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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
References: Abarbanell, J., and R. Lehavy, 2003. Biased forecasts or biased earnings? The role of
reported earnings in explaining apparent bias and over/underreaction in analysts’ earnings forecasts. Journal of Accounting & Economics 36, 105-146.
Abel, A. and F. Mishkin, 1983. On the econometric testing of rationality-market efficiency.
The Review of Economics and Statistics 65, 318-323. Ali, A., L. Hwang, and M. Trombley, 2001. Accruals and future stock returns: tests of the
naïve investor hypothesis. Journal of Accounting, Auditing and Finance, 161-181. Ball, R., and E. Bartov, 1996. How naïve is the stock market’s use of earnings information?
Journal of Accounting & Economics 21, 319-337. Bernard, V., 1987. Cross-sectional dependence and problems in inference in market-based
accounting research. Journal of Accounting Research 77, 755-792. Bernard, V., and J. Thomas, 1989. Post earnings announcement drift: delayed price response
or risk premium? Journal of Accounting Research 27, 1-36. Bernard, V., and J. Thomas, 1990. Evidence that stock prices do not fully reflect the
implications of current earnings for future earnings. Journal of Accounting & Economics 18, 305-340.
Bradshaw, M., S. Richardson, and R. Sloan, 2001. Do analysts and auditors use information
in accruals? Journal of Accounting Research 39, 45-74. Brown, L., and M. Rozeff, 1978. The superiority of analyst forecasts as measures of
expectations: evidence from earnings. Journal of Finance 33, 1-16. Brown, L., and M. Rozeff, 1979. Univariate time series models of quarterly accounting
earnings per share: a proposed model. Journal of Accounting Research 17, 179-189. Collins, D., and P. Hribar, 2000. Earnings-based and accrual-based market anomalies: one
effect or two?” Journal of Accounting & Economics 29, 101-123. Dechow, P., 1994. Accounting earnings and cash flows as measures of firm performance: the
role of accounting accruals. Journal of Accounting & Economics 18, 3-42. Dechow, P., S.P. Kothari, and R. Watts, 1998. The relation between earnings and cash flows.
Journal of Accounting & Economics 25, 133-168. Desai, H., S. Rajgopal, and M. Venkatachalam, 2004. Value-glamour and accrual mispricing:
one anomaly or two? Accounting Review 79, 355-385.
52
Drtina R., and J. Largay, 1985. Pitfalls in calculating cash flows from operations. Accounting Review 52, 1-21.
Easton, P., and M. Zmijewski, 1993. SEC form 10K/10Q reports and annual reports to
shareholders: reporting lags and squared market model prediction errors. Journal of Accounting Research 31, 314-326.
Fairfield, P., J. Whisenant, and T. Yohn, 2003. Accrual earnings and growth: implications for
future profitability and market mispricing. Accounting Review 78, 353-371. Fama, E. and F. French, 1993. Common risk factors in the returns on stock and bonds.
Journal of Financial Economics 33, 3-56. Fama, E., and J. MacBeth, 1973. Risk, return and equilibrium: empirical tests. Journal of
Political Economy 81, 607-636. Fried, D., and D. Givoly, 1982. Financial analysts’ forecasts of earnings: a better surrogate
for market expectations. Journal of Accounting & Economics 4, 85-107. Greene, W., 2003. Econometric analysis. MacMillan, New York. Gu, Z., and J. Wu, 2003. Earnings skewness and analyst forecast bias. Journal of Accounting
& Economics 35, 5-29. Henry, D., 2004a. A market scholar strikes gold. Business Week, October 4, 2004. Henry, D., 2004b. Fuzzy numbers. Business Week, October 4, 2004. Hribar, P., and D. Collins, 2002. Errors in estimating accruals: implications for empirical
research. Journal of Accounting Research 40, 105-134. Jegadeesh, N., and S. Titman, 1993. Returns to buying winners and selling losers:
implications for stock market efficiency. Journal of Finance 56, 699-720. Jegadeesh, N., and S. Titman, 2001. Profitability of momentum strategies: an evaluation of
alternative explanations. Journal of Finance 56, 699-720. Khan, M., 2005. Are accruals really mispriced? Evidence from tests of an intertemporal
capital asset pricing model. Working paper. Knez, P., and M. Ready, 1997. On the robustness of size and book-to-market in cross-
sectional regressions. Journal of Finance 101, 1355-1382. Kraft, A., A. Leone, and C. Wasley, 2005a. On the use of Mishkin’s rational expectations
approach to testing efficient-markets hypotheses in accounting research. Working paper.
53
Kraft, A., A. Leone, and C. Wasley, 2005b. An analysis of the theories and explanations offered for the mispricing of accruals and accrual components. Working paper,
Kothari, S.P., 2001. Capital markets research in accounting. Journal of Accounting &
Economics 31, 105-231. LaFond, R., 2005. Is the accrual anomaly a global anomaly? Working paper. Maddala, G.S., 2001. Introduction to econometrics. 3rd Edition. Prentice Hall. Mashruwala, C., S. Rajgopal, and T. Shevlin, 2004. Why is the accrual anomaly not
arbitraged away? Working paper. Mishkin, F., 1983. A rational expectations approach to macroeconometrics: Testing policy
effectiveness and efficient markets models. Chicago, IL: University of Chicago Press for the National Bureau of Economic Research.
Newey, W., and K. West, 1987. A simple, positive semi-definite, heteroskedasticity and
autocorrelation consistent covariance matrix. Econometrica 55, 703-708. O’Brien, P., 1988. Analysts’ forecasts as earnings expectations. Journal of Accounting &
Economics 10, 53-83. Pincus, M., S. Rajgopal, and M. Venkatachalam, 2005. The accrual anomaly: international
evidence. Working paper. Richardson, S., 2003. Earnings quality and short sellers. Accounting Horizons, 49-61. Richardson, S., R. Sloan, M. Soliman, and I. Tuna, 2005. Accrual reliability, earnings
persistence and stock prices. Journal of Accounting & Economics 39, 437-485. Sloan, R., 1996. Do stock prices fully reflect information in accruals and cash flows about
future earnings? Accounting Review 71, 289-315. Talley, K., 2003. Small-stock focus: ‘accrual investing’ seeks to clear away bluster. The Wall
Street Journal. January 27, 2003. Thomas, J., and H. Zhang, 2002. Inventory changes and future returns. Review of Accounting
Studies 7, 163-187. Watts, R., and J. Zimmerman, 1986. Positive accounting theory. Prentice-Hall. Wooldridge, J., 2003. Introductory econometrics: a modern approach. South-Western
College Publishing. Xie, H., 2001. The mispricing of abnormal accruals. Accounting Review 76, 357-373.
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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.