the empirical facts about the returns patterns are not in dispute.

The value-glamour strategies require information about share price and shares outstanding (both

are obtained from CRSP) as well as accounting fundamentals: net income before extraordinary items

(Compustat #18), book value of equity (Compustat #60) and cash flows from operations, CFO. The latter

is calculated, following Kothari, Leone and Wasley [2002], as net income before extraordinary items less

total accruals, TA = , where = firm j’s

change in current assets (Compustat #4) between year t-1 and year t,

tj , , , , ,j t j t j t j t j tCA CL Cash STDEBT DEPN∆ − ∆ − ∆ + ∆ −

jCL ,

, tjCA ,∆

t∆ = firm j’s change in current

liabilities (Compustat #5) between year t-1 and year t, tjCash ,∆ = firm j’s change in cash (Compustat #1)

between year t-1 and year t, ∆ = firm j’s change in debt in current liabilities (Compustat #34)

between year t-1 and year t, = firm j’s depreciation and amortization expense (Compustat #14)

in year t.

tjSTDEBT ,

tjDEPN ,

At the end of fiscal year t, the firm’s accounting fundamental is divided by its market value. The

accounting information is assumed to be known at the beginning of the fourth month following the firm’s

fiscal year end, and the value-glamour signal stays constant for that firm until the next fiscal year’s signal

becomes available. For example, a firm with a fiscal year end in January 1995 will have its

corresponding value-glamour signal from May 1995 until April 1996. We employ a dynamic portfolio

formation technique for each signal to accommodate firms with different fiscal year ends and to avoid

differentially stale information (as would be the case if we rebalanced only once per calendar year). At

the beginning of each month, firms are ranked into portfolios based on the distribution of all available

accounting fundamental-to-price ratios for that month. Implementation choices for the construction of the

portfolios generally follow Lakonishok, Shleifer and Vishny [1994]. Specifically, we require firms to

have positive values of the accounting fundamental, we form deciles based on the ranked distribution of

the fundamental-to-price signal and take long positions in the 20% of stocks with the largest values of the

34

signal and short positions in the 20% with the smallest values of the signal, and we equal-weight the

returns within each portfolio.

A.3. Accruals anomalies

Several studies have investigated whether investors correctly price accruals. For example, Sloan

[1996] finds that a strategy that takes long positions in stocks with the most negative total accruals and

short positions in stocks with the most positive total accruals earns significant positive abnormal returns.

Collins and Hribar [2000] find similar results for quarterly data and Xie [2001] finds that the total

accruals anomaly is largely driven by abnormal accruals, as estimated from a Jones [1991] model. Chan,

Chan, Jegadeesh and Lakonishok [2001] corroborate the total accruals and abnormal accruals anomalies,

and document that most of the effect is due to changes in current accruals, namely inventories. Finally,

Richardson, Sloan, Soliman and Tuna [2002] show that most of the information in accruals is associated

with firms experiencing changes in asset turnover, rather than growth in sales.

The accruals anomalies require information about firm j’s accruals (total or abnormal) in year t.

Following Sloan [1996], the total accruals signal equals total accruals scaled by beginning-of-year total

assets, ,

, 1

j t

j t

TAAssets −

. Abnormal accruals are calculated using the modified Jones model estimated, by year,

for each of the 48 Fama-French [1997] industry groups, requiring the industry to have a minimum of 20

observations per year to be included in the sample:

,1 2 3

, 1 , 1 , 1 , 1

1j t j,t j tj t

j t j t j t j t

TA Rev PPEAsset Asset Asset Asset

κ κ κ− − − −

∆= + + ,

,ε+ (A1)

where = firm j’s total assets (Compustat #6) at the beginning of year t, , 1j tAsset −

,j tRev∆ = firm j’s change in revenues (Compustat #12) between year t-1 and year t,

tjPPE , = 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 (A1) are used to

estimate firm-specific normal accruals (as a percent of lagged total assets),

35

, ,, 1 2 3

, 1 , 1 , 1

( )1ˆ ˆ ˆj t j t j tj t

j t j t j t

Rev AR PPENA

Asset Asset Assetκ κ κ

− −

∆ − ∆= + + ,

−

, where ,j tAR∆ = firm j’s change in accounts

receivable (Compustat #2) between year t-1 and year t. The abnormal accrual in year t is the difference

between total accruals and normal accruals, ,

, 1

j tj t

j t

TAAA N

Asset −

= −, ,j tA .

We assume that information about is available at the beginning of the fourth month

following firm j’s fiscal year end; it remains the same for the following 12 months. Using the same

dynamic technique as used for the value-glamour strategies, each month the accruals portfolios are

rebalanced based on the distribution of the accruals metric available at the beginning of that month. We

take long (short) positions in the 20% of firms with the most negative (most positive) values of each

accruals metric, and we equal-weight returns within each portfolio.

,j tAA

36

Figure 1a

0.0000.0100.0200.0300.0400.0500.0600.0700.0800.090

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

SRW PEAD Anomaly deciles (D1 most neg surprise, D10 most pos surprise)

Mean earnings quality

Figure 1b

0.0000.0100.0200.0300.0400.0500.0600.0700.0800.0900.100

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Cash Flow-to-Price Anomaly deciles (D1 smallest values, D10 largest values)

Mean earnings quality

Figure 1a shows the mean value of each earnings quality metric ( AA top line, ˆ( )vσ bottom line) for the ranked deciles of the SRW-based PEAD anomaly. Figure 1b shows similar information for the ranked deciles of the cash flow-to-price anomaly.

37

Figure 2

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

Month past portfolio formation, h

Abnormalreturn

(bp per month)

Good Poor

Figure 2 shows the mean abnormal return in period h, to the long-minus-short position in a book-to-market strategy taken at time h=0 in Good or Poor earnings quality securities. For example, the point h=4 represents the average abnormal return to the portfolio in the fourth month following the month in which the position was taken.

38

Figure 3a

0.000

0.020

0.040

0.060

0.080

0.100

0.120

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

1-factor alpha deciles (D1 most negative alphas, D10 most positive alphas)

Mean earningsquality

Figure 3b

0.000

0.020

0.040

0.060

0.080

0.100

0.120

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

3-factor alpha deciles (D1 most negative alphas, D10 most positive alphas)

Mean earningsquality

Figure 3a shows the mean value of each earnings quality metric ( AA top line, ˆ( )vσ bottom line) for the ranked

deciles of the estimated intercepts from firm-specific CAPM regressions ( ). Figure 3b shows similar

information for firm-specific 3-factor regressions (

CAPMjα

3 fjα ).

39

Table 1 Descriptive Statistics about Earnings Quality Metrics

Panel A: Number of firms with data on earnings quality metrics, by year

Year ˆ( )σ ν AA Year ˆ( )σ ν AA 1981 2,509 3,048 1991 2,402 3,756 1982 2,500 3,163 1992 2,569 3,925 1983 2,447 3,270 1993 2,790 4,191 1984 2,369 3,383 1994 2,870 4,487 1985 2,289 3,475 1995 2,899 4,690 1986 2,194 3,479 1996 2,906 4,909 1987 2,184 3,648 1997 2,860 5,239 1988 2,172 3,772 1998 2,798 5,138 1989 2,233 3,757 1999 2,795 4,823 1990 2,335 3,743 2000 2,564 4,282

Panel B: Summary information on pooled sample earnings quality metrics Earnings quality N mean std. dev. 10% 25% median 75% 90%

ˆ( )σ ν 50,682 0.0553 0.0379 0.0180 0.0279 0.0453 0.0726 0.1079 AA 80,177 0.0766 0.0787 0.0082 0.0218 0.0509 0.1029 0.1821

Panel C: Correlations between earnings quality metrics Spearman Pearson correlation 0.3423 0.3260 p-value (.0000) (.0000) Variable definitions: ˆ( )σ ν is the standard deviation of the residuals from rolling five-year regressions of current accruals on lagged, current and future cash flows from operations; AA is the absolute value of the performance-matched abnormal accrual. a The samples consist of all firms with the necessary data to calculate the noted earnings quality metric in year t=1981-2000.

40

Table 2

Average Monthly Abnormal Returns to Extreme Anomaly Portfoliosa

Panel A: Post earnings announcement drift

Unrestricted Sample ˆ( )σ ν Sample AA Sample

Analysts' forecasts 1-factor 3-factor 1-factor 3-factor 1-factor 3-factor Short (most neg. surprise) -0.332 -0.292 -0.247 -0.219 -0.382 -0.255 Long (most pos. surprise) 0.420 0.400 0.318 0.266 0.378 0.424 Long-Short 0.753 0.692 0.566 0.485 0.760 0.679 t-stat. (Long-Short) 5.11 4.98 4.19 3.94 5.26 5.05 SRW forecasts Short (most neg. surprise) -0.608 -0.573 -0.258 -0.240 -0.520 -0.410 Long (most pos. surprise) 0.411 0.386 0.474 0.448 0.436 0.486 Long-Short 1.020 0.958 0.733 0.688 0.955 0.897 t-stat. (Long-Short) 9.87 9.17 7.30 6.73 9.27 8.51 Panel B: Value-glamour strategies

Unrestricted Sample ˆ( )σ ν Sample AA Sample Book-to-market 1-factor 3-factor 1-factor 3-factor 1-factor 3-factor Short (smallest value) -0.869 -0.510 -0.263 -0.064 -0.625 -0.264 Long (largest value) 0.722 0.452 0.755 0.520 0.759 0.562 Long-Short 1.591 0.962 1.018 0.584 1.384 0.826 t-stat. (Long-Short) 7.23 6.86 6.43 4.88 6.95 6.08 Cash flow-to-price Short (smallest value) -0.379 -0.160 -0.061 0.019 -0.311 -0.120 Long (largest value) 0.750 0.474 0.724 0.402 0.777 0.501 Long-Short 1.128 0.634 0.785 0.384 1.088 0.620 t-stat. (Long-Short) 6.17 5.00 5.29 3.48 6.16 4.90 Earnings-to-price Short (smallest value) -0.400 -0.314 -0.017 -0.006 -0.286 -0.166 Long (largest value) 0.580 0.278 0.569 0.306 0.543 0.305 Long-Short 0.980 0.592 0.586 0.312 0.829 0.471 t-stat. (Long-Short) 5.91 5.04 4.33 2.69 5.22 4.00 Panel C: Accruals anomalies

Unrestricted Sample ˆ( )σ ν Sample AA Sample Total accruals 1-factor 3-factor 1-factor 3-factor 1-factor 3-factor Short (most positive) -0.710 -0.579 -0.235 -0.226 -0.476 -0.371 Long (most negative) 0.058 0.222 0.473 0.399 0.249 0.350 Long-Short 0.769 0.801 0.708 0.625 0.725 0.721 t-stat. (Long-Short) 5.57 5.69 6.57 5.69 5.42 5.28 Abnormal accruals Short (most positive) -0.436 -0.353 -0.131 -0.157 -0.397 -0.324 Long (most negative) 0.321 0.467 0.513 0.490 0.343 0.489 Long-Short 0.757 0.820 0.644 0.646 0.740 0.813 t-stat. (Long-Short) 7.21 7.94 7.85 7.60 6.87 7.77

41

a The Unrestricted Sample contains firms with monthly returns data and the necessary data to calculate each anomaly signal. The Restricted Samples are the sub-sets of Unrestricted observations with data on each earnings quality metric: ˆ( )σ ν and AA . For each sample, we report the average monthly abnormal return to the noted portfolio (short, long, long-short), for the period 1982-2001. We report abnormal returns based on both a CAPM and a three-factor model of expected returns. The abnormal return is the intercept from a calendar-time portfolio regression of each portfolio (long, short, long-short) return on RMRF in the CAPM regression, and on RMRF, SMB, and HML in the three-factor regressions. RMRF is the excess market return, SMB is a size factor mimicking portfolio, and HML is a book-to-market factor mimicking portfolio (Fama and French [1993, 1996]). The Appendix details the construction of each accounting signal and the implementation of the trading strategies.

42

Table 3

Average Earnings Quality of Securities in Anomaly Decilesa Panel A: Post earnings announcement drift Anomaly decile (1=most negative surprises, 10=most positive surprises) Analysts' forecasts D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 Diff t-stat # mos

ˆ( )σ ν 0.050 0.043 0.037 0.035 0.034 0.034 0.034 0.035 0.037 0.041 0.008 27.58 210 AA 0.079 0.066 0.062 0.059 0.058 0.059 0.059 0.060 0.060 0.062 0.007 18.54 147

SRW forecasts ˆ( )σ ν 0.061 0.051 0.044 0.038 0.036 0.037 0.042 0.046 0.051 0.061 0.015 41.98 240

AA 0.083 0.074 0.065 0.059 0.058 0.060 0.067 0.071 0.074 0.085 0.016 51.18 238 Panel B: Value-glamour strategies Anomaly decile (1=smallest values, 10=largest values) Book-to-market D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 Diff t-stat # mos

ˆ( )σ ν 0.066 0.051 0.048 0.046 0.042 0.042 0.044 0.047 0.050 0.048 0.009 63.52 239 AA 0.110 0.087 0.078 0.074 0.068 0.064 0.064 0.065 0.068 0.065 0.014 61.52 240

Cash flow-to-price ˆ( )σ ν 0.058 0.048 0.043 0.040 0.040 0.037 0.037 0.038 0.044 0.050 0.011 59.31 240

AA 0.074 0.060 0.053 0.051 0.050 0.051 0.051 0.054 0.071 0.090 0.022 77.91 240 Earnings-to-price

ˆ( )σ ν 0.057 0.050 0.044 0.041 0.039 0.040 0.038 0.038 0.044 0.047 0.010 47.12 240 AA 0.086 0.080 0.073 0.067 0.063 0.061 0.058 0.060 0.063 0.066 0.010 34.77 196

Panel C: Accruals anomalies Anomaly decile (1=most positive values, 10=most negative valules) Total accruals D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 Diff t-stat # mos

ˆ( )σ ν 0.070 0.050 0.044 0.039 0.037 0.036 0.041 0.047 0.055 0.071 0.021 72.05 240 AA 0.169 0.076 0.051 0.041 0.036 0.034 0.040 0.051 0.079 0.175 0.082 172.46 240

Abnormal accruals ˆ( )σ ν 0.072 0.054 0.045 0.041 0.038 0.036 0.038 0.043 0.053 0.070 0.022 76.17 240

AA 0.190 0.084 0.050 0.033 0.023 0.021 0.029 0.047 0.082 0.193 0.103 207.57 240 Variable definitions: see Table 1. a We report the mean value (over the 240 monthly portfolios, 1982-2001) of the average of each earnings quality metric calculated across the securities in each anomaly decile in month m. The column labeled “Diff.” shows the difference between the mean values of the noted earnings quality metric for securities in the extreme deciles (1, 2, 9 and 10) versus the non-extreme deciles (3-8). The t-statistic for the test of whether this difference is reliably different from zero is based on the standard error of the time series of differences. #mos is the number of months where the t-statistic of the single-period cross-sectional test of the difference in mean earnings quality between extreme and non-extreme deciles exceeds 1.96.

43

Table 4

Frequency and Proportion of Good and Poor Earnings Quality Securities Within Extreme Anomaly Portfolios: Unbalanced Designa

Panel A: Post earnings announcement drift

ˆ( )σ ν Sample AA Sample

Good EQ Poor EQ Diff. Good EQ Poor EQ Diff. Analysts' forecasts # obs % pos # obs % pos t-test # obs % pos # obs % pos t-test Short (most neg. surprise) 33 14.7% 60 27.2% 38.3 61 17.6% 85 24.7% 20.8 Long (most pos. surprise) 51 22.6% 46 19.9% -7.9 79 21.7% 69 18.5% -10.6 SRW forecasts Short (most neg. surprise) 106 14.1% 194 26.1% 36.2 197 17.7% 256 22.8% 25.6 Long (most pos. surprise) 116 14.0% 215 27.0% 25.1 215 17.7% 282 22.8% 16.4 Panel B: Value-glamour strategies

ˆ( )σ ν Sample AA Sample

Good EQ Poor EQ Diff. Good EQ Poor EQ Diff. Book-to-market # % # % t-test # % # % t-test Short (smallest value) 66 13.7% 142 29.2% 49.7 109 13.9% 240 31.0% 64.6 Long (largest value) 79 16.0% 93 19.3% 10.5 161 20.6% 124 15.9% -20.7 Cash flow-to-price Short (smallest value) 38 9.8% 110 27.7% 69.6 80 14.0% 138 24.0% 44.6 Long (largest value) 70 17.8% 92 23.4% 12.1 92 16.1% 170 30.0% 40.3 Earnings-to-price Short (smallest value) 45 11.7% 112 29.3% 50.8 84 14.9% 153 27.3% 50.1 Long (largest value) 85 22.2% 84 22.1% -0.1 124 22.3% 102 18.2% -9.0 Panel C: Accruals anomalies

ˆ( )σ ν Sample AA Sample

Good EQ Poor EQ Diff. Good EQ Poor EQ Diff. Total accruals # % # % t-test # % # % t-test Short (most positive) 38 7.7% 154 30.9% 116.6 47 6.0% 351 43.7% 222.1Long (most negative) 56 11.2% 141 28.5% 72.8 55 6.9% 338 41.9% 153.9 Abnormal accruals Short (most positive) 48 9.6% 148 29.8% 124.6 10 1.3% 382 47.6% 366.5Long (most negative) 40 8.1% 153 30.9% 120.7 13 1.7% 388 48.3% 312.1

44

Variable definitions and sample description: see Tables 1 and 2. a We report the mean number (#) and fraction (%) of total securities within the noted extreme anomaly portfolios (which comprise the short and long position) with Good versus Poor earnings quality. Good EQ (earnings quality) securities are defined as those in the bottom two deciles of the ranked distribution of the noted earnings quality metric, while Poor EQ are in the top two deciles. Mean values are based on the 240 monthly portfolios over 1982-2001. The column labeled “Diff.” shows the t-statistic for whether the mean percentage of Poor is greater than the mean percentage of Good; positive values indicate that the percentage of Poor securities exceeds the percentage of Good securities, while negative values indicate the opposite. The t-test of whether this difference is significant is based on the standard error of the time series of monthly differences.

45

Table 5

Average Monthly Abnormal Returns to Good and Poor Earnings Quality Securities Within Extreme Anomaly Portfolios: Unbalanced Designa

Panel A: Post earnings announcement drift CAPM Abnormal Returns 3-factor Abnormal Returns

ˆ( )σ ν Sample AA Sample ˆ( )σ ν Sample AA Sample

Analysts' forecasts Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQShort (most neg. surprise) 0.114 -0.763 0.142 -0.920 -0.162 -0.529 0.233 -0.748 Long (most pos. surprise) 0.493 0.304 0.449 0.362 0.213 0.403 0.335 0.495 Long-Short 0.379 1.067 0.307 1.282 0.375 0.931 0.102 1.242 t-stat (Long-Short) 2.22 4.20 1.40 5.05 2.13 3.64 0.49 4.84 Diff: Poor - Good 0.687 t=2.42 0.975 t=3.72 0.557 t=1.92 1.140 t=4.27 SRW forecasts Short (most neg. surprise) -0.064 -0.328 -0.117 -0.824 -0.298 -0.115 -0.087 -0.621 Long (most pos. surprise) 0.479 0.463 0.509 0.435 0.190 0.624 0.415 0.628 Long-Short 0.543 0.791 0.626 1.258 0.488 0.739 0.501 1.249 t-stat (Long-Short) 3.25 4.53 3.60 8.26 2.83 4.10 2.90 7.92 Diff: Poor - Good 0.248 t=1.04 0.632 t=2.89 0.251 t=1.01 0.748 t=3.38 Panel B: Value-glamour strategies CAPM Abnormal Returns 3-factor Abnormal Returns

ˆ( )σ ν Sample AA Sample ˆ( )σ ν Sample AA Sample

Book-to-market Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQShort (smallest value) 0.158 -0.506 -0.434 -0.966 0.167 -0.134 -0.134 -0.465 Long (largest value) 0.524 1.007 0.646 0.795 0.219 0.872 0.366 0.692 Long-Short 0.366 1.513 1.081 1.761 0.051 1.006 0.499 1.157 t-stat (Long-Short) 1.99 5.82 4.63 6.44 0.31 4.3 2.70 5.10 Diff: Poor - Good 1.147 t=4.00 0.680 t=2.95 0.954 t=3.39 0.658 t=2.77 Cash flow-to-price Short (smallest value) 0.079 -0.002 -0.362 -0.757 0.002 0.182 -0.130 -0.465 Long (largest value) 0.595 0.898 0.570 0.961 0.283 0.747 0.254 0.783 Long-Short 0.516 0.900 0.932 1.719 0.282 0.565 0.384 1.248 t-stat (Long-Short) 3.06 4.12 3.71 7.64 1.72 2.70 1.92 6.30 Diff: Poor - Good 0.384 t=1.69 0.786 t=3.11 0.283 t=1.21 0.864 t=3.43 Earnings-to-price Short (smallest value) 0.242 -0.109 0.046 -0.770 0.024 0.095 0.099 -0.495 Long (largest value) 0.532 0.522 0.648 0.405 0.302 0.324 0.359 0.278 Long-Short 0.290 0.630 0.602 1.174 0.277 0.229 0.260 0.773 t-stat (Long-Short) 1.72 3.20 2.98 5.53 1.60 1.32 1.45 4.09 Diff: Poor - Good 0.340 t=1.37 0.573 t=2.41 -0.048 t=-.20 0.513 t=2.09

46

Panel C: Accruals anomalies CAPM Abnormal Returns 3-factor Abnormal Returns

ˆ( )σ ν Sample AA Sample ˆ( )σ ν Sample AA Sample

Total accruals Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQShort (most positive) 0.010 -0.375 -0.433 -0.777 -0.130 -0.220 -0.364 -0.612 Long (most negative) 0.327 0.605 0.001 0.237 0.025 0.785 -0.015 0.450 Long-Short 0.318 0.981 0.435 1.014 0.155 1.006 0.349 1.062 t-stat (Long-Short) 1.71 4.87 1.42 6.87 0.83 4.85 1.10 7.06 Diff: Poor - Good 0.663 t=2.52 0.579 t=1.97 0.851 t=3.22 0.713 t=2.36 Abnormal accruals Short (most positive) 0.030 -0.209 -0.685 -0.674 -0.211 -0.053 -0.788 -0.504 Long (most negative) 0.607 0.460 -0.603 0.217 0.368 0.577 -0.314 0.403 Long-Short 0.577 0.669 0.082 0.891 0.579 0.631 0.474 0.908 t-stat (Long-Short) 3.54 3.87 0.13 6.72 3.43 3.52 0.75 6.64 Diff: Poor - Good 0.092 t=0.38 0.810 t=1.28 0.051 t=0.20 0.434 t=.70 Variable definitions and sample description: see Tables 1 and 2. a We report the mean monthly abnormal return to the Good and Poor securities within each of the extreme anomaly portfolios (short, long, long-short), for the period 1982-2001. Good EQ (earnings quality) securities are defined as those in the bottom two deciles of the ranked distribution of the noted earnings quality metric, while Poor EQ securities are in the top two deciles. The number and percentage of securities within the extreme portfolios that are classified as Good versus Poor is shown in Table 4. We report abnormal returns based on both a CAPM and a three-factor model of expected returns.

47

Table 6

Average Monthly Abnormal Returns to Good and Poor Earnings Quality Securities Within Extreme Anomaly Portfolios: Balanced Designa

Panel A: Post earnings announcement drift CAPM Abnormal Returns 3-factor Abnormal Returns

ˆ( )σ ν Sample AA Sample ˆ( )σ ν Sample AA Sample

Analysts' forecasts Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQShort (most neg. surprise) 0.046 -0.833 0.207 -1.215 -0.135 -0.547 0.265 -0.980 Long (most pos. surprise) 0.435 0.329 0.443 0.432 0.164 0.425 0.323 0.552 Long-Short 0.389 1.163 0.236 1.647 0.299 0.972 0.058 1.532 t-stat (Long-Short) 2.21 4.05 1.06 5.71 1.72 3.37 0.28 5.24 Diff: Poor - Good 0.773 t=2.61 1.411 t=4.72 0.673 t=2.21 1.474 t=4.79 SRW forecasts Short (most neg. surprise) -0.224 -0.321 -0.124 -0.921 -0.465 -0.060 -0.092 -0.703 Long (most pos. surprise) 0.527 0.484 0.528 0.385 0.264 0.685 0.465 0.580 Long-Short 0.751 0.805 0.653 1.306 0.729 0.745 0.557 1.283 t-stat (Long-Short) 5.06 4.07 3.97 8.31 4.76 3.61 3.34 7.89 Diff: Poor - Good 0.055 t=.27 0.654 t=3.19 0.016 t=.06 0.726 t=3.45 Panel B: Value-glamour strategies CAPM Abnormal Returns 3-factor Abnormal Returns

ˆ( )σ ν Sample AA Sample ˆ( )σ ν Sample AA Sample

Book-to-market Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQShort (smallest value) 0.148 -0.588 -0.387 -1.141 0.129 -0.154 -0.126 -0.618 Long (largest value) 0.623 0.926 0.616 0.807 0.311 0.782 0.338 0.686 Long-Short 0.475 1.514 1.003 1.948 0.182 0.936 0.464 1.305 t-stat (Long-Short) 2.72 5.45 4.64 6.85 1.21 3.86 2.70 5.62 Diff: Poor - Good 1.039 t=3.52 0.945 t=3.91 0.754 t=2.72 0.840 t=3.42 Cash flow-to-price Short (smallest value) 0.051 -0.111 -0.332 -0.892 0.000 0.125 -0.152 -0.576 Long (largest value) 0.626 0.903 0.606 0.892 0.287 0.750 0.296 0.752 Long-Short 0.575 1.014 0.937 1.784 0.288 0.625 0.449 1.329 t-stat (Long-Short) 3.57 3.98 4.11 6.96 1.92 2.56 2.38 5.57 Diff: Poor - Good 0.440 t=1.71 0.847 t=3.23 0.338 t=1.27 0.880 t=3.31 Earnings-to-price Short (smallest value) 0.164 -0.180 -0.078 -0.933 -0.064 0.050 -0.029 -0.631 Long (largest value) 0.512 0.499 0.631 0.393 0.261 0.323 0.344 0.256 Long-Short 0.348 0.679 0.709 1.326 0.325 0.273 0.373 0.887 t-stat (Long-Short) 1.90 3.18 3.68 5.93 1.72 1.41 2.21 4.52 Diff: Poor - Good 0.331 t=1.20 0.616 t=2.69 -0.052 t=-.19 0.514 t=2.18

48

Panel C: Accruals anomalies CAPM Abnormal Returns 3-factor Abnormal Returns

ˆ( )σ ν Sample AA Sample ˆ( )σ ν Sample AA Sample

Total accruals Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQ Good EQ Poor EQShort (most positive) -0.116 -0.365 -0.278 -1.023 -0.267 -0.186 -0.244 -0.834 Long (most negative) 0.397 0.519 0.058 -0.056 0.086 0.753 0.043 0.260 Long-Short 0.513 0.883 0.336 0.967 0.354 0.939 0.286 1.094 t-stat (Long-Short) 3.50 3.63 1.51 4.62 2.45 3.75 1.25 5.13 Diff: Poor - Good 0.370 t=1.31 0.631 t=2.83 0.585 t=2.07 0.808 t=3.56 Abnormal accruals Short (most positive) -0.017 -0.202 -0.192 -0.971 -0.242 -0.025 -0.225 -0.766 Long (most negative) 0.513 0.356 0.461 -0.123 0.311 0.535 0.630 0.199 Long-Short 0.529 0.558 0.653 0.848 0.553 0.561 0.855 0.965 t-stat (Long-Short) 4.35 2.44 2.66 4.51 4.39 2.36 3.80 5.02 Diff: Poor - Good 0.029 t=.11 0.195 t=.79 0.008 t=.03 0.111 t=.46 Variable definitions and sample description: see Tables 1 and 2. a We report the mean monthly abnormal return to the Good and Poor securities within each of the extreme anomaly portfolios (short, long, long-short), for the period 1982-2001. Good earnings quality securities are defined as those in the bottom two deciles of the ranked distribution of the noted earnings quality metric, while Poor earnings quality securities are in the top two deciles. In this table, the ranking of securities on earnings quality is performed within each of the anomaly deciles; hence, equal numbers of securities are classified as having Good versus Poor earnings quality. We report abnormal returns based on both a CAPM and a three-factor model of expected returns.

49

Table 7

Regression of Abnormal Returns on Number of Periods Post Portfolio Formation, For Good and Poor Earnings Quality Securities in Extreme Anomaly Portfoliosa

Panel A: Post earnings announcement drift (Number of periods = 12 quarters) CAPM Abnormal Returns 3-factor Abnormal Returns

ˆ( )σ ν Sample AA Sample ˆ( )σ ν Sample AA Sample

Analysts' forecasts Coef. Est. t-stat. Coef. Est. t-stat. Coef. Est. t-stat. Coef. Est. t-stat.Poor -0.067 -1.86 -0.129 -3.05 -0.075 -2.14 -0.152 -3.53 Good -0.008 -0.40 -0.016 -0.91 -0.018 -0.77 0.003 0.14 Poor - Good -0.058 -1.87 -0.112 -2.88 -0.057 -1.71 -0.155 -3.37 SRW forecasts Poor -0.061 -1.35 -0.068 -1.58 -0.066 -1.50 -0.068 -1.61 Good -0.048 -2.46 -0.035 -1.32 -0.033 -1.68 -0.031 -1.22 Poor - Good -0.013 -0.35 -0.033 -1.15 -0.033 -0.88 -0.037 -1.21 Panel B: Value-glamour strategies (Number of periods = 36 months) CAPM Abnormal Returns 3-factor Abnormal Returns

ˆ( )σ ν Sample AA Sample ˆ( )σ ν Sample AA Sample

Book to market Coef. Est. t-stat. Coef. Est. t-stat. Coef. Est. t-stat. Coef. Est. t-stat.Poor -0.022 -17.92 -0.042 -29.18 -0.013 -10.01 -0.036 -20.66Good -0.010 -6.46 -0.012 -7.48 -0.004 -2.44 0.001 0.58 Poor - Good -0.012 -5.52 -0.030 -12.47 -0.009 -3.55 -0.037 -13.22 Cash flow to price Poor -0.014 -10.64 -0.029 -7.29 -0.009 -5.60 -0.026 -7.81 Good -0.002 -0.80 -0.009 -4.07 0.003 1.65 0.005 2.48 Poor - Good -0.012 -7.37 -0.020 -5.54 -0.012 -6.27 -0.031 -11.24 Earnings to price Poor -0.018 -12.64 -0.031 -17.19 -0.018 -12.64 -0.027 -17.76Good -0.004 -2.25 -0.013 -10.39 -0.004 -2.25 -0.003 -2.27 Poor - Good -0.014 -8.16 -0.019 -8.77 -0.014 -8.16 -0.024 -10.77

50

Panel C: Accruals anomalies (Number of periods = 36 months) CAPM Abnormal Returns 3-factor Abnormal Returns

ˆ( )σ ν Sample AA Sample ˆ( )σ ν Sample AA Sample

Total accruals Coef. Est. t-stat. Coef. Est. t-stat. Coef. Est. t-stat. Coef. Est. t-stat.Poor -0.021 -12.61 -0.019 -6.43 -0.023 -16.74 -0.022 -8.10Good 0.003 2.29 0.005 1.35 0.007 4.45 0.003 0.90 Poor - Good -0.024 -11.27 -0.024 -6.93 -0.030 -14.30 -0.025 -6.51 Abnormal accruals Poor -0.025 -14.99 -0.016 -6.21 -0.025 -13.41 -0.018 -7.64Good -0.017 -7.66 -0.011 -0.87 -0.013 -5.09 -0.019 -1.50Poor - Good -0.008 -2.91 -0.006 -0.42 -0.012 -3.64 0.001 0.06 Variable definitions and sample description: see Tables 1 and 2. a We report the coefficient estimate and t-statistic from regressing the abnormal return in post-portfolio formation period h on h, where h= 1,2, …, 12 quarters for the PEAD strategies and h=1,2, …, 36 months for the value-glamour and accruals strategies. The rows labeled “Poor” and “Good” respectively, show the results for abnormal returns to securities classified as poor and good earnings quality; the row labeled “Poor-Good” shows the results when the dependent variable is the difference in abnormal returns in period h between Poor and Good securities. Good earnings quality securities are defined as those in the bottom two deciles of the ranked distribution of the noted earnings quality metric, while Poor earnings quality securities are in the top two deciles.

51

Table 8

Abnormal Returns Estimates from 1-factor and 3-factor Asset Pricing Regressions Panel A: Intercepts (alphas) from firm-specific 1-factor and 3-factor regressionsa ˆ( )σ ν sample Abnormal return N mean std. dev. 10% 25% median 75% 90%

CAPMα 605,421 -0.33 1.74 -2.50 -1.22 -0.15 0.69 1.57 3 fα 605,421 -0.34 1.80 -2.53 -1.28 -0.22 0.69 1.67

AA sample

Abnormal return N mean std. dev. 10% 25% median 75% 90% CAPMα 914,033 -0.64 2.20 -3.44 -1.74 -0.35 0.66 1.68 3 fα 914,033 -0.52 2.29 -3.29 -1.66 -0.33 0.75 1.94

Panel B: Mean earnings quality by alpha decileb 1-factor alpha decile (1=most negative, 10=most positive) Earnings quality D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 Diff. t-stat

ˆ( )σ ν 0.081 0.067 0.058 0.053 0.049 0.045 0.044 0.044 0.049 0.062 0.016 47.77AA 0.101 0.086 0.079 0.072 0.067 0.063 0.061 0.062 0.069 0.089 0.019 52.93

3-factor alpha decile (1=most negative, 10=most positive) Earnings quality D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 Diff. t-stat

ˆ( )σ ν 0.079 0.065 0.057 0.051 0.046 0.043 0.044 0.048 0.054 0.066 0.018 59.30AA 0.099 0.085 0.076 0.070 0.065 0.061 0.060 0.065 0.075 0.093 0.022 86.03

Panel C: Regression of the absolute value of alpha on earnings qualityc Raw values of earnings quality metric Decile rank values of earnings quality metric 1-factor 3-factor 1-factor 3-factor Indep. variable Coef. Est t-stat Coef. Est t-stat Coef. Est t-stat Coef. Est t-stat Intercept 0.687 76.48 0.745 71.83 0.560 53.81 0.610 53.81

ˆ( )σ ν 9.588 68.93 9.603 72.37 0.118 63.47 0.118 98.09 Indep. variable Intercept 1.269 93.18 1.318 111.03 1.059 80.75 1.106 87.12 AA 3.208 100.34 3.142 88.99 0.082 92.24 0.081 87.49

52

Variable definitions: see Table 1 and below. a Panel A reports summary information about the distribution of intercepts, or alphas, estimated from rolling five-year firm-specific CAPM regressions ( ) and 3-factor regressions (CAPMα 3 fα ). b Panel B reports the mean value of the earnings quality metrics by alpha decile. Stocks with the most negative values of ( or CAPMα 3 fα ) are in decile 1, while stocks with the most positive values of ( or CAPMα 3 fα ) are in decile 10. The column labeled “Diff.” shows the difference between the mean value of the noted earnings quality metric between the extreme alpha deciles (1, 2, 9 and 10) and the non-extreme deciles (3-8). The rightmost column reports the t-statistic for the test of whether this difference is reliably different from zero. The test is based on the time-series standard error of the monthly differences. C Panel C reports the coefficient estimates and t-statistics from regressions of the absolute abnormal return ( CAPMα and, separately, 3 fα ) on the raw and decile rank values of each earnings quality metric.

53

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