The Pennsylvania State University

The Graduate School

The Mary Jean and Frank P. Smeal College of Business Administration

OVERREACTION OR UNDERREACTION?

A REEXAMINATION OF THE ACCRUAL ANOMALY

A Thesis in

Business Administration

by

Yong Yu

Submitted in Partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy

August 2006

The thesis of Yong Yu was reviewed and approved* by the following: Orie E. Barron Associate Professor of Accounting Thesis Co-Adviser Co-Chair of Committee Dan Givoly Ernst&Young Professor of Accounting Chair of the Department of Accounting Thesis Co-Adviser Co-Chair of Committee Bin Ke Associate Professor of Accounting James C. McKeown Smeal Chaired Professor of Accounting Karl A. Muller Associate Professor of Accounting Mark J. Roberts Professor of Economics *Signatures are on file in the Graduate School.

iii

ABSTRACT This study reexamines the evidence underlying the prior conclusion that investors overreact

to accruals – accruals are negatively associated with subsequent abnormal returns (i.e., the

“accrual anomaly”). This study shows that the two features of the research design used to

document the accrual anomaly – the omission of cash flows and the use of an annual setting

– both bias downward the association between accruals and subsequent returns. After

controlling for cash flows and using a quarterly setting, this study presents evidence that

accruals are positively associated with subsequent returns, and this positive association is

weaker than the positive association between cash flows and subsequent returns. These

results hold for the full sample of firms on average and are even stronger for sub-samples of

firms where accruals are likely to play a more important role in measuring firm performance.

These results suggest that investors underreact to accruals and underreact to cash flows even

more. Further, this study shows that the puzzling inconsistency between the results generated

by the two approaches of testing investors’ reaction to accruals (i.e., the general one-equation

approach and the two-equation Mishkin test) is due to the absence of controls for some

common risk factors and the use of pooled regressions in the Mishkin test. Finally, this study

provides evidence that financial analysts, like investors, also underreact to accruals and

underreact to cash flows even more in their forecasts of future earnings.

iv

TABLE OF CONTENTS List of Tables v Acknowledgements vi

1. Introduction 1

2. Features of Sloan’s (1996) Research Design 7

2.1 Omission of Cash Flows 7

2.2 Use of an Annual Setting 10

3. Sample Selection and Variable Measurement 13

3.1 Sample Selection 13 3.2 Variable Measurement 13

4. Results of Examining the Association between Accruals and Subsequent Returns 16

4.1 Descriptive Statistics and Correlations 16 4.2 Annual Test 18

4.3 Quarterly Test 24

4.4 Further Sub-sample Test 31

4.5 Additional Analyses 36

4.6 Inconsistency between Results from Two Approaches of Testing Investors’

Reaction to Accruals 39

5. Tests of Analysts’ Earnings Forecasts 43 6. Conclusion 49

References 51 Appendix: Two Approaches of Testing Over- vs. Under-reaction 54

v

LIST OF TABLES

Table 1 Summary Statistics for the Annual and Quarterly Samples 17 Table 2 Time-series Means of Portfolios Abnormal Returns (BHARANN) of Ten

Portfolios Formed Annually Based on either Prior Annual Accruals or Cash Flows

19

Table 3 Fama-MacBeth Regression Analyses of Relations between BHARANN

and Prior Annual Accruals and Cash Flows 21

Table 4 Time-series Means of Portfolios Abnormal Returns (BHARQTR) of Ten

Portfolios Formed Quarterly Based on either Prior Quarterly Accruals or Cash Flows

25

Table 5 Fama-MacBeth Regression and Portfolio Analyses of Relations between

BHARQTR and Prior Quarterly Accruals and Cash Flows 27

Table 6 Sub-sample Analyses Based on the Absolute Magnitude of Accruals or

on the Length of Operating Cycles 33

Table 7 Additional Analyses of Relations between BHARQTR and Prior Quarterly

Accruals and Cash Flows 37

Table 8 Results of the Two-Equation Mishkin Test 41 Table 9 Summary Statistics for the Analysts’ Forecast Samples 45 Table 10 Fama-MacBeth Regression Analyses of Relations between Forecast

Errors and Prior Quarterly Accruals and Cash Flows 47

vi

ACKNOWLEDGEMENTS

I am very grateful to my dissertation committee, Orie Barron, Dan Givoly, Bin Ke,

Jim McKeown, Karl Muller, and Mark Roberts, for their guidance, insight, support, and

encouragement. I thank Donal Byard, Paul Fisher, Carla Hayn, Steve Huddart, Andy Leone,

Henock Louis, Shail Pandit, Santosh Ramalingegowda, and Hal White for helpful comments.

I also wish to acknowledge helpful feedback from workshop participants at Baruch College,

University of Texas at Austin, University of Georgia, University of Utah, University of

Toronto, University of Minnesota, Southern Methodist University, University of California at

Los Angeles, Washington University at St. Louis, University of Rochester, Northwestern

University, Georgetown University, Purdue University, University of Washington, and

Arizona State University. I thank IBES International, Inc. for providing earnings forecast

data.

1

1. Introduction

This study reexamines the evidence underlying the prior conclusion that investors

overreact to accruals – that the accrual component of earnings is negatively associated with

subsequent abnormal stock returns.1 This observed overreaction to accruals, which is first

documented by Sloan (1996) and has been replicated by many following studies, has come to

be known as the “accrual anomaly” and has generated interest among both researchers and

investors.2 3 The purpose of this study is to investigate how two features of the research

design used to document this accrual anomaly affect inferences regarding investors’ reaction

to accruals (i.e., overreaction vs. underreaction).

The first feature is the omission of cash flows from the examination of the association

between accruals and subsequent returns. This omission is problematic because cash flows

are likely to be a significant correlated omitted variable. Given a negative relation between

accruals and cash flows and an underreaction to cash flows, the omission of cash flows is

expected to bias downward the association between accruals and subsequent returns, i.e., in

favor of finding an overreaction to accruals. I analyze the impact of this correlated omitted

variable problem and examine whether, upon inclusion, accruals are still negatively

associated with subsequent returns.

1 In this study, accruals and cash flows refer to the accrual and cash flow components of earnings, and subsequent returns are the abnormal returns in the periods following the reporting date. 2 Studies on the accrual anomaly have taken different paths. One line of studies investigates how the behavior of financial analysts, short sellers, and other third parties is related to this anomaly (e.g., Bradshaw et al., 2001; Richardson, 2003). Another line examines the role of different components of accruals in creating this anomaly (e.g., Xie, 2001; Thomas and Zhang, 2002; Richardson et al., 2005). A third line of research seeks to relate this anomaly to other market anomalies (e.g., Collins and Hribar, 2000; Fairfield et al., 2003; Desai et al., 2004). Some studies examine the relation of this anomaly to various firm characteristics and risk measures (e.g., Ali et al., 2001; Mashruwala et al., 2004; Khan, 2005). Other studies attempt to determine how widespread this anomaly is (e.g., LaFond, 2005; Pincus et al., 2005). 3 Following Sloan (1996), selling high-accrual firms’ stock and buying low-accrual firms’ stock has become a popular trading strategy (see, e.g., Talley, 2003; Henry, 2004a, 2004b). Reportedly, “now investors are clamoring to exploit this market inefficiency.” (Business Week, October 4, 2004, cover story)

2

The second feature is the use of an annual setting whereby annual accruals and

returns subsequent to the annual filing date are examined. The most serious problem with the

use of the annual setting is that the returns over the period following the annual filing date

capture the reversal of the price continuation (i.e. drift) associated with the prior year’s first

three quarters’ accruals. For example, accruals of the first fiscal quarter are shown to be

positively associated with returns following the reporting of the first quarter’s accruals after

controlling for cash flows (presented later in Table 5, Panel A). However, when returns are

measured after the annual filing date (almost one year after the reporting of the first quarter’s

accruals), this positive association becomes much weaker and even turns to be slightly

negative (presented later in Table 3, Panel B). Thus, like the omission of cash flows, the use

of the annual setting also biases downward the association between accruals and subsequent

returns. To correct this downward bias, I examine quarterly accruals and returns subsequent

to the quarterly filing date.

To test investors’ reaction to accruals and cash flows, I run Fama-MacBeth

regressions of subsequent abnormal returns on prior accruals and cash flows and interpret a

negative (positive) coefficient as overreaction (underreaction) (i.e., the one-equation

approach). Abel and Mishkin (1983) prove that this one-equation approach is equivalent to

the two-equation Mishkin test in testing overreaction vs. underreaction but requires fewer

assumptions (i.e., more general than) the Mishkin test (see Appendix).

The main findings that emerge from the analyses are as follows. First, after

controlling for cash flows and using a quarterly setting, accruals are found to be significantly

positively associated with subsequent returns, suggesting that investors underreact to

accruals. This positive association is weaker than the positive association between cash flows

3

and subsequent returns, suggesting that while investors underreact to accruals, they

underreact to cash flows to a greater extent. Second, the results indicate that when cash flows

are omitted, the stronger underreaction to cash flows than to accruals, combined with the

negative correlation between accruals and cash flows, results in a severe downward bias on

the association between accruals and subsequent returns. This bias conceals the underlying

underreaction of investors to accruals, leading to the observed “overreaction” to accruals.

To provide further evidence, I analyze two sub-samples of firms where cash flows are

likely to suffer from more timing and matching problems and accruals are likely more

important in measuring firm performance. Based on the findings of prior research (Dechow

1994; Dechow et al. 1998), the first sub-sample consists of firms with more volatile working

capital requirements and the second consists of firms with longer operating cycles. I find the

above results based on the whole sample are even stronger for these sub-samples of firms

where accruals are likely to play a more important informational role in measuring firm

performance.

Further, this study investigates a puzzling inconsistency: on one hand, the Mishkin

test results reported by Sloan (1996) suggest an overreaction to accruals in the annul setting

even after controlling for cash flows. On the other hand, using the one-equation approach,

Desai et al. (2004) and this study find no mispricing of accruals after controlling for cash

flows in the same annual setting. This inconsistency is puzzling because the Mishkin test

should lead to the same conclusion regarding over- vs. under-reaction as the one-equation

approach if the additional assumptions required by the Mishkin test are satisfied (Abel and

Mishkin 1983). I find that this puzzle can be explained by the absence of controls for some

common risk factors and the use of pooled regressions in the Mishkin test. After controlling

4

for market-to-book and size factors or using the Fama-MacBeth regression approach in the

Mishkin test, I find that the two-equation Mishkin test generates results consistent with those

from the one-equation approach.

Finally, to tie my results to past research on the manner by which financial analysts

process the accrual anomaly, I examine how financial analysts react to accruals using their

forecasts of future earnings. In line with my earlier results on the accrual anomaly, after a

proper control for cash flows, financial analysts are found to underreact to accruals and to

underreact even more to cash flows. Similarly, the results indicate that Bradshaw et al.’s

(2001) finding of analysts’ overreaction to accruals is driven by the omission of cash flows

from their analyses.

My findings make several contributions. First, whether investors use accruals

efficiently in pricing stocks and (if not) what kind of mistake they make (over- vs. under-

pricing) are central questions in accounting. This study is the first that provides empirical

evidence that both investors and financial analysts underprice accruals and they underprice

cash flows even more. The prior conclusion of investors overpricing accruals has sent

researchers off searching for reasons why investors overprice accruals. My findings suggest

that it might be useful to investigate this market anomaly from a different perspective, that is,

why do investors underprice accruals? And why do investors underprice cash flows more

than accruals? (See Section 6 for a discussion of some possible explanations.)

Second, my results help resolve a puzzling finding by previous studies of an

overreaction to one major component of earnings (accruals) and an underreaction to the other

major component of earnings (cash flows). 4 I show that there is no conflict between

4 As noted by Kothari (2001), “one challenge is to understand why the market underreacts to earnings, but its reaction to its two components, cash flows and accruals, is conflicting.”

5

investors’ (and analysts’) reactions to accruals and to cash flows – they consistently

underreact to both accruals and cash flows.

While the focus of this study is on whether investors underreact or overreact to

accruals, the findings have important implications for investors who wish to exploit this

market anomaly. The results indicate that the accrual strategy of shorting high-accrual stocks

and buying low-accrual stocks, though profitable (before transaction costs), is not optimal. If

investors wish to trade on only one information signal, a cash-flow strategy of shorting low-

cash stocks and buying high-cash stocks is shown to earn significantly higher returns than the

accrual strategy. This is not surprising because investors underreact more to cash flows than

to accruals. If investors wish to trade on both accruals and cash flows, the strategy based on

the prior conclusion of investors overpricing accruals and underpricing cash flows (i.e.,

shorting high-accrual and low-cash stocks and buying low-accrual and high-cash stocks) is

shown to earn significantly less abnormal returns than the strategy suggested by my findings

that investors underprice both cash flows and accruals (i.e., shorting low-cash and low-

accrual stocks and buying high-cash and high-accrual stocks).

This study is related to, but distinct from, prior studies. Desai et al. (2004) test

whether the accrual anomaly is subsumed by the value-glamour anomaly. They argue that

cash flows capture the value-glamour distinction. Using an annual setting like Sloan, they

find that when cash flows are added to accruals in the regression, the coefficient on accruals

is negative but becomes statistically and economically insignificant. I confirm their finding in

my annual test. Collins and Hribar (2000) examines whether the accrual anomaly is

subsumed by the post-earnings-announcement-drift anomaly. They find that accruals are still

negatively associated with future stock returns in a quarterly setting even after controlling for

6

unexpected quarterly earnings (SUE). The key difference between the two studies and mine

is that neither of them examines the pricing of accruals after both controlling for cash flows

and using a quarterly setting. Desai et al. do not test the accrual anomaly in a quarterly

setting, and Collins and Hribar do not control for cash flows. As a result, these studies

provide no evidence of investors underpricing accruals.5 In addition, these studies do not

examine how financial analysts react to accruals. In contrast, my study is the first that

provides evidence that investors and financial analysts underreact to accruals and underreact

to cash flows even more.

In section 2, I analyze the two features of the research design used to test the

association between accruals and subsequent returns. Data and variables used in the tests are

discussed in section 3, and the results of testing the association between accruals and

subsequent stock returns are presented in section 4. In section 5, I examine how financial

analysts react to accruals using their forecasts of future earnings. Section 6 contains

conclusions and possible explanations for the findings in this study. The Appendix discusses

the relation between the general one-equation approach and the two-equation Mishkin test in

terms of testing over- vs. under-reaction.

5 Note that my results cannot be inferred from Collins and Hribar (2000). They find that a strategy of combining SUE and accruals generates higher returns than either alone. Their finding can be summarized as showing that

01 <δ and 02 >δ in a model: ttt SUEACCRUALSRETURN 2101 δδδ ++=+ . In contrast, my finding

regarding investors’ reaction to accruals can be summarized as showing that 01 >β , 02 >β and 21 ββ < in a

model: ttt CASHFLOWSACCRUALSRETURN 2101 βββ ++=+ . In order to infer my results from theirs, one must first assume that SUE is equivalent to the level of earnings. This assumption is implausible because unexpected earnings are fundamentally different from the level of earnings. Second, even if we are willing to accept that unexpected earnings are equivalent to the level of earnings, we still need to assume that

0)( 21 >+ δδ in order to infer my results from theirs. However, Collins and Hribar do not provide any

evidence of 0)( 21 >+ δδ .

7

2. Features of Sloan’s (1996) Research Design

2.1 Omission of Cash Flows

Sloan (1996) omits cash flows in his examination of the association between accruals

and subsequent returns.6 This omission is problematic because cash flows are likely to be a

significant correlated omitted variable. To analyze this problem, consider the following

model which examines the association between the two earnings components and subsequent

returns (firm subscripts are omitted for brevity):

)1(12101 ++ +++= tttt εCASHFLOWSβACCRUALSββRETURN

where 1+tRETURN = abnormal returns over period t+1;

tACCRUALS = scaled decile portfolio rank based on accruals in period t;

tCASHFLOWS = scaled decile portfolio rank based on cash flows in period t;

1+tε = an error term.

In Equation (1), the accrual (cash flow) decile ranks are scaled to [0,1] such that firms

with the most positive accruals (cash flows) have a portfolio rank of 1 and firms with the

most negative accruals (cash flows) have a rank of 0. Under this construction, the

coefficients can be interpreted as abnormal returns on portfolios with certain useful

properties (see, e.g., Fama and MacBeth, 1973; Bernard and Thomas, 1990). For example,

1β ( )2β represents the abnormal returns earned by a zero-investment hedge portfolio

strategy of buying firms in the highest accrual (cash flow) decile and selling firms in the

6 Note that Sloan does consider cash flows in another part of his analyses. Using the two-equation Mishkin test, Sloan finds results in the annual setting suggesting an over-reaction to accruals even after controlling for cash flows. In section 4.6, I investigate the puzzling inconsistency between the “no-mispricing” results from the one-equation approach reported in Desai et al. and my annual test and the “over-reaction” results from Sloan’s two-equation Mishkin test.

8

lowest accrual (cash flow) decile. Note that the “accrual anomaly” strategy would then earn

an abnormal return of 1β− .

Equation (1) presents a model that allows us to conveniently test investors’ reaction

to accruals and cash flows. A negative coefficient on accruals ( 01 <β ) indicates that

investors overestimate the persistence of accruals in determining firm value, that is, overact

to accruals. In contrast, 01 >β indicates an underreaction to accruals. The coefficient on cash

flows should be interpreted similarly. Abel and Mishkin (1983) prove that this one-equation

approach is equivalent to the two-equation Mishkin test in testing overreaction vs.

underreaction but requires fewer assumptions (i.e., more general than) the Mishkin test (also

see Mishkin 1983, section 3.3.1) The appendix provides a detailed discussion of the relation

between the two approaches in testing over- vs. under-reaction.

Sloan (1996) finds that a trading strategy of shorting stocks in the highest accrual

decile and buying stocks in the lowest accrual decile earns significant subsequent abnormal

returns. This is equivalent to estimating Equation (1) excluding tCASHFLOWS and finding

that the estimated coefficient on tACCRUALS is significantly negative. However, when

tCASHFLOWS are omitted, the estimated coefficient on tACCRUALS , denoted ∧

1β , is a

biased estimate of 1β .7 Specifically,

)2()(

),()( 211 βββt

tt

ACCRUALSVarCASHFLOWSACCRUALSCovE +=

∧

where ),( tt CASHFLOWSACCRUALSCov is the covariance between tACCRUALS and

tCASHFLOWS , and tACCRUALSVar( ) is the variance of tACCRUALS .

7 See Wooldridge (2003, Chapter 3) and Greene (2003, Chapter 8).

9

Since both tACCRUALS and tCASHFLOWS are decile portfolio ranks ranging from

[0,1], they have the same variance. Therefore, Equation (2) can be rewritten as:

)3(),()( 211 βββ tt CASHFLOWSACCRUALSCorrE +=∧

where ),( tt CASHFLOWSACCRUALSCorr is the correlation between tACCRUALS and

tCASHFLOWS . Equation (3) shows that the bias in ∧

1β is determined by two factors: the

correlation between accruals and cash flows, and the mispricing of cash flows.8

The primary role of accruals in mitigating timing and matching problems inherent in

cash flows results in a negative correlation between the two earnings components. Given an

underreaction to cash flows (i.e., 02 >β ), the omission of cash flows causes a downward bias

in ∧

1β (i.e., )0*),( 2 <βtt CASHFLOWSACCRUALSCorr . Depending on the severity of this

downward bias, the observed “accrual anomaly” ( )01 <∧

β is consistent with three potential

explanations:

• Investors overreact to accruals (i.e., 01 <β ). The accrual anomaly indeed holds.

However, because its magnitude is overstated due to the downward bias, the question

remains as to whether or not the anomaly is economically significant.

• Investors price accruals correctly (i.e., 01 =β ). The observed “overreaction” to

accruals is driven by the downward bias, and there is no mispricing of accruals.

8 Similar to the omission of cash flows in examining accruals and subsequent returns, Sloan (1996) also omits accruals in documenting a positive association between cash flows and subsequent returns. By examining both accruals and cash flows concurrently, this study also provides evidence that the omission of accruals biases downward the association between cash flows and subsequent returns and thus understates investors’ underreaction to cash flows (see section 4 for the results).

10

• Investors underreact to accruals (i.e., 01 >β ). There appears to be an “accrual

anomaly” because the downward bias dominates the positive coefficient ( 1β ).

Specifically, [ ] 12*),( ββ >− tt CASHFLOWSACCRUALSCorr . Because

[ ]),( tt CASHFLOWSACCRUALSCorr− is between 0 and 1, this suggests that

12 ββ > , that is, investors underreact to cash flows to a greater extent than they

underreact to accruals. In other words, the apparent “accrual anomaly” is driven by

the more severe underreaction to cash flows than to accruals, combined with the

negative correlation between accruals and cash flows.

To summarize, the above analysis shows that the omission of cash flows from Sloan’s

analysis leaves the existence of the accrual anomaly an open question. To address this

question, I examine the association between accruals and subsequent returns while

controlling for the effect of cash flows.9

2.2 Use of an Annual Setting

Sloan (1996) finds the accrual anomaly in tests using annual accruals and returns

subsequent to the annual filing date. Ex ante, the use of this annual setting has two

limitations. First, annual accruals play a lesser role in improving cash flows as a measure of

firm performance than accruals over shorter measurement intervals (e.g., quarters). The

accrual process is hypothesized to mitigate the timing and matching problems inherent in

9 Since accruals and cash flows are correlated, one might argue that the accrual anomaly is largely driven by the “common” variation shared by both accruals and cash flows and controlling for cash flows is inappropriate because it “takes away” this “common” part. However, this argument is incorrect. First, this “common” part cannot be the driver of the accrual anomaly simply because the accrual anomaly is documented even after controlling for cash flows (i.e., “takes away” this “common” part) in the two-equation Mishkin test (Sloan 1996, Table 5). Second, even if this is the case, one cannot conclude any mispricing of accruals based on the “common” part because the “common” part cannot be attributed uniquely to accruals.

11

cash flows over finite measurement intervals (e.g., Watts and Zimmerman, 1986; Dechow,

1994; Dechow et al., 1998). Because cash flows suffer from more timing and matching

problems over shorter intervals, accruals over such intervals are more important in providing

value-relevant information about firm performance. Over longer intervals, cash flows have

fewer problems and converge to earnings; so the role of accruals diminishes. This property of

accruals suggests that quarterly accruals provide a more powerful setting than annual

accruals to examine investors’ reaction to accruals.

Second, the use of the annual setting ignores accrual information provided in interim

reports, which preempts at least part of the accrual information released in annual reports. As

a result, abnormal returns measured over the period following the annual filing date reflect

primarily the potential mispricing of the fourth-quarter accruals and fail to fully capture the

potential mispricing of the first three quarters’ accruals. For example, consider the

information conveyed by first-quarter accruals. By the fourth month after fiscal year-end

(when returns begin to be measured in the tests using the annual setting), first-quarter accrual

information has been released for about one year; so only part, if any, of investors’ initial

(anomalous) reaction to this information is captured by the post-annual-report returns.

Besides the above two limitations, a more serious problem is that the use of the

annual setting biases downward the association between accruals and subsequent stock

returns. Specifically, I find that each quarter’s accruals are positively associated with returns

after this quarter’s filing date (after controlling for cash flows). However, the first three fiscal

quarters’ accruals of a given year are positively associated with returns after the three

quarter’s respective filing dates but turns to be negatively (though insignificantly) associated

with returns after this fiscal year’s annual filing date.

12

For example, consider the first fiscal quarter of a December year-end firm in year t.

The first quarter’s accruals are positively associated with returns in the 12-month period

following the first quarter’s filing date - from June of year t till May of year t+1 (See Table

5, Panel A). However, when returns are measured in the 12-month period after the year t’s

annual filing date - from May of year t+1 till April of year t+2, the accrual-return

association turns to be slightly negative (see Table 3, Panel B). This shows that measuring

returns long after the reporting of quarterly accruals (in this example, the return measure

starts in May of year t+1 while accruals are reported in April to May of year t – with a one-

year gap) captures the reversal of the initial price continuation and causes a downward bias

on the association between accruals and subsequent returns.

To overcome the two limitations and, more importantly, correct the downward bias

arising from the use of the annual setting, I examine the relation between quarterly accruals

and returns subsequent to the quarterly filing date.

13

3. Sample Selection and Variable Measurement

3.1 Sample Selection

The sample used in the annual (quarterly) test consists of all available NYSE/AMEX

firm-years (firm-quarters) from 1988 through 2002 with required financial statement data on

the Compustat database and monthly return data on the CRSP database.10 11 In order to

ensure that cash flows and accruals are accurately measured, the sample period begins in

1988 when cash flow statement data became available.12 Following prior research, I exclude

closed-end funds, investment trusts, foreign companies, and financial institutions (SIC code

6000-6999) due to the difficulty of interpreting accruals for financial firms.13 This results in a

sample of 25,540 firm-years for the annual test (the annual sample) and a sample of 79,809

firm-quarters for the quarterly test (the quarterly sample), spanning a sixty-quarter period

from 1988 through 2002.

3.2 Variable Measurement

Accruals are measured as the difference between earnings and cash flows from

operations taken from the statement of cash flows. Earnings are income from continuing

10 NYSE/AMEX firms are identified using the historical exchange code (EXCHCD) from the CRSP monthly event file in the month before the return calculation. Using current exchange listing (e.g., Compustat’s Zlist or CRSP’s header exchange code) introduces a selection bias because changes in exchange listing are correlated with firm performance and a firm currently on the NYSE/AMEX may be traded on other exchanges in the past. Using EXCHCD avoids this selection bias (Kraft et al., 2005b). 11 The results are robust to the inclusion of NSDQ firms. 12 Sloan (1996) uses a balance sheet approach to measure accruals. This approach introduces measurement errors into the accruals measure, particularly when a firm has been involved in mergers, acquisitions, or divestitures. Measuring accruals using cash flows statement data is more precise (see, e.g., Drtina and Largay, 1985; Hribar and Collins, 2002). 13 The results are similar if these observations are included.

14

operations, and cash flows are cash flows from continuing operations. All three variables are

scaled by average total assets.14 15

The abnormal return measure is the annual size-adjusted buy-and-hold returns as used

in Sloan (1996). Raw returns are obtained from the CRSP monthly return file. Abnormal

returns are computed by subtracting a firm’s size-matched buy-and-hold returns from the raw

buy-and-hold returns. Size portfolio returns are provided by CRSP and calculated using all

NYSE/AMEX firms based on their beginning-of-year market capitalizations. A firm’s return

is set to zero for any month if it is missing due to lack of trading.16 If a firm is delisted during

the return accumulation period, the delisting return as reported in the CRSP event file for the

delisting period is used, and a return equal to the firm’s size portfolio return for the rest of the

accumulation period is employed. If a firm is delisted due to liquidation or a forced delisting

by either the exchange or the SEC and the delisting return is missing, the delisting return is

set to -100%.17

Following Sloan (1996), the future buy-and-hold abnormal returns in the annual test,

denoted ANNBHAR , are measured from four months after the fiscal year-end through the

fourth month of the subsequent fiscal year. Similarly, the future buy-and-hold abnormal

returns in the quarterly test, denoted QTRBHAR , span the twelve-month period beginning two

months after the fiscal quarter-end for the first three fiscal quarters and four months after the

14 For the annual sample, earnings are Compustat Annual Item 123, cash flows are Compustat Annual (Item 308 – Item 124), and total assets are Compustat Annual Item 6. For the quarterly sample, earnings are Compustat Quarterly Item 76, cash flows are Compustat Quarterly (Item 108 – Item 78), and total assets are Compustat Quarterly Item 44. Note that for quarterly cash flow statement items, Compustat reports data for the cumulative interim period year to date. 15 The results remain unchanged if these variables are scaled by market value of equity or net sales. 16 This is identified using CRSP code “.B” in the return field. Excluding firms with missing returns due to a lack of trading activity disproportionately affects firms with bad stock performance, and thus excluding their returns imposes an upward bias in measuring abnormal returns (Kraft et al., 2005b). Nevertheless, the results are robust to excluding these observations or replacing these missing returns with the corresponding size decile returns. 17 The results remain unchanged if I delete these delisting firms or assume a delisting return of zero.

15

fiscal quarter-end for the fourth fiscal quarter.18 Within this two-month interval, almost all

firms have filed 10-Q reports for the first three fiscal quarters, and within the four-month

interval, almost all firms have filed 10-K reports (Easton and Zmijewski, 1993).

18 I repeat the analyses using 3- and 6-month windows. The results using these shorter return windows are stronger (see Section 4.5 for a discussion and results).

16

4. Results of Examining the Association between Accruals and Subsequent Returns

Section 4.1 provides descriptive statistics and correlation analyses. Section 4.2

examines the association between annual accruals and returns subsequent to the annual filing

date (hereafter, the annual test). Section 4.3 conducts the main analysis in a quarterly setting,

examining quarterly accruals and returns subsequent to the quarterly filing date (hereafter,

the quarterly test). Section 4.4 provides further evidence by focusing on sub-samples of firms

where accruals play a more important role (hereafter, the sub-sample test). Additional

analyses are reported in Section 4.5. Section 4.6 investigates the puzzling inconsistency

between the “overreaction” results from the two-equation Mishkin test reported in Sloan and

the “no-mispricing” results from the one-equation approach reported in Desai et al. and the

annual test of this study.

4.1 Descriptive Statistics and Correlations

Table 1 provides descriptive statistics (Panel A) and a correlation analysis (Panel B)

for both the annual and quarterly samples. Panel A indicates that on average accruals are

negative and cash flows are positive. Panel B shows that accruals are highly negatively

correlated with cash flows, consistent with the primary role of accruals in mitigating the

timing and matching problems inherent in cash flows. Moreover, the magnitude of the

negative correlation between cash flows and accruals is larger in the quarterly sample

(Spearman = -0.752) than in the annual sample (Spearman = -0.511), consistent with cash

flows suffering more severely from timing and matching problems and accruals playing a

more important role in mitigating these problems over shorter performance measurement

intervals (Dechow, 1994).

17

Table 1 Summary Statistics for the Annual and Quarterly Samplesa

Panel A: Descriptive statistics Variable Mean Median Std.Dev. 25% 75%

Annual sample (N = 25,540 firm-years)

Earnings 0.024 0.041 0.173 0.009 0.076 Cash flows 0.074 0.084 0.155 0.037 0.131 Accruals -0.050 -0.046 0.108 -0.084 -0.010

Quarterly sample (N = 79,809 firm-quarters)

Earnings 0.005 0.010 0.055 0.002 0.021 Cash flows 0.018 0.020 0.062 -0.001 0.041 Accruals -0.013 -0.011 0.059 -0.030 0.008 Panel B: Pearson (upper diagonal) and Spearman (lower diagonal) correlationsb

Annual sample (N = 25,540 firm-years)

Earnings Cash flows Accruals Earnings 1.000 0.786 0.467 Cash flows 0.554 1.000 -0.179 Accruals 0.292 -0.511 1.000

Quarterly sample (N = 79,809 firm-quarters)

Earnings Cash flows Accruals Earnings 1.000 0.493 0.418 Cash flows 0.385 1.000 -0.584 Accruals 0.169 -0.752 1.000 a The annual and quarterly samples include all U.S. common stocks (except financial firms) on NYSE or AMEX that have the necessary financial data on Compustat and monthly return data on CRSP from 1988 through 2002. Earnings = income from continuing operations (Compustat Annual Item 123 for the annual sample and Compustat Quarterly Item 76 for the quarterly sample). Cash flows = cash flows from continuing operations (Compustat Annual (Item 308 – Item 124) for the annual sample and Compustat Quarterly (Item 108 – Item 78) for the quarterly sample). Accruals = the difference between Earnings and Cash flows. All three variables are scaled by average total assets (Compustat Annual Item 6 for the annual sample and Compustat Quarterly Item 44 for the quarterly sample). bAll reported correlations are significant at the 0.001 level, using a two-tailed test.

18

4.2 Annual Test

Table 2, Panel A replicates the accrual anomaly using the annual sample. To conduct

this analysis, each year firms are ranked by their prior annual accruals and placed into ten

equal-size portfolios, denoted A1 to A10. An equally-weighted abnormal return is computed

for each portfolio. The reported t-statistics are calculated using the Fama-MacBeth (1973)

method and corrected for auto-correlation using Newey and West (1987) standard errors.

Panel A presents the average portfolio returns, accruals, and cash flows over fifteen years for

each of the ten accrual portfolios.

The results are consistent with the accrual anomaly: a hedge portfolio strategy of

selling the most positive accrual firms (portfolio A10) and buying the most negative accrual

firms (portfolio A1) yields an annual abnormal return of 9.3%. On the other hand, given the

strong negative correlation between accruals and cash flows, it is not surprising to find that

firms in the most positive (negative) accrual portfolio also have extremely negative (positive)

cash flows. Because this univariate analysis does not control for the effect of cash flows, the

negative association between accruals and subsequent returns cannot be unambiguously

interpreted as evidence that investors overreact to accruals. Panel B repeats the above

analysis on cash flows. The results indicate that a strategy of selling the most negative cash

flow firms (portfolio C1) and buying the most positive cash flow firms (portfolio C10) yields

an annual abnormal return of 11.9%. It should be noted that the cash-flow strategy earns

higher abnormal returns than the accruals strategy.

To control for the confounding effect of cash flows in testing investors’ reaction to

accruals, I regress subsequent returns on the scaled accrual decile ranks (ACCRUALS) and

19

Table 2 Time-series Means of Portfolio Abnormal Returns ( ANNBHAR ) of Ten Portfolios

Formed Annually Based on either Prior Annual Accruals or Cash Flowsa Panel A: Accrual portfolios (N = 24,540 firm-years) Accrual Deciles

A1 (lowest)

A2 A3 A4 A5 A6 A7 A8 A9 A10 (highest)

Hedge (A1-A10)b (t-stat)c

ANNBHAR 0.050 0.039 0.004 0.035 0.009 0.019 0.001 -0.027 -0.035 -0.043

Accruals -0.240 -0.113 -0.084 -0.067 -0.053 -0.040 -0.027 -0.009 0.018 0.114

Cash flows 0.110 0.125 0.116 0.106 0.095 0.080 0.072 0.059 0.038 -0.051

0.093

(3.68)

Panel B: Cash flow portfolios (N = 24,540 firm-years) Cash flow Decile

C1 (lowest)

C2 C3 C4 C5 C6 C7 C8 C9 C10 (highest)

Hedge (C10-C1) b (t-stat)

ANNBHAR -0.083 -0.019 -0.024 0.024 0.017 0.021 0.009 0.036 0.033 0.037

Accruals 0.011 -0.010 -0.026 -0.036 -0.044 -0.055 -0.063 -0.071 -0.084 -0.124

Cash flows -0.175 0.004 0.036 0.058 0.075 0.092 0.109 0.131 0.161 0.247

0.119

(4.08)

aThis table reports the time-series means of the annual portfolio abnormal returns over 15 years from 1988 through 2002 using the annual sample. To form the portfolios, each year firms are ranked by their prior annual accruals (Panel A) or cash flows (Panel B) and placed into ten equal-size portfolios, and an equally-weighted abnormal return ( ANNBHAR ) is computed for each portfolio. ANNBHAR is annual size adjusted buy-and-hold abnormal returns, beginning four months after the fiscal year end through the fourth month of the subsequent fiscal year. The time-series means of the average accruals and cash flows of the annual portfolios are also reported. See Table 1 for additional variable definitions. bThe accrual hedge portfolio strategy (Panel A) buys firms in the lowest accrual decile (A1) and sells firms in the highest accrual decile (A10). The cash flow hedge portfolio strategy (Panel B) buys firms in the highest cash flow decile (C10) and sells firms in the lowest cash flow decile (C1). cT-statistics are calculated using Fama-MacBeth type time-series mean portfolio returns with Newey-West (1987) standard errors.

20

the scaled cash flow decile ranks (CASHFLOWS).19 The scaled decile ranks are constructed

by ranking all firms in each period independently on accruals and cash flows into deciles 0-9

and then dividing the decile ranks by 9 so that they range from 0 (for the lowest decile) to 1

(for the highest decile).

Under this construction, the coefficient on ACCRUALS can be interpreted as the

abnormal returns to a zero-investment trading strategy of buying firms in the highest accrual

decile and selling firms in the lowest accrual decile (Bernard and Thomas, 1990). The

coefficient on CASHFLOWS can be interpreted similarly. To ensure that the results are not

merely driven by the size or market-to-book effects, the scaled decile ranks for size (SIZE)

and market-to-book ratios (MB), constructed in a similar way, are included as additional

controls (see Kothari, 2001, for a discussion).20

Table 3, Panel A reports Fama-MacBeth mean coefficient estimates from annual

regressions of ANNBHAR on the scaled decile ranks based on prior annual accruals

(ACCRUALS) and cash flows (CASHFLOWS). The coefficient on ACCRUALS, before

controlling for cash flows, is -0.086 (significant at the 0.01 level), consistent with the accrual

anomaly. However, after controlling for cash flows, the coefficient on ACCRUALS decreases

to -0.024 and becomes statistically insignificant (t-stat = -0.93).21 The omission of cash flows

causes a downward bias of -0.061 (significant at the 0.01 level) in the coefficient on

19 None of the inferences are changed when continuous variables are used instead of rank variables. 20 Size is included as an additional control because size-adjusted returns may not fully control for the size effect (Bernard, 1987). The results are similar if these controls are not included. The results are robust to controlling for the market beta calculated using the prior 60-month return period. Note that controlling for the momentum factor is inappropriate because the underreaction to accruals and cash flows examined in this study is a momentum (drift) phenomenon. 21 Untabulated analyses indicate that this result is sensitive to some possible outliers. After deleting 1% of the annual sample with the largest squared residuals (Knez and Ready, 1997), I find that the coefficient on ACCRUALS is 0.048 (t-stat = 2.81) after controlling for cash flows.

21

Table 3 Fama-MacBeth Regression Analyses of Relations between ANNBHAR and

Prior Annual Accruals and Cash Flowsa Panel A: Using prior annual accruals and cash flows (N = 24,540 firm-years)

Intercept ACCRUALS CASHFLOWS SIZE MB Ave. R2 Mean

(t-stat)b 0.084**

(2.79) -0.086***

(-6.84) 0.007

(0.24) -0.079** (-2.62)

0.009

Mean (t-stat)

0.005 (0.14)

0.130*** (5.86)

-0.025 (-0.99)

-0.103*** (-3.80)

0.016

Mean (t-stat)

0.019 (0.42)

-0.024 (-0.93)

0.117*** (3.40)

-0.024 (-1.10)

-0.098*** (-3.67)

0.019

Bias in ACCRUALS (t-stat)

-0.061*** (-3.81)

Panel B: Using the quarterly components of prior annual accruals and cash flows (t-statistics provided in parentheses)b Using prior year’s fourth-quarter

(Q4) cash flows and accruals Using prior year’s four quarterly (Q1-4) cash flows and accruals

Intercept -0.047 (-1.01)

-0.006 (-0.08)

Q4ACCRUALS 0.075** (2.54)

0.075*** (3.34)

Q4CASHFLOWS 0.143*** (3.81)

0.154*** (4.13)

Q3ACCRUALS -0.021 (-1.05)

Q3CASHFLOWS 0.080*** (3.71)

Q2ACCRUALS -0.067** (-2.86)

Q2CASHFLOWS -0.020 (-0.70)

Q1ACCRUALS -0.045 (-1.11)

Q1CASHFLOWS -0.009 (-0.21)

SIZE -0.018 (-0.79)

-0.034 (-1.32)

MB -0.090** (-2.60)

-0.086** (-2.67)

Ave. R2 0.016 0.027 N 19,973 19,529

22

Table 3 (continued) *, **, *** denote two-tailed significance levels of 10%, 5%, and 1%, respectively. a This table reports Fama-MacBeth mean coefficient estimates from 15 annual regressions of

ANNBHAR on prior annual accruals and cash flows (Panel A) and on the quarterly components of prior annual accruals and cash flows (Panel B). Panel A uses the annual sample and Panel B requires additional non-missing quarterly data. ANNBHAR is annual size adjusted buy-and-hold abnormal returns, beginning four months after the fiscal year end through the fourth month of the subsequent fiscal year. All regressors are assigned to deciles annually and scaled so that they range from 0 (for the lowest decile) to 1 (for the highest decile). ACCRUALS and CASHFLOWS are scaled decile ranks based on prior annual accruals and cash flows, respectively. QiACCRUALS and QiCASHFLOWS are scaled decile ranks based on prior year’s quarter i accruals and cash flows, respectively (i = 1,2,3 or 4). SIZE and MB are scaled decile ranks for firm size (Compustat Annual Item 199 * Item 25) and market-to-book ratios (Compustat Annual (Item 199 * Item 25)/Item 60) measured at the prior year-end. bT-statistics are calculated using Fama-MacBeth type time-series mean coefficients with Newey-West (1987) standard errors.

23

ACCRUALS.22 This insignificant relation between accruals and subsequent returns after

controlling for cash flows is consistent with two potential explanations: (1) investors price

accruals correctly, or (2) the annual test has limited ability to detect the mispricing of

accruals. This evidence also explains why the cash flows strategy is more profitable than the

accrual strategy (Table 2). This is because the negative association between annual accruals

and subsequent returns merely captures part of investors’ underreaction to annual cash flows.

The analyses in Panel A constrain the coefficients on the quarterly components of

annual accruals to be equal. As discussed in section 2.2, one problem that arises with the use

of this annual setting is that the dependent variable, ANNBHAR , reflects primarily the potential

mispricing of the fourth-quarter accruals and fails to fully capture the potential mispricing of

the first three quarters’ accruals. In Table 3, Panel B, I allow the coefficient to vary across the

quarterly components of annual accruals and focus on the association between ANNBHAR and

the fourth-quarter accruals. Column 1 reports the mean coefficient estimates from annual

regressions of ANNBHAR on the scaled decile ranks based on the prior year’s fourth-quarter

accruals (Q4ACCRUALS) and cash flows (Q4CASHFLOWS). The sample consists of all the

firm-years in the annual sample with the required fourth-quarter data for that firm-year. The

coefficient on Q4ACCRUALS (after controlling Q4CASHFLOWS) is 0.075 (significant at the

0.05 level). The coefficient on Q4CASHFLOWS is also significantly positive (0.143,

significant at the 0.01 level) and almost twice as large as the coefficient on Q4ACCRUALS. In

Column 2, I repeat the analyses in Column 1 but control for the first three quarters’ accruals

22 To assess potential multicollinearity for the regression analyses including both accruals and cash flows, I compute the variance-inflation factor (VIF) for all the regressions. A general rule of thumb is that a VIF less than 20 does not indicate severe multicollinearity. Untabulated results show that no variable in any regression has a VIF more than 10 (e.g., in the 60 quarterly regressions including both accruals and cash flows as reported in Table 5, the median (maximum) VIF for ACCRUALS and CASHFLOWS is 2.43 (5.41) and 2.58 (5.66) respectively), indicating multicollinearity is not a problem. (For a discussion about multicollinearity, see Maddala, 2001, and Greene, 2003).

24

and cash flows. The results are very similar: the coefficient on Q4ACCRUALS is significantly

positive (0.075, significant at the 0.01 level), and the coefficient on Q4CASHFLOWS is twice

as large as the coefficient on Q4ACCRUALS (0.154, significant at the 0.01 level).23

While Q4ACCRUALS are positively associated with returns after annul filing date

(i.e., returns following the reporting of Q4ACCRUALS), the coefficients on QiACCRUALS (i

= 1,2,3) are negative. This finding suggests that quarterly accruals may be positively

associated with returns following the respective reporting dates, but when returns are

measured long after the actual quarterly reporting dates, the positive accrual-return

association reverses. In Section 4.3, I investigate this issue by testing the association between

each quarter’s accruals and returns following the respective quarterly filing date.

4.3 Quarterly Test

Table 4 replicates the accrual anomaly using the quarterly sample. To conduct this

analysis, ten equal-sized portfolios are formed each quarter based on prior quarterly accruals,

and an equally-weighted abnormal return ( QTRBHAR ) is then computed for each portfolio. T-

statistics are calculated using Fama-MacBeth type time-series mean portfolio returns with

Newey-West (1987) standard errors. Panel A of Table 4 reports the average portfolio return

and accruals and cash flows over sixty quarters for each of the ten portfolios. The results are

consistent with the accrual anomaly: a trading strategy of selling the most positive accrual

firms and buying the most negative accrual firms yields a significant annual abnormal return

of 6.8%. Panel B indicates that a trading strategy of selling firms with the most negative cash

23 The coefficients on QiACCRUALS (i = 1,2,3) are generally not significant except Q2ACCRUAL (-0.067, t-stat = -2.86). Further analyses indicate that this is caused by a few extreme observations. After deleting 1% of the sample with the largest squared residuals, this coefficient becomes -0.023 (t-stat = -0.88).

25

Table 4 Time-series Means of Portfolio Abnormal Returns ( QTRBHAR ) of Ten Portfolios

Formed Quarterly Based on either Prior Quarterly Accruals or Cash Flowsa Panel A: Accrual portfolios (N = 79,809 firm-quarters) Accrual Deciles

A1 (lowest)

A2 A3 A4 A5 A6 A7 A8 A9 A10 (highest)

Hedge (A1-A10)b (t-stat)c

QTRBHAR 0.023 0.022 0.020 0.014 0.007 0.005 -0.001 -0.015 -0.022 -0.045

Accruals -0.109 -0.046 -0.031 -0.022 -0.015 -0.008 -0.001 0.008 0.022 0.077

Cash flows 0.075 0.047 0.038 0.030 0.024 0.019 0.012 0.004 -0.010 -0.060

0.068

(3.95)

Panel B: Cash flow portfolios (N = 79,809 firm-quarters) Cash flow Decile

C1 (lowest)

C2 C3 C4 C5 C6 C7 C8 C9 C10 (highest)

Hedge (C10-C1) b (t-stat)

QTRCAR -0.079 -0.050 -0.022 -0.010 0.011 0.016 0.018 0.021 0.050 0.052

Accruals 0.050 0.014 0.003 -0.004 -0.010 -0.015 -0.020 -0.026 -0.037 -0.080

Cash flows -0.086 -0.017 -0.001 0.009 0.017 0.024 0.032 0.041 0.055 0.105

0.131

(7.25)

aThis table reports the time-series means of the quarterly portfolio abnormal returns over 60 quarters from 1988 through 2002 using the quarterly sample. To form the portfolios, each quarter firms are ranked by their prior quarterly accruals (Panel A) or cash flows (Panel B) and placed into ten equal-size portfolios, and an equally-weighted abnormal return ( QTRBHAR ) is computed for each portfolio. QTRBHAR is annual size adjusted buy-and-hold abnormal returns, beginning 2 months after the prior fiscal quarter-end for the first three fiscal quarters and four months after the prior fiscal quarter-end for the fourth fiscal quarter. The time-series means of the average accruals and cash flows of the quarterly portfolios are also reported. See Table 1 for additional variable definitions. bThe accrual hedge portfolio strategy (Panel A) buys firms in the lowest accrual decile (A1) and sells firms in the highest accrual decile (A10). The cash flow hedge portfolio strategy (Panel B) buys firms in the highest cash flow decile (C10) and sells firms in the lowest cash flow decile (C1). cT-statistics are calculated using Fama-MacBeth type time-series mean portfolio returns with Newey-West (1987) standard errors.

26

flow and buying firms with the most positive cash flow yields an even greater abnormal

return, 13.1% per year.

Table 5, Panel A reports Fama-MacBeth mean coefficient estimates from quarterly

regression analyses of QTRBHAR on the scaled decile ranks based on prior quarterly accrual

(ACCRUALS) and cash flow (CASHFLOWS). When cash flows are omitted, the coefficient

on ACCRUALS is -0.062 (significant at the 0.01 level), consistent with the accrual anomaly.

However, the sign of the coefficient on ACCRUALS, after controlling for cash flows,

becomes positive, and this positive coefficient is both economically and statistically

significant (0.084, significant at the 0.05 level). Thus, when cash flows are omitted, the

omission of cash flows causes a downward bias (-0.146, significant at the 0.01 level) in the

coefficient on ACCRUALS. This bias is so severe that it dominates the underlying positive

relation between accruals and subsequent returns.

Similarly, the results indicate that the omission of accruals also biases downward (but

does not dominate) the association between cash flows and subsequent returns. Specifically,

the coefficient on CASHFLOWS is 0.196 when accruals are controlled for, but is reduced to

0.130 by the omission of accruals.

The relative magnitude of the coefficients on ACCRUALS and CASHFLOWS is

noteworthy. When both are included in the regression, the positive coefficient on

CASHFLOWS is more than twice as large as the positive coefficient on ACCRUALS, with the

difference of 0.112 between the two coefficients (significant at the 0.01 level). This large

difference between the two coefficients explains why the omission of cash flows not only

biases downward the coefficient on accruals but turns it negative and significant (see section

27

Table 5 Fama-MacBeth Regression Analyses of Relations between QTRBHAR and

Prior Quarterly Accruals and Cash Flowsa

Panel A: Fama-MacBeth regression analyses (N = 79,809 firm-quarters) a

Intercept ACCRUALS CASHFLOWS SIZE MB Avg. R2 Mean (t-stat)

0.052*** (2.92)

-0.062*** (-5.10)

0.033 (1.37)

-0.073** (-2.01)

0.010

Mean (t-stat)

-0.028 (-1.32)

0.130*** (9.52)

0.010 (0.46)

-0.082** (-2.31)

0.015

Mean (t-stat)

-0.094** (-2.67)

0.084** (2.32)

0.196*** (5.19)

-0.003 (-0.17)

-0.086** (-2.40)

0.019

Bias in ACCRUALS (t-stat)

-0.146*** (-5.39)

Panel B: Portfolios sorting on cash flows and Accruals (N=79,809 firm quarters) b

Mean (median) portfolio returns Cashflow Quintiles

Lowest Highest Accrual Quintiles C1 C2 C3 C4 C5

All Stock

A1(lowest) -0.119 (-0.135)

-0.039 (-0.045)

-0.011 (-0.029)

0.016 (0.012)

0.040 (0.033)

-0.023 (-0.024)

A2 -0.060 (-0.059)

-0.014 (-0.025)

0.017 (0.017)

0.025 (0.018)

0.071 (0.060)

0.008 (0.007)

A3 -0.051 (-0.058)

-0.016 (-0.012)

0.019 (0.015)

0.035 (0.028)

0.049 (0.046)

0.007 (0.011)

A4 -0.045 (-0.045)

-0.020 (-0.014)

0.017 (0.013)

0.015 (0.015)

0.050 (0.046)

0.003 (0.008)

A5(highest) -0.048 (-0.056)

0.008 (0.025)

0.024 (0.024)

0.005 (0.004)

0.042 (0.035)

0.006 (0.009)

A1-A5 -0.071** -0.047** -0.035* 0.011 -0.002 -0.029** t-stat -2.37 -2.52 -1.75 0.61 -0.11 -2.14 *, **, *** denote two-tailed significance levels of 10%, 5%, and 1%, respectively. aPanel A reports Fama-MacBeth mean coefficient estimates from 60 quarterly regressions of

QTRBHAR on prior quarterly accruals and cash flows and controls using the quarterly sample. QTRBHAR is annual size adjusted buy-and-hold abnormal returns, beginning two months after the

prior fiscal quarter-end for the first three fiscal quarters and four months after the prior fiscal quarter-end for the fourth fiscal quarter. All regressors are assigned to deciles quarterly and scaled so that they range from 0 (for the lowest decile) to 1 (for the highest decile). ACCRUALS and CASHFLOWS are scaled decile ranks based on prior quarterly accruals and cash flows, respectively. SIZE and MB are scaled decile ranks for firm size (Compustat Quarterly Item 14 * Item 61) and market-to-book

28

ratios (Compustat Quarterly (Item 14 * Item 61)/Item 59) measured at the prior quarter-end, respectively. T-statistics are calculated using Fama-MacBeth type time-series means with Newey-West (1987) standard errors. b Panel B reports time-series mean abnormal returns for 25 portfolios formed each quarter on prior quarterly cash flows and accruals. Each quarter, all the firms in the quarterly sample are assigned into one of 5 portfolios based on prior quarterly cash flows and then all the firms in each cash flows quintile are further ranked into five quintile portfolios based on prior quarterly accruals. Mean abnormal returns for each of 25 portfolios are calculated each quarter and then averaged over the 60 quarters. The table reports average quarterly abnormal portfolio returns; t-statistics are calculated using Fama-MacBeth type time-serious mean portfolio returns.

29

2.1). The stronger underreaction to cash flows than accruals also explains why the cash-flow

strategy is more profitable than the accrual strategy in a quarterly setting (Table 4).

The quarterly sample includes all four fiscal quarters. However, because of

seasonality and other differences across fiscal quarters, the results in Table 5, Panel A might

be driven by one particular fiscal quarter (e.g., the fourth quarter), or may differ

systematically across different fiscal quarters. To investigate this possibility, I rerun the

analyses separately for each of the four fiscal quarters (unreported). I find that the results for

the whole sample hold for each fiscal-quarter sample and there is little systematic difference

in the results across different fiscal quarters.

The evidence that each quarter’s accruals are positively associated with returns

following the respective quarterly filing date, combined with the evidence in Panel B of

Table 3, highlights the downward bias on the accrual-return association caused by the use of

the annual setting. Although the first three quarters’ accruals are all positively associated

with returns following their respective reporting dates, this positive association becomes

much weaker and turns to be negative when we measure returns long after the first three

quarters’ reporting dates (i.e., after the annual filing date in the annual setting).

In addition to the regression approach, an alternative way to investigate the

association between accruals and subsequent returns while controlling for the confounding

effect of cash flows is a two-way portfolio analysis which sorts stocks into cash flows and

accruals sequentially. Each quarterly all firms in the quarterly sample are assigned into 5

portfolios based on prior quarter’s cash flows and then all the firms in each cash flow quintile

are further ranked into five portfolios based on prior quarter’s accruals. Panel B of Table 5

reports the time-series mean abnormal returns for the 25 portfolios over the 60 quarters. The

30

results in Panel B of Table 5 show that on average the high-accrual portfolios earn higher

abnormal returns than the low-accrual portfolios after controlling for cash flows (see the last

column to the right), and the return difference between low and high accrual portfolios is

stronger for firms with relatively low cash flows. This evidence is consistent with the

regression results and confirms that investors underreact to accruals.

The results in Table 5 have important implications for investors who wish to trade on

both cash flows and accruals. The prior conclusion that investors overprice accruals and

underprice cash flows suggests that investors should buy stocks with high cash flows and low

accruals and short stocks with low cash flows and high accruals. However, this strategy is

significantly less profitable than the strategy based on the finding in this study that investors

underreact to both cash flows and accruals (i.e., buying stocks with high cash flows and high

accruals and shorting stocks with low cash flows and low accruals). The evidence in Panel B

shows that the strategy of buying the portfolio in the highest cash-flow quintile and highest

accrual quintile (4.2%, see the low-right cell) and shorting the portfolio in the lowest cash-

flow quintile and lowest accrual quintile (11.9%, see the up-left cell) earns 16.1% annual

abnormal returns.24 By contrast, the competing strategy of buying the portfolio in the highest

cash-flow quintile and lowest accrual quintile (4.0%, see the up-right cell) and shorting the

portfolio in the lowest cash-flow quintile and highest accrual quintile (4.2%, see the low-left

cell) earns only 8.8% annual abnormal returns.

24 This strategy is different from a simple earnings strategy of buying stocks with the highest earnings and shorting stocks with the lowest earnings. Because the underreaction to cash flows is much stronger than the underreaction to accruals, this earnings strategy, which puts equal weight to cash flows and accruals, is suboptimal. To make a comparison, I sort all firms in the quarterly sample each quarter based on prior quarter’s earnings into 25 earnings portfolios and calculate the time-series mean portfolio returns as in Panel B of Table 5. I find that the highest earnings portfolio earns 1.9% annual abnormal returns and the lowest earnings portfolio earnings -11.3% annual abnormal returns - the earnings strategy earns 13.2% annual abnormal returns. By contrast, the strategy of buying stocks with highest cash flows and highest accruals and selling stocks with lowest cash flows and lowest accruals generates higher returns (16.1%).

31

In sum, the results suggest: (1) investors underreact to accruals; (2) while

underreacting to accruals, investors underreact even more to cash flows; and (3) when cash

flows are omitted from the analysis, the stronger underreaction to cash flows than to accruals,

combined with the negative correlation between the two, imposes a downward bias on the

association between accruals and subsequent returns. This bias dominates the underlying

underreaction to accruals, leading to the observed “overreaction” to accruals.25

4.4 Further Sub-sample Test

The analyses so far are conducted on the entire sample of firms (i.e., all firms with

data available). However, the importance of accruals in measuring firm performance is likely

to vary across firms. For some firms, cash flows suffer from more timing and matching

problems than for other firms, and therefore their accruals play a more important role in

measuring performance. By contrast, for some other firms, cash flows have fewer problems

and are closely aligned with earnings; so the role of accruals diminishes. For these firms, the

mispricing of accruals, if any, is likely to have a relatively minor impact on stock returns and

harder to detect statistically. The inclusion of these firms in the tests reduces the power to

detect investors’ reaction to accruals.

In this section, I analyze two sub-samples of firms where accruals are likely to play a

more important role in measuring firm performance. These firms are identified as those with

more volatile working capital requirements and investment and financing activities and those

with longer operating cycles. Prior research documents that for these firms, cash flows suffer

25 Xie (2001) finds that the negative association between accruals and subsequent returns is primarily attributable to abnormal accruals calculated from the Jones model. This finding is not surprising given that the negative correlation between accruals and cash flows is primarily attributable to the abnormal accruals (see, e.g., Xie, 2001, Table 1). Therefore, the downward bias caused by the omission of cash flows is expected to be largely captured by the abnormal accruals. The untabulated results indicate this is the case.

32

from more timing and matching problems and accruals are therefore more important in

measuring performance (Dechow, 1994; Dechow et al., 1998). Because examining these

firms provides a relatively more powerful test of investors’ reaction to accruals than

examining all firms, I expect to find even stronger evidence of investors’ underreacting to

accruals in this sub-sample test.

Following Dechow (1994), the volatility of working capital requirements and

investment and financing activities is measured by the absolute magnitude of accruals, and

the length of operating cycles is measured each quarter as follows:

)5(90/

2/)(90/

2/)( 11⎟⎟⎠

⎞⎜⎜⎝

⎛ ++⎟

⎠⎞

⎜⎝⎛ +

= −−

SOLDGOODSofCOSTINVINV

SALESARARcycleOperating tttt

where AR is accounts receivable (Compustat Quarterly Item 37), INV is inventory

(Compustat Quarterly Item 38), SALES are net sales (Compustat Quarterly Item 2), and

COST of GOODS SOLD is cost of good sold (Compustat Quarterly Item 30). In Equation (5),

the first component captures the speed of converting credit sales into cash, and the second

measures the number of days it takes to produce and sell products.26

Table 6, Panel A reports the results for sub-samples partitioned based on the absolute

magnitude of accruals (a measure of the volatility of working capital requirements and

investment and financing activities). The quarterly sample is partitioned into two sub-

samples with an equal number of firms based on firms’ median absolute magnitudes of

quarterly accruals. The same analysis as in Table 5 is performed separately for the two sub-

26 I also use a second measure proposed by Dechow (1994) for the length of operating cycles, which is calculated as:

⎟⎠⎞

⎜⎝⎛ +

−⎟⎟⎠

⎞⎜⎜⎝

⎛ ++⎟

⎠⎞

⎜⎝⎛ +

= −−−

90/2/)(

90/2/)(

90/2/)( 111

PURCHASESAPAP

SOLDGOODSofCOSTINVINV

SALESARARcycleTrade tttttt

where AP is accounts payable. The results using this second measure are similar to those using the first measure.

33

Table 6 Sub-sample Analyses Based on the Absolute Magnitude of Accruals

or on the Length of Operating Cyclesa Panel A: Sub-samples partitioned on the absolute magnitude of accruals Model Intercept ACCRUALS CASHFLOWS SIZE MB Avg. R2

Firms with larger absolute magnitudes of accruals (N = 35,386 firm-quarters)

Mean (t-stat)b

0.049** (2.09)

-0.065*** (-3.28)

0.050 (1.38)

-0.100** (-2.23)

0.012

Mean (t-stat)

-0.050** (-2.03)

0.164*** (10.11)

0.015 (0.44)

-0.096** (-2.24)

0.017

Mean (t-stat)

-0.177*** (-3.93)

0.155*** (3.10)

0.289*** (5.99)

-0.013 (-0.43)

-0.094** (-2.40)

0.024

Bias in ACCRUALS (t-stat)

-0.221*** (-6.11)

Firms with smaller absolute magnitudes of accruals

(N = 44,423 firm-quarters)

Mean (t-stat)

0.059*** (3.28)

-0.061*** (-6.19)

-0.006 (-0.22)

-0.033 (-0.93)

0.013

Mean (t-stat)

-0.003 (-0.16)

0.092*** (5.75)

-0.016 (-0.54)

-0.052 (-1.45)

0.016

Mean (t-stat)

-0.015 (-0.49)

0.014 (0.56)

0.103*** (3.28)

-0.016 (-0.58)

-0.053 (-1.47)

0.019

Bias in ACCRUALS (t-stat)

-0.075***(-3.37)

Difference between Bias in ACCRUALS

-0.146***(-4.58)

34

Panel B: Sub-samples partitioned on the length of operating cycles Model Intercept ACCRUALS CASHFLOWS SIZE MB Avg. R2

Firms with longer operating cycles

(N = 42,727 firm-quarters)

Mean (t-stat)

0.064*** (3.04)

-0.074*** (-4.69)

0.049* (1.80)

-0.097** (-2.48)

0.011

Mean (t-stat)

-0.033 (-1.39)

0.156*** (9.66)

0.020 (0.77)

-0.106*** (-2.78)

0.017

Mean (t-stat)

-0.128*** (-3.33)

0.120*** (3.06)

0.253*** (6.33)

0.001 (0.04)

-0.115*** (-3.02)

0.023

Bias in ACCRUALS (t-stat)

-0.195*** (-6.59)

Firms with shorter operating cycles (N = 37,082 firm-quarters)

Mean (t-stat)

0.038 (1.70)

-0.046*** (-3.71)

0.018 (0.60)

-0.048 (-1.32)

0.010

Mean (t-stat)

-0.021 (-0.86)

0.098*** (5.38)

0.002 (0.08)

-0.058 (-1.57)

0.015

Mean (t-stat)

-0.065 (-1.52)

0.056 (1.35)

0.141*** (3.09)

-0.006 (-0.23)

-0.060 (-1.58)

0.020

Bias in ACCRUALS (t-stat)

-0.102***(-3.09)

Difference between Bias in ACCRUALS

-0.093***(-2.70)

*, **, *** denote two-tailed significance levels of 10%, 5%, and 1%, respectively. a This table reports the results of separate Fama-MacBeth regression analyses of relations between

QTRBHAR and prior quarterly accruals and cash flows (comparable to Table 5) using sub-samples portioned based on the absolute magnitude of accruals (Panel A) or on the length of operating cycles (Panel B). In Panel A, the quarterly sample used in Table 5 is partitioned into two sub-samples with an equal number of firms, based on firms’ median absolute magnitude of accruals. In Penal B, the quarterly sample is partitioned into two sub-samples with an equal number of firms, based on firms’ median length of operating cycles. Operating cycle is calculated for the quarterly interval as follows:

⎟⎟⎠

⎞⎜⎜⎝

⎛ ++⎟

⎠⎞

⎜⎝⎛ +

= −−

90/2/)(

90/2/)( 11

SOLDGOODSofCOSTINVINV

SALESARARcycleOperating tttt

where AR is accounts receivable, INV is inventory, SALES is net sales, and COST of GOODS SOLD is cost of good sold. bT-statistics are calculated using Fama-MacBeth type time-series mean coefficients with Newey-West (1987) standard errors.

35

samples. Compared with the results based on the full quarterly sample (see Table 5), the test

based on a sub-sample of firms with larger magnitudes of accruals yields stronger evidence

of investors underreacting to accruals. For this sub-sample of firms, the coefficient on

ACCRUALS, after controlling for cash flows, is 0.155 (significant at the 0.01 level), and

much larger compared with that for the full sample (0.084, Table 5). For other firms with

smaller magnitudes of accruals, the coefficient on ACCRUALS, after controlling for cash

flows, is only weakly positive and statistically insignificant (0.014, t-stat = 0.56). In addition,

when cash flows are omitted, the downward bias in the coefficient on ACCRUALS is more

severe for firms with larger magnitudes of accruals (-0.221) than for other firms (-0.075).

Table 6, Panel B reports the results for sub-samples partitioned based on the length of

operating cycles. For each firm-quarter, an operating cycle is computed using Equation (5). A

firm-specific operating cycle is calculated as the median of all the computed operating cycles

for this firm. The quarterly sample is then partitioned into two sub-samples with an equal

number of firms based on firm-specific operating cycles. The analyses are conducted

separately for the two sub-samples. As expected, the test using firms with longer operating

cycles provides stronger evidence of an underreaction of investors to accruals. For firms with

longer operating cycles, the coefficient on ACCRUALS, after cash flows are controlled for, is

0.120 (significant at the 0.01 level), compared with 0.084 for the full sample (Table 5) and

0.056 for firms with shorter operating cycles. Also, the downward bias in the coefficient on

ACCRUALS caused by the omission of cash flows is more severe for firms with longer

operating cycles (-0.195) than for firms with shorter operating cycles (-0.102).

36

4.5 Additional Analyses

Shorter return windows

The analyses so far have used a 12-month return window, in line with Sloan (1996).

However, previous studies show that most of the market’s delayed response (drift) occurs in

the subsequent 3 to 6-month period (see, e.g., Bernard and Thomas, 1989; Jegadeesh and

Titman, 1993), suggesting that tests using a shorter return window are relatively more

powerful. I repeat the analyses using 3- and 6-month return windows. Panel A and B of Table

7 report the results of repeating the analyses in Table 5 using a 3-month window and a 6-

month window respectively. As expected, the results for these shorter windows show

stronger evidence of an underreaction of investors to accruals.

December year-end firms

The analyses so far have used firms with all fiscal year-ends to maximize sample size.

One potential concern is that the portfolio assignment is based on the distribution for all

firms in each period, including some that have not yet reported their accruals for that period.

If the distribution of accruals varies systematically with fiscal year-end, this may cause a

hindsight problem. I repeat the analyses using only December year-end firms and find that

my inferences remain unaltered (see Panel C of Table 7).

Influential observations

To ensure that the results are not driven by a small number of influential

observations, I repeat the analyses after excluding 1% of observations with the largest

squared residuals (Knez and Ready, 1997) and find that my inferences remain unchanged

(see Panel D of Table 7).

37

Table 7 Additional Analyses of Relations between QTRBHAR and

Prior Quarterly Accruals and Cash Flowsa

Intercept ACCRUALS CASHFLOWS SIZE MB Avg. R2

Panel A: Using a 3-month return window

(N = 79,809 firm-quarters)

Mean (t-stat)b

-0.002 (-0.51)

-0.006 (-1.34)

0.006 (0.62)

-0.006 (-0.49)

0.006

Mean (t-stat)

-0.017*** (-2.69)

0.031*** (6.86)

-0.001 (-0.01)

-0.007 (-0.63)

0.008

Mean (t-stat)

-0.051*** (-5.96)

0.043*** (4.70)

0.065*** (7.34)

-0.006 (-0.82)

-0.010 (-0.88)

0.012

Panel B: Using a 6-month return window (N = 79,809 firm-quarters)

Mean (t-stat)

0.004 (0.38)

-0.017*** (-3.32)

0.013 (0.78)

-0.018 (-0.80)

0.008

Mean (t-stat)

-0.030** (-2.55)

0.066*** (8.16)

0.001 (0.04)

-0.021 (-0.98)

0.012

Mean (t-stat)

-0.089*** (-4.66)

0.076*** (4.15)

0.125*** (6.12)

-0.011 (-0.87)

-0.026 (-1.19)

0.017

Panel C: Using only December year-end firms

(N = 48,983 firm-quarters)

Mean (t-stat)

0.061*** (2.70)

-0.067*** (-4.95)

0.018 (0.66)

-0.069* (-2.00)

0.011

Mean (t-stat)

-0.022 (-0.86)

0.137*** (8.20)

-0.006 (-0.25)

-0.082** (-2.40)

0.017

Mean (t-stat)

-0.081** (-2.01)

0.075** (2.14)

0.196*** (4.77)

-0.017 (-0.74)

-0.088** (-2.48)

0.024

38

Table 7 (continued)

Intercept ACCRUALS CASHFLOWS SIZE MB Avg. R2

Panel D: Excluding 1% of the quarterly sample

with the largest squared residuals (N = 79,011 firm-quarters)

Mean (t-stat)

-0.040** (-2.25)

-0.035*** (-3.48)

0.144***(5.62)

-0.092*** (-3.01)

0.018

Mean (t-stat)

-0.107*** (-5.37)

0.127*** (11.86)

0.123***(5.05)

-0.100*** (-3.31)

0.026

Mean (t-stat)

-0.216*** (-7.86)

0.140*** (5.38)

0.236*** (8.69)

0.101***(4.48)

-0.110*** (-3.65)

0.033

Panel E: Excluding firms with stock prices

lower than $5 or that are in the bottom NYSE/AMEX size decile

(N = 64,794 firm-quarters)

Mean (t-stat)

0.045*** (3.40)

-0.061*** (-5.40)

0.014 (0.66)

-0.038 (-1.20)

0.012

Mean (t-stat)

-0.027 (-1.66)

0.105*** (11.68)

0.007 (0.31)

-0.053* (-1.71)

0.017

Mean (t-stat)

-0.079*** (-3.21)

0.063** (2.20)

0.157*** (5.81)

0.003 (0.13)

-0.061* (-1.82)

0.021

*, **, *** denote two-tailed significance levels of 10%, 5%, and 1%, respectively. aThis table reports additional analyses of relations between QTRBHAR and prior quarterly accruals and cash flows (comparable to Table 5). Panel A and B report the results of using a 3-month return window and a 6-month return window, respectively. Panel C reports the results using only December year-end firms. Panel D reports the results after excluding 1% of the quarterly sample with the largest squared residuals. Panel E reports the results after excluding firms with stock prices lower than $5 or that are in the bottom NYSE/AMEX size decile. bT-statistics are calculated using Fama-MacBeth type time-series mean coefficients with Newey-West (1987) standard errors.

39

Small and illiquid firms

To investigate whether the results are primarily driven by small, illiquid firms, I

repeat the analyses after excluding all firms with stock prices lower than $5, and all firms

with a market capitalization that would put them into the smallest NYSE/AMEX size decile

(Jegadeesh and Titman, 2001). I find that my inferences remain unchanged after excluding

these small, illiquid stocks (see Panel E of Table 7).

4.6 Inconsistency between Results from Two Approaches of Testing Investors’ Reaction

to Accruals

Although Sloan (1996) omits cash flows when testing the association between

accruals and subsequent returns, he does consider cash flows in the two-equation Mishkin

test and finds evidence of investors overreacting to accruals in that test using the annual

setting. This raises an inconsistency between the results from the Mishkin test of Sloan and

the results of Desai et al. (2004) and this study. In the same annual setting, Desai et al. and

my annual test find no mispricing of accruals after controlling for cash flows in a one-

equation approach. This inconsistency is puzzling because the Mishkin test should lead to the

same conclusion regarding over- vs. under-reaction as the one-equation approach if the

additional assumptions required by the Mishkin test are satisfied (see Abel and Mishkin

(1983) for a formal proof; see also Appendix for a discussion).

One explanation for the inconsistency is that the additional assumptions required by

the Mishkin test are violated (see Kraft et al. 2005a). One such assumption is that the

prediction model is correct. However, as pointed out by Kraft et al. (2005a), the AR(1)

prediction model presumed in the Mishkin test is misspecified. Another explanation for the

40

inconsistency is differences in the research design. One design difference is that MB and size

are controlled for in the one-equation approach but not in Sloan’s Mishkin test.27 Another

design difference is that the use of pooled regressions over years for the Mishkin test and the

use of Fama-MacBeth yearly regressions in the one-equation approach.

Using the annual sample, I first investigate whether the inconsistency can be

explained by the absence of controls for two common risk factors – MB and size (Fama and

French 1993) – in Sloan’s Mishkin test. The results are reported in Table 8. In Panel A, I

replicate Sloan’s Mishkin test results in my sample. The coefficient on ACCRUALS in the

pricing equation (0.601) is significantly larger than the coefficient on ACCRUALS in the

forecasting equation (0.457) and this difference is statistically significant at 0.001 level. This

result is similar to Sloan’s, suggesting that investors overreact to accruals. In Panel B, I rerun

the Mishkin test after using MB and Size as control variables, similar to their use by Desai et

al. in their one-equation approach. The resulting coefficient on ACCRUALS in the pricing

equation (0.495) is still larger than the coefficient on ACCRUALS in the forecasting

equation (0.457). This difference, however, is economically and statistically insignificant.

The result from the Mishkin’s test after controlling for MB and SIZE is consistent with the

result from the one-equation approach reported in Table 3 of this study and that found by

Desai et al. (2004), suggesting no mispricing of accruals after controlling for cash flows in

the annual setting. In sum, the results in Table 8 indicate that the inconsistency between the

two-equation Mishkin test results reported by Sloan and the one-equation results reported in

this study and Desai et al. can be explained by the absence of controls for the two common

risk factors in Sloan’s Mishkin test.

27 The size-adjusted returns do not fully control for the size effect (Bernard 1987).

41

Table 8 Results of the Two-Equation Mishkin Testa

121*2

*1

*01

12101

)( ++

++

+++−−−=

+++=

ttttANN

tttt

MBSIZECASHFLOWSACCRUALSEARNINGSBHAR

CASHFLOWSACCRUALSEARNINGS

εππλγγγ

μγγγ

Panel A: Results without Controlling for SIZE or MB

Parameter Estimate Asymptotic Standard Error 0γ -0.095 0.005 *0γ -0.129 0.026

1γ 0.457 0.006 *1γ 0.601 0.028

2γ 0.733 0.006 *2γ 0.653 0.028 λ 0.513 0.016

Test *

11 γγ = : Likelihood ratio statistic = 25.18, marginal significance level: 0.000 Test *

22 γγ = : Likelihood ratio statistic = 7.83, marginal significance level: 0.005 Panel B: Results with Controlling for SIZE and MB

Parameter Estimate Asymptotic Standard Error 0γ -0.095 0.005 *0γ -0.211 0.023

1γ 0.457 0.006 *1γ 0.495 0.027

2γ 0.733 0.006 *2γ 0.492 0.027

1π -0.047 0.014

2π -0.202 0.014 λ 0.580 0.016

Test *

11 γγ = : Likelihood ratio statistic = 2.21, marginal significance level: 0.137 Test *

22 γγ = : Likelihood ratio statistic = 75.54, marginal significance level: 0.000 aThis table reports the results from the two-equation Mishkin test of investors’ reaction to accruals and cash flows. The sample (23,456 firm-years) consists of all firm-years in the annual sample with non-missing earnings for year t+1. 1+tEARNINGS is scaled decile ranks based on earnings in period t+1. See Table 3 for the definitions for the other variables.

42

Second, I investigate how the use of pooled regressions over years vs. the use of

Fama-MacBeth yearly regressions affects the results of the Mishkin test. Using my annual

sample, I run the Mishkin test, without controlling for MB or SIZE, separately for each year

and calculate the mean coefficient on ACCRUALS in the forecasting and pricing equations

(unreported). The mean coefficient on ACCRUALS in the pricing equation is larger than the

mean coefficient on ACCRUALS in the forecasting equation, however, this difference is not

significant based on the test using the time-series yearly coefficients. In addition, in 7 out of

15 years in the annual sample, the coefficient on ACCRUALS in the pricing equation is

actually smaller than the coefficient on ACCRUALS in the forecasting equation. This

evidence suggests that using a pooled regression in the Mishkin test also contributes to the

inconsistency between the Mishkin test results reported by Sloan and the one-equation results

reported by this study and Desai et al.

43

5. Tests of Analysts’ Earnings Forecasts

In this section, I investigate financial analysts’ reaction to accruals through the

examination of the relation between accruals and their forecasts of future earnings. To the

extent that analysts’ forecasts of future earnings can be used as a proxy for investors’

expectations (e.g., Brown and Rozeff, 1978; Fried and Givoly, 1982; O’Brien, 1988), this

analysis provides me a setting to directly examine the link between accruals and investors’

expectations of future firm performance. Since this analysis does not rely on stock prices, it

helps mitigate some of the concerns that unknown risk factors or research design flaws may

confound the return-based tests reported in Section 4.

Bradshaw et al. (2001) also investigate how analysts react to accruals. They find a

negative association between accruals and errors in analysts’ forecasts of future earnings

(defined as actual earnings minus forecast earnings). They interpret this negative association

as evidence that financial analysts, like investors, also overreact to accruals. They conclude

that this evidence confirms and complements the accrual anomaly reported by Sloan (1996).

However, Bradshaw et al. (2001) omit cash flows in their examination of the association

between accruals and analyst forecasts. So their result is potentially biased by a similar

correlated omitted variable problem that affects the inferences concerning the accrual

anomaly.

To assess the presence and extent of such a bias, I examine the association between

accruals and analysts’ forecast errors while controlling for the effect of cash flows. Specially,

I estimate the following model:

)6(12101 ++ +++= tttt CASHFLOWSACCRUALSFERROR υααα

44

where 1+tFERROR is forecast errors for earnings in period t+1, tACCRUALS is accruals in

period t, and tCASHFLOWS is cash flows in period t. If analysts incorporate the information

in accruals efficiently, there should be no relation between accruals and forecast errors.

Otherwise, consistent with Bradshaw et al. (2001), a negative (positive) coefficient on

accruals is interpreted as an overreaction (underreaction) to accruals by financial analysts. A

similar interpretation applies to cash flows.

The sample used for estimating Equation (6) consists of all the observations in the

quarterly sample for which analysts’ median consensus forecasts and IBES actual earnings

are available on the IBES summary statistics file. Following Bradshaw et al. (2001), the

equation is estimated for each fiscal month from the month following quarter t earnings

announcement through the month before quarter t+1 earnings announcement. Specifically, I

initially measure the forecast for quarter t+1 earnings in the first month after the quarter t’s

earnings announcement and then track forecast errors over the months leading up to the

quarter t+1’s earnings announcement. I use Month 1, Month 2, and Month 3 to denote the

first, second, and third month after the quarter t announcement but before the quarter t+1

announcement. Forecast errors are calculated as the difference between IBES realized

earnings and analysts’ median consensus forecasts, scaled by the stock price at the end of

quarter t. There are 53,923, 52,316 and 42,327 observations in the samples for Month 1, 2,

and 3 respectively.28

Table 9 reports the summary statistics of the three monthly samples. The mean

forecasts suggest that analysts are optimistic. This optimism declines from Month 1 to Month

3. The median forecast, however, does not show any obvious optimism or pessimism. These 28 The return results remain unchanged after deleting firm-quarters with missing analysts’ forecasts, that is, using the same firm-quarters as in the forecast test.

45

Table 9 Summary Statistics for the Analysts’ Forecast Samplesa

Panel A: Descriptive statistics

Month Variable N Mean Median S.D. 25% 75%

1 1,1 +tFError 53,923 -0.0029 0.0000 0.0133 -0.0029 0.0011

2 1,2 +tFError 52,316 -0.0022 0.0000 0.0116 -0.0021 0.0012

3 1,3 +tFError 42,327 -0.0016 0.0000 0.0107 -0.0012 0.0012 Panel B: Correlations between 1, +tsFError and tAccruals (p-value, two-tailed) Month N

Pearson correlation between

1, +tsFError and tAccruals Spearman correlation between

1, +tsFError and tAccruals 1 53,923 0.011

(p=0.011) -0.030

(p<0.0001) 2 52,316 0.002

(p=0.652) -0.039

(p<0.0001) 3 42,327 -0.001

(p=0.884) -0.038

(p<0.0001) Panel C: Correlations between 1, +tsFError and tCashflows (p-value, two-tailed) Month N Pearson correlation between

1, +tsFError and tCashflows Spearman correlation between

1, +tsFError and tCashflows 1 53,923 0.105

(p<0.0001) 0.110

(p<0.0001) 2 52,316 0.099

(p<0.0001) 0.098

(p<0.0001) 3 42,327 0.098

(p<0.0001) 0.080

(p<0.0001) aThe samples include all the firm-quarters (quarter t) in the quarterly sample for which median consensus forecasts and actual earnings for quarter t+1 are available on the IBES summary file. The forecast for quarter t+1 earnings is initially measured in the first month after the quarter t’s earnings announcement, and then tracked over the months leading up to the quarter t+1’s announcement. Month 1, 2, and 3 denote the first, second, and third month, respectively, following the quarter t announcement and before the quarter t+1 announcement.

1, +tsFError is the monthly forecast error for quarter t+1 earnings in month s (s = 1, 2, or 3) following quarter t earnings announcement and before quarter t+1 announcement, calculated as quarter t+1 earnings less median consensus forecasts in month s, scaled by the stock price at the end of quarter t.

tAccruals and tCashflows are quarter t accruals and cash flows, scaled by average total assets. See Table 1 for additional variable definitions.

46

patterns are consistent with prior findings (e.g., O’Brien, 1988; Abarbanell and Lehavy,

2003). For all three samples, the Spearman correlation between accruals and forecast errors is

consistently negative and significant, while the Spearman correlation between cash flows and

forecast errors is consistently positive and significant.

Table 10 reports the results from estimating Equation (6). To mitigate the influence of

potential outliers caused by data error or extreme forecast errors (e.g., Abarbanell and

Lehavy, 2003; Gu and Wu, 2003), I perform a rank regression analysis using scaled decile

ranks for all the variables.29 Forecast errors, accruals, and cash flows are assigned into

deciles each quarter, and the quarterly decile ranks are scaled to the range [0,1] as before. A

separate estimation of Equation (6) is performed for each quarter, and the mean coefficients,

Fama-MacBeth t-statistics with Newey-West standard errors, and average R-squares for the

60 quarterly estimations are reported in Table 10.

The tests on the three monthly samples (Month 1, 2, and 3) generate similar findings.

Specifically, when the effect of cash flows is controlled for, the association between accruals

and forecast errors is positive and significant. This positive association is significantly

smaller than the positive association between cash flows and forecast errors. When cash

flows are omitted, the association between accruals and forecast errors is biased downward to

such an extent that this association becomes negative and significant, consistent with

Bradshaw et al. (2001).

These results complement and reinforce the evidence concerning investors’ reaction

to accruals reported in Section 4. The results suggest: (1) financial analysts underreact to

accruals; (2) analysts underreact to cash flows to a greater extent; and (3) when cash flows

are omitted, the stronger underreaction to cash flows than to accruals, combined with the 29 The inferences are unchanged if I use winsorized raw forecast errors instead of ranks.

47

Table 10 Fama-MacBeth Regression Analyses of Relations between Forecast Errors ( 1, +tsFError )

and Prior Quarterly Accruals and Cash Flowsa

Intercept ACCRUALS CASHFLOWS Avg. 2R

Panel A: Month 1 Sample (N = 53,923 firm-quarters)

Mean (t-stat)b

0.510*** (172.49)

-0.021*** (-3.46)

0.003

Mean (t-stat)

0.448*** (128.36)

0.104*** (15.39)

0.014

Mean (t-stat)

0.298*** (17.57)

0.167*** (9.94)

0.237*** (13.59)

0.028

Bias in ACCRUALS (t-stat)

-0.188*** (-12.89)

Panel B: Month 2 Sample (N = 52,316 firm-quarters)

Mean (t-stat)

0.512*** (179.76)

-0.024*** (-4.35)

0.003

Mean (t-stat)

0.457*** (121.38)

0.087*** (11.59)

0.010

Mean (t-stat)

0.343*** (20.17)

0.126*** (7.77)

0.188*** (10.35)

0.021

Bias in ACCRUALS (t-stat)

-0.150*** (-9.98)

Panel C: Month 3 Sample (N = 42,327 firm-quarters)

Mean (t-stat)

0.514*** (170.96)

-0.029*** (-6.53)

0.003

Mean (t-stat)

0.465*** (113.26)

0.069*** (8.48)

0.008

Mean (t-stat)

0.395*** (20.70)

0.078*** (4.43)

0.132*** (6.30)

0.016

Bias in ACCRUALS (t-stat)

-0.107*** (-6.18)

*, **, *** denote two-tailed significance levels of 10%, 5%, and 1%, respectively. aThis table reports Fama-MacBeth mean coefficient estimates from 60 quarterly regressions of monthly forecast errors for quarter t+1 earnings, 1, +tsFError (s = 1, 2, or 3), on quarter t accruals and cash flows. All variables are assigned to deciles quarterly and scaled so that they range from 0 (for the lowest decile) to 1 (for the highest decile). See Table 8 for variable definitions. bT-statistics are calculated using Fama-MacBeth type time-series mean coefficients with Newey-West (1987) standard errors.

48

negative correlation between accruals and cash flows, produces a severe downward bias on

the association between accruals and forecast errors. This bias dominates the underlying

underreaction of analysts to accruals, leading to Bradshaw et al.’s (2001) finding that

analysts overreact to accruals.

49

6. Conclusion

In this study, I reexamine the evidence underlying the prior conclusion that investors

overreact to accruals – that accruals are negatively associated with subsequent abnormal

returns (i.e., the accrual anomaly). I focus on how two features of the research design used to

document the “overreaction” to accruals affect inferences regarding investors’ reaction to

accruals (i.e., overreaction vs. underreaction). The first is the omission of cash flows and the

second is the use of an annual setting. I show that both research design features bias

downward the association between accruals and subsequent returns (i.e., in favor of finding

an “overreaction” to accruals).

After controlling for cash flows and conducting the test of the anomaly in a quarterly

setting, the evidence shows that investors underreact to accruals and they underreact to cash

flows to a greater extent. When cash flows are omitted from the analyses, the stronger

underreaction to cash flows than to accruals, combined with the negative correlation between

the two, imposes a severe downward bias on the association between accruals and subsequent

returns. This bias conceals the underlying underreaction of investors to accruals, leading to

the prior conclusion of an overreaction to accruals. These results hold on average for the full

sample of firms and, as expected, are even stronger for firms where accruals play a relatively

more important role in measuring firm performance.

Further, this study shows that the puzzling inconsistency between the “overreaction”

results from the Mishkin test reported in Sloan (1996) and the “no-mispricing” results from

the one-equation approach reported in Desai et al. (2004) and the annual test of this study is

due to the absence of controls for some common risk factors and the use of pooled

regressions in the Mishkin test. Finally, this study provides evidence that financial analysts,

50

like investors, underreact to accruals and underreact to cash flows even more in their

forecasts of future firm performance.

The challenge presented by the findings in this paper is to explain why investors and

analysts appear to underreact to both accruals and cash flows and why they appear to

underreact more to cash flows than to accruals. Possible explanations include risk mis-

measurement or unknown research design flaws. Another possibility is that investors do not

fully understand the time-series properties of quarterly earnings (see, e.g., Bernard and

Thomas, 1989, 1990; Ball and Bartov, 1996). Investors may act as if quarterly earnings

follow a seasonal random walk process, while the true earnings process might be a seasonally

differenced first-order auto-regressive process with a seasonal moving-average term to reflect

the seasonal negative autocorrelation (Brown and Rozeff, 1979). Although this explanation

was originally proposed for investors’ underreaction to earnings information in the post-

earnings-announcement-drift literature, it also provides a possible explanation for the

findings in this study. Assuming that cash flows are more persistent than accruals, when

earnings surprises consist relatively more of cash flow (accrual) surprises, the positive

autocorrelation between adjacent earnings surprises is relatively stronger (weaker). If

investors ignore this autocorrelation when forming their expectations of future earnings, we

would observe a stronger (weaker) underreaction (or drift) when earnings surprises are due

more to cash flow (accrual) surprises. The investigation of these and other possible

explanations for what appears to be an underreaction to accruals and cash flows represents

fertile avenues for further work aimed at understanding how investors value accruals and

cash flows.

51

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Appendix: Two Approaches of Testing Over- vs. Under-reaction

This section discusses the brief proof by Mishkin (1983) that the two-equation Mishkin test is equivalent to a more general one-equation approach in testing overreaction vs. underreaction to an information signal given that the additional assumptions required by the Mishkin test are valid. For a more detailed and formal proof, see Abel and Mishkin (1983). Specially, I show the relation between Equation (1) I use and the two-equation Mishkin test in Sloan in testing investors’ reaction to accruals and cash flows.

The general condition required by market efficiency is:

)7(0)|( 1 =+ ttARE φ where

1+tAR = abnormal or unexpected return for a stock in t+1, equal to the return in t+1 minus the expected return from a model of market equilibrium,

tφ = the set of l information variables at time t. )|(... tE φ = the expectation conditioned on tφ .

Equation (7) implies that abnormal returns in t+1 should be uncorrelated with any available information in t, that is, one cannot predict future abnormal returns based on past information. The most common test of market efficiency is the regression below:

)8(11 ++ += ttt ZAR νβ where tZ = the l-element row vector containing variables contained in tφ ,

β = 1×l vector of coefficients,

1+tν = error term where )|( 1 ttE φν + is assumed to equal zero. Assuming that the market equilibrium model is correct, 0≠iβ (i=1,2…l) suggests that investors fail to use information variable i contained in tφ efficiently in setting prices.

Compared to the above one-equation approach, the two-equation Mishkin test estimates a system of equations, which contains a linear forecasting equation (9) and a linear pricing equation (10) as below:

)10()(

)9(

1*

11

11

+++

++

+−=

+=

tttt

ttt

ZXAR

ZX

ελγ

μγ

where 1+tX = the k-element row vector containing variables relevant to the pricing of the

security at time t+1, *,γγ = kl × matrix of coefficients,

55

1+tμ = error term where )|( 1 ttE φμ + is assumed to equal zero.

1+tε = error term where )|( 1 ttE φε + is assumed to equal zero. Assuming that the market equilibrium model and the forecasting model are correct, ii γγ ≠* suggests that investors fail to use information variable i contained in tφ efficiently in setting prices. Specifically, ii γγ >* suggests that the weight investors actually put on information variable i inferred from the pricing equation is higher than the benchmark weight calculated from the forecasting equation, that is, investors overreact to information i. In contrast,

ii γγ <* suggests an underreaction to information i. It is important to note that the assumptions required by the one-equation approach is a subset of the assumptions required by the two-equation Mishkin test. For example, the two-equation Mishkin test requires the assumption of a correct forecasting model.

Assuming the additional assumptions required by the Mishkin test are valid, these two approaches are equivalent in testing over- vs. under-reaction. Abel and Mishkin (1983) provide a detailed formal proof. To keep it simple, I follow the brief proof by Mishkin (1983). Note that Equation (10) can be re-written as:

)10()( 111 AZZXAR ttttt +++ ++−= εθλγ

where λγγθ )( *−= . Therefore, comparing *γ to γ is equivalent to comparing θ to zero, depending on the sign of λ . For example, if 0>λ (i.e., investors react positively to the surprise in information i), showing ii γγ >* is equivalent to showing 0<β , and showing

ii γγ <* is equivalent to showing 0>θ .

Because the residuals from Equation (9), ∧

++

∧

−= γμ ttt ZX 11 , is orthogonal to tZ by

construction, the estimate of θ should not be affected if )( 1

∧

+ − γtt ZX is omitted from Equation (10A). Thus, the estimate of θ is numerically identical to the estimate of β in Equation (8). This proves that one can test investors’ reaction to information i by either comparing *γ to γ using the two-equation Mishkin test or testing θ against zero using the one-equation approach; the two approaches are equivalent if the additional assumptions required by the two-equation Mishkin test are satisfied.

Testing investors’ reaction to accruals and cash flows is a special case of the above

general proof. In this case, 1+tX is simply earnings in t+1, 1+tEARNINGS , and tZ contains two information variables, accruals in t, tACCRUALS , and cash flows in t, tCASHFLOWS . The two-equation Mishkin test (Sloan 1996) will be:

)11()(

)10(

1*2

*1

*011

12101

+++

++

+−−−=

+++=

ttttt

tttt

CASHFLOWSACCRUALSEARNINGSAR

CASHFLOWSACCRUALSEARNINGS

ελγγγ

μγγγ

56

Recall the one-equation approach used in this study:

)1(12101 ++ +++= tttt εCASHFLOWSβACCRUALSββRETURN

Note that λγγβ )( *000 −= , λγγβ )( *

111 −= and λγγβ )( *222 −= . Becauseλ captures

earnings response coefficient and is positive, showing 01 >β ( 01 <β ) in Equation (1) is equivalent to showing 1

*1 γγ < ( )1

*1 γγ > in Sloan’s two-equation Mishkin test, both

suggesting that investors underreact (overreact) to accruals. In other words, the interpretation of 0>iβ as an underreaction and 0<iβ as an overreaction in Equation (1) is identical to the interpretation of ii γγ <* as an underreaction and ii γγ >* as an overreaction in Sloan’s two-equation Mishkin test (i=1,2).

Vita Yong Yu grew up in Bengbu, Anhui Province of China. After graduating from Bengbu No.2

High School, Yong attended Tsinghua University at Beijing where he earned a B.A. degree

in International Accounting. He completed his M.A. degree in Economics from Tulane

University and his Ph.D. in Business Administration with a concentration in accounting at

the Pennsylvania State University.