two accrual anomalies: a dichotomy of accrual-return...
TRANSCRIPT
Two Accrual Anomalies: A Dichotomy of Accrual-Return
Relations∗
Qiang Kang †
University of Miami
Qiao Liu ‡
University of Hong Kong
Rong Qi §
St. John’s University
First Draft: March 2008
This Draft: February 2009
∗We thank Jerold Zimmerman and seminar participants at the University of Hong Kong for useful comments. Liugratefully acknowledges financial support from the Hong Kong Research Grants Council (CERG HKU 7472/06H,and CERG HKU 747107H). All errors remain our own.†Finance Department, University of Miami, P.O. Box 248094, Coral Gables, FL 33124-6552. Phone: (305)284-
8286. Fax: (305)284-4800. E-mail: [email protected].‡School of Economics and Finance, University of Hong Kong, Pokfulam, Hong Kong. Phone: (852)2859-1059.
Fax: (852)2548-1152. E-mail: [email protected].§Peter J. Tobin College of Business, St. John’s University, Jamaica, NY 11439. Phone: (718) 990-7320. E-mail:
Two Accrual Anomalies: A Dichotomy of Accrual-Return Relations
Abstract
Motivated by the findings that the aggregate (discretionary) accruals positively predicts one-
year-ahead firm-level stock returns and that there is a considerable amount of co-movement
in firm-level (discretionary) accruals, we decompose firm-level (discretionary) accruals into a
market-wide component and a firm-specific component. We document robust evidence that
the two orthogonal (discretionary) accrual components affect stock returns in qualitatively
opposite ways — while the firm-specific component negatively predicts next-period stock returns,
firms with a higher level of market-wide component have on average higher next-period stock
returns. Moreover, the two accrual-return relations co-exist and the accrual anomaly due to the
firm-specific component of (discretionary) accruals largely supersedes the conventional accrual
anomaly documented in Sloan (1996) and Xie (2001). Furthermore, a hedge strategy explicitly
exploiting the two accrual anomalies yields a significantly higher return than that of a typical
accrual strategy built only on firm-level (discretionary) accruals. Our analysis shows that
accounting information such as (discretionary) accruals affects the stock market through both
market-wide and firm-specific channels. We briefly discuss potential economic rationales behind
each of the two accrual anomalies.
JEL Classification: G1, G3, M4
Keywords: Accrual anomalies, market-wide and firm-specific components of (discretionary)
accruals, asset pricing, hedge strategy
1 Introduction
One of the robust market anomalies in the empirical asset pricing and accounting literatures is the
accrual anomaly, namely, on average, firms with high (discretionary) accruals earn abnormally lower
returns than firms with low (discretionary) accruals (Sloan, 1996; Teoh, Welch, and Wong, 1998;
Xie, 2001).1 The accrual anomaly has been conventionally referred to as a firm- and portfolio-
level anomaly. Two recent studies find that the (discretionary) accrual-return relation can be
generalized to the aggregate level but with an qualitatively opposite sign: both Hirshleifer, Hou,
and Teoh (2008) and Kang, Liu, and Qi (2008) document that different measures of the aggregate
accruals positively predict one-year-ahead aggregate stock returns. Kang, Liu, and Qi also provide
robust evidence that the accrual-return relation at the aggregate level is mainly driven by the
discretionary component of accruals.
The existence of two accrual-return relations at the firm level and at the aggregate level
immediately lead to an important research question: are the two relations the same? In other
words, is the accrual-return relation at the aggregate level just a manifestation of the conventional
accrual anomaly at the firm level or vice versa? If the answer is no, then it would be interesting
to examine whether the two distinct accrual-return relations co-exist in a unified empirical setting
and whether the different accrual measures affect stock returns in different ways. We address these
questions in this paper, aiming to gain further insights on the nature of the accrual anomaly and
to improve our understanding of the potential channels through which accounting information such
as accruals affects the stock market.
As a motivation, we first study the roles of firm-level (discretionary) accruals and aggregate
(discretionary) accruals in predicting firm-level stock returns. We run a time-series regression, for
each firm, of the firm’s stock returns against the firm’s one-year-lagged (discretionary) accruals
and the value-weighted (discretionary) aggregate accruals. The predictive coefficient estimates
on the firm-level (discretionary) accruals and the aggregate (discretionary) accruals, on average,
turn out to be negative and positive, respectively. The finding suggests that the two qualitatively1A large body of research examine this anomaly and have offered two primary explanations: (1) the stock market
is inefficient and investors fail to identify the transitory nature of the accruals, so they implicitly assign a higherweight to (discretionary) accruals in pricing stocks (see, e.g., Sloan, 1996; Xie, 2001, and Richardson et al., 2005);and (2) higher returns to firms with low accruals are compensation for a certain risk (see, e.g, Ng, 2005; Zhang, 2007;Khan, 2008; Wu, Zhang and Zhang, 2008).
1
different (discretionary) accrual-return relations coexist in a unified empirical framework and that
there might be another accrual “anomaly” — while the negative coefficient estimate on the firm-
level (discretionary) accruals mirrors the conventional accrual anomaly, the significantly positive
coefficient estimate on the aggregate (discretionary) accrual measure implies a different sort of
accrual anomaly.
In an analogy to the CAPM and/or to the commonality in liquidity, we regress each firm-
level (discretionary) accruals against the aggregate (discretionary) accruals to decompose firm-
level (discretionary) accruals into two components — the residual from the regression, and
the co-movement with the aggregate (discretionary) accruals which is captured either by the
estimated coefficient on the regressor (β) or by the regression R2 (See Footnote 4). We find
that there exists considerable amount of comovement in firm-level (discretionary) accruals. Note
that aggregating the fitted values (excluding intercepts) from this comovement regression across
firms yields the aggregate (discretionary) accruals that serves as the market-wide (discretionary)
accrual measure (See Footnote 5). Our finding above thus also implies that (discretionary)
accruals affects stock returns through both a market-wide channel (i.e., the comovement with the
aggregate (discretionary) accruals) and a firm-specific channel (i.e., residuals from the comovement
regression). Consequently, we conjecture that there might be two sorts of accrual anomalies driven
by different (discretionary) accrual components — the conventional accrual anomaly is mainly due
to the firm-specific component of (discretionary) accruals, and the second accrual anomaly is likely
driven by the market-wide component of (discretionary) accruals.
We conduct a battery of tests on this conjecture. In particular, we establish the co-existence
and the orthogonality of the two accrual anomalies through both a portfolio test and a regression
analysis. The portfolio test evaluates abnormal returns to hedge portfolios formed on the basis
of various accrual measures such as the market-wide component of (discretionary) accruals and
the firm-specific component of (discretionary) accruals. The regression analysis enlists various
(discretionary) accrual-based return factors constructed from the portfolio test and executes both
time-series regressions and cross-sectional regressions. The tests show that the two accrual
anomalies are largely orthogonal to each other, and moreover, the accrual anomaly driven by
the firm-specific components of total or discretionary accruals largely supersedes the conventional
accrual anomaly documented in Sloan (1996) and Xie (2001).
2
We start with the portfolio test. On the one hand, a standard zero-cost investment strategy
taking a long position on stocks with low residuals of the comovement regressions (i.e., the firm-
specific component of firm accruals) and a short position on stocks with high residuals yields
significant abnormal returns; the magnitude is comparable to that of the conventional accrual
anomaly for which stocks are sorted into groups by firm-level accruals. On the other hand, the hedge
portfolio holding a long position on stocks with high accrual βs (i.e., the market-wide component of
firm accruals) and a short position on stocks with low accrual βs also yields statistically significant
abnormal returns, signaling a plausible second accrual anomaly. This dichotomy of the accrual-
return relation becomes more striking in the case of discretionary accruals. As a result, the portfolio
test suggests that there are two sorts of accrual anomalies – one is based on the firm-specific
component of (discretionary) accruals; and the other is based on the market-wide component.
Notably, if we apply the comovement regression to the firm-level normal accruals and sort stocks
based respectively on the market-wide and firm-specific components of normal accruals, we do not
observe either accrual anomaly.
We proceed to do the regression analysis in steps. We first construct factor-mimicking portfolios
based on the market-wide component (β and R2) and the firm-specific component (the residual from
the comovement regression) of accruals, and label them as AC COM , AC COMR, and AC RES
respectively. The factor-mimicking portfolio AC COM (or AC COMR) is formed by taking a long
position on stocks with high βs (or R2’s) and a short position on stocks with low βs (or R2’s); the
portfolio AC RES is formed by holding a long position on stocks with low residuals and a short
position on stocks with high residuals. Similarly, we construct another three factor-mimicking
portfolios based on the market-wide and firm-specific components of discretionary accruals, and
label them as DAC COM , DAC COMR, and DAC RES, respectively.2 Note that all the six
factors earn significantly positive premiums that cannot be explained by the Fama-French four
factors.
We then estimate the time-series regressions, in which we regress returns of each decile formed
on rankings of firm-level (discretionary) accruals against the various (discretionary) accrual based
return factors along with the Fama-French four factors. Several patterns arise from the time-series2We do not apply the same analysis to normal accruals and its different components because we fail to document
either accrual anomaly in the case of the normal accruals.
3
regressions. First, the six accrual-related return factors all obtain significantly positive loadings
across the deciles, suggesting that there is a considerable amount of return comovement associated
with either the market-wide component or the firm-specific component of (discretionary) accruals.
Second, after we control for the factors based on the market-wide component of (discretionary)
accruals in the regressions, the conventional accrual anomaly still holds. That is, for the hedge
portfolio with a long position on stocks in the bottom (discretionary) accrual decile and a short
position on stocks in the top (discretionary) accrual decile, its abnormal returns which are adjusted
by Fama-French four factors and the factor due to the market-wide component of (discretionary)
accruals remain significantly positive with a magnitude similar to the raw returns. Also, the two
findings combined suggest that the two accrual-return relations due respectively to the market-wide
component and the firm-specific component of (discretionary) accruals are likely orthogonal to each
other. Third, if we control for the factors based on the firm-specific component of (discretionary)
accruals in the time-series regressions, the conventional accrual anomaly weakens significantly and
even disappears. This evidence implies that the conventional accrual anomaly is likely driven by
the firm-specific component of (discretionary) accruals, or that the latter likely supersedes the
conventional accrual anomaly.
We further estimate Fama and MacBeth’s (1973) cross-sectional regressions on the Fama-
French 10 × 10 size/book-to-market portfolios. The loadings on the various (discretionary)
accrual component based factors (e.g., AC COMR, AC RES, DAC COMR, and DAC RES)
are strongly positive even in the presence of the Fama-French four factors. The evidence shows
that the market-wide component and the firm-specific component of (discretionary) accruals are
both significantly and positively related to the cross-sectional variations in average returns, thereby
lending support to the co-existence and the orthogonality of the two accrual anomalies.
Given the above findings, we venture to gauge the economic significance of the two accrual-
return relations. We design a hedging strategy that explicitly exploits the return-predicability with
the two different components of (discretionary) accruals. We find that the hedge portfolio taking
a long position on stocks with both low accrual residuals and high accrual βs (or R2’s) and a short
position on stocks with both high accrual residuals and low accrual βs (or R2’s) yields significantly
higher abnormal returns than that of a hedge portfolio based only on the conventional accrual
anomaly. Specifically, taking into account the return effect of the market-wide component of firm-
4
level accruals (or discretionary accruals) improves the performance of a pure accrual strategy by
32-86% (or 50-112%). This evidence not only pinpoints the economic magnitude of the two accrual
anomalies but also further demonstrates the existence and distinctness of the two accrual anomalies.
Our paper makes several incremental contributions to the accrual literature and the asset
pricing literature. First, we show that the conventional accrual anomaly is due to the firm-specific
component of (discretionary) accruals. Moreover, on top of the conventional accrual anomaly,
there is a second accrual anomaly that is driven by the market-wide component of (discretionary)
accruals. We further show that the two accrual anomalies co-exist and they are largely orthogonal
to each other. Second, we identify strong evidence of co-movement in firm-level (discretionary)
accruals, based on which we introduce a novel way to decompose (discretionary) accruals. We
document robust evidence that the different components of (discretionary) accruals affect stock
returns in different ways. Third, our analysis helps understand the nature of the accrual-return
relation, and our findings demonstrate that accounting information such as (discretionary) accruals
affects stock returns through both market-wide and firm-specific channels. Fourth, our analysis
creates several new factors based on different (discretionary) accrual components and show that
those factors exhibit the power independent from the Fama-French four factors to account for cross-
sectional differences in stock returns. Last but not the least, our findings pose several interesting
questions for future research. For example, are the two accrual anomalies risk-based or behavior-
based? How do the two accrual anomalies distribute across firms, industries, and business cycles?
How do the factors constructed based on different (discretionary) accrual components relate to
other well-documented factors such as size, value, momentum, etc.? Further efforts to address
those remaining questions are important and can help uncover the ultimate economic rationales
behind the two accrual anomalies.
The remainder of the paper is structured as follows. Section 2 summarizes data and offers details
on how we construct various factor-mimicking portfolios based on different (discretionary) accrual
components. Section 3 discusses the motivation and present the evidence of the existence of a
second accrual anomaly. Section 4 explores the relations among the various accrual anomalies.
Section 5 demonstrates the economic magnitudes of the two accrual anomalies and discusses
potential economic rationales behind each of the accrual anomalies. Section 6 concludes.
5
2 Data and Variable Constructions
We conduct the empirical analysis using all the U.S. firms listed on NYSE, AMEX, and NASDAQ
with December fiscal year ends but excluding financial firms (SIC codes between 6000 and 6999).
Because sufficient accounting information for calculating accruals and discretionary accruals is not
available prior to 1965, our sample spans the period from 1965 to 2005. We obtain accounting data
and stock return data from Standard & Poor’s Compustat database and the Center for Research
in Security Prices (CRSP) database, respectively. The total number of firm-year observations in
our sample is 36,585.
2.1 Accrual Measures
We rely on the balance-sheet method (Sloan, 1996) to calculate accruals throughout our empirical
analysis as the data on cash flow statement are only available after 1987:
AC = (∆CA− ∆Cash) − (∆CL− ∆STD − ∆TP ) −Dep, (1)
where ∆CA = change in current assets (Compustat item 4), ∆Cash = change in cash/cash
equivalents (Compustat item 1), ∆CL = change in current liabilities (Compustat item 5), ∆STD
= change in debt included in current liabilities (Compustat item 34), ∆TP = change in income
taxes payable (Compustat item 71), and Dep = depreciation and amortization expense (Compustat
item 14). Following Sloan (1996), we scale a firm’s accruals by the firm’s average total assets (TA,
Compustat item 6) from the beginning to the end of a fiscal year.
Because Xie (2001) and Kang et al. (2008) respectively find that the accrual-return relations at
the disaggregate and aggregate levels are driven by discretionary components of accruals, we also
use discretionary accruals in our empirical analysis. We use the cross-sectional Jones’ (1991) model
6
to compute firm-level discretionary accruals.3 The model is specified as follows:
Accrualsit/TAit = a1/TAit + a2∆Revit/TAit + a3PPEit/TAit + eit, (2)
where ∆Revit is the change in revenues in year t (Compustat item 12) and PPEit is gross property,
plant, and equipment in year t (Compustat item 7). We estimate equation (2) year by year and
for each two-digit SIC industry, and we require each industry to contain at least ten firms. We
compute normal accruals and discretionary accruals respectively as the fitted value and the residual
from Equation (2).
We then calculate the value-weighted aggregate accruals (AAC), weighted by each firm’s market
capitalization at the beginning of the fiscal year. To reduce the potential impact of outliers, we
delete from our sample the firms whose accruals are ranked at the top and bottom 0.5 percentiles.
(Our main results remain quantitatively similar if we retain those observations or if we truncate the
sample at other percentiles.) Likewise, we compute the value-weighted aggregate normal accruals
(ANAC) and the value-weighted aggregate discretionary accruals (ADAC).
As our goal is to examine the effects of different components of accrual measures on stock
returns, we decompose a firm’s accruals (ACit) into two components as follows:
ACit = αi,t + βitAACt + εit, (3)
where ACit is firm i’s accruals in year t, AACt stands for the value-weighted aggregate accruals
in year t. For each sample firm in year t, we run the regression over a ten-year period from years
t − 10 to t − 1, and we denote by FITACit and RESACit the fitted value and the residual from
Equation (3), respectively.
It is easy to show that both the estimated coefficient on the regressor, βit, and the regression R2
from Equation (3) capture the co-movement of firm i’s accruals, ACit, with the aggregate accruals,3For robustness, we also estimate the time-series Jones’ (1991) model firm by firm to decompose the total accruals
into discretionary accruals and normal accruals. Besides the Jones’(1991) model, we use other accrual-decompositionmodels such as Dechow et al. (1995), Dechow et al. (1998), and Dechow and Dichev (2002). The results using thealternative accrual decomposition models are similar to the results as reported in the text. Moreover, our results arerobust to an alternative discretionary accruals measure that controls for accounting conservatism. For brevity we donot report those results and they are available upon request.
7
AACt.4 The two variables are thus proxies for the market-wide component of firm-level accruals
for firm i in year t. Accordingly, RESACit, the residual from Equation (3), measures the firm-
specific component of accruals for firm i in year t. Further note that aggregating the fitted values
excluding the intercepts from the decomposition equation across firms yields the aggregate accrual
measure.5 Our decomposition of firm-level accrual ACit may appear to be mechanical for the time
being, and we defer to Section 3 to explain the motivation and the economic rationales of such a
decomposition.
Similarly, we decompose a firm’s discretionary accruals (DACit) into both the market-wide and
firm-specific components as follows:
DACit = αi,t + βitADACt + εit, (4)
where ADACt stands for the value-weighted aggregate discretionary accruals in year t. Again, for
each sample firm in year t we run the time-series regression over the period from years t−10 to t−1,
and we denote by FITDACit and RESDACit the fitted value and the residual from Equation (4),
respectively.
2.2 Construction of Factors
Our empirical analysis enlists several other variables. We obtain the Fama-French four factors,
Rm −Rf , SMB, HML, and UMD, from Professor Kenneth French’s website. The market factor
Rm−Rf is the the value-weighed market return minus the one-month Treasury bill rate, and SMB,
HML, and UMD are returns to three factor-mimicking portfolios designed to capture the size,
book-to-market, and momentum effects, respectively.
To perform our empirical analysis, we construct various (discretionary) accrual-measure-based
return factors in a way similar to the construction of the Fama-French factors. We start
with the accrual-based components. We construct three factor-mimicking portfolios, AC COM ,
AC COMR, and AC RES, based respectively on the market-wide accrual component, measured4In a univariate regression such as y=a + bx + e, the estimated coefficient on the regressor, b=ρx,y
σy
σx, and the
regression R2=b2σ2
xσ2
y=ρ2
x,y, where ρx,y is the correlation coefficient between x and y.5It is easy to show that
∑wiβiX=X because
∑wiβi=1, where wi is the weight attached to firm i, and βi is the
coefficient estimate from the following univariate regression for firm i: yi=αi + βiX + e, with X ≡∑wiyi.
8
by β and R2 from Equation (3), and the firm-specific accrual component, measured by the residual
from Equation (3). Take AC RES as an example. We first estimate for each firm Equation (3) over
the period from year t− 10 to year t− 1, and we rank the firms into three portfolios according to
the residuals from Equation (3), where the top and bottom groups each contain 30% of the sample
firms. We then match the firm-level accounting data with monthly stock returns over the period
from April of year t through March of year t+1.6 We further compute the equal-weighted monthly
returns on each of the three residual-based portfolios, and we obtain AC RES as the monthly return
spreads of the bottom residual group over the top residual group. The return spread captures the
return effect of the firm-specific component of firm-level accruals. Similarly, we construct two return
factors based on the market-wide components of firm-level accruals: AC COM is formed by taking
a long position on stocks with a high level (top 30%) of accrual β from Equation (3) and a short
position on stocks with a low level (bottom 30%) of β; and AC COMR is obtained by taking a
long position on stocks with a high level (top 30%) of R2 from Equation (3) and a short position on
stocks with a low level (bottom 30%) of R2. Both AC COM and AC COMR capture the return
effects of the market-wide component of firm-level accruals.
Similarly, we construct another three factor-mimicking portfolios based on the market-wide
and firm-specific components of discretionary accruals. They are labeled, in the same order, as
DAC COM , DAC COMR, and DAC RES. The first two factors measure the the impact on
stock returns by the market-wide component of firm-level discretionary accruals; and the latter
captures the return effect of the firm-specific component of firm-level discretionary accruals.
We also adopt the similar approach to construct two other factor-mimicking portfolios,
AC Factor and DAC Factor, which are based on rankings of firm-level accruals and firm-level
discretionary accruals, respectively. Again, in forming the two portfolios, the stocks are assigned to
different groups according to their year-end (discretionary) accruals in year t− 1 and the portfolio
returns are computed on a monthly basis from April of year t until March of year t+ 1.
Finally, note that, due to the way of constructing the factor-mimicking portfolios based on the
various accrual components as described above, the sample for the accrual-related factors spans
the period from 1980 to 2005 in our ensuing analysis.6We also construct factors by matching the firm-level accounting data with monthly stock returns over other time
periods, i.e., from May to next April, from June to next May, and form July to next June. Our analysis yieldsqualitatively similar results which are available upon request.
9
2.3 Descriptive Statistics
Table 1 presents summary statistics of the main variables used in our empirical analysis,
including the firm-level accruals (ACit), firm-level discretionary accruals (DACit), firm-level
normal accruals (NACit), value-weighted aggregate accruals (AACt), value-weighted aggregate
discretionary accruals (ADACt), value-weighted aggregate normal accruals (ANACt), the Fama-
French four return factors (Rmt − Rft, SMBt, HMLt, and UMDt), and the six return factors
constructed based on different components of (discretionary) accruals. Table 1 shows that both the
mean and the median of the firm-level accruals (ACit), firm-level discretionary accruals (DACit)
and their corresponding aggregate-level measures are all negative; both the mean and the median
of the factor returns based on (discretionary) accrual components are positive and significantly
different from zero.
We will discuss in detail the return factors based on (discretionary) accruals and their various
components in Section 3. Here, as an informal start, we plot in Figure 1 the cumulative returns
of the four total accrual based return factors: AC factor, AC COM , AC COMR, and AC RES.
Two features stand out in the graph. First, the dynamic behavior of the two factors capturing
the market-wide component of total accruals — AC COMR and AC RES — is quite similar; and
the dynamic behavior of AC factor and AC RES is similar too. Second, the cumulative returns
of the four factors are mostly positive for the sample period (January 1980 – March 2006) with
one exception — the cumulative returns of AC COM and AC COMR are sometimes negative in
the 1980s. Figure 2 plots the cumulative returns of the four discretionary accrual based factors.
While the dynamic behavior of DAC factor and DAC RES follows similar pattern, the dynamic
behavior of DAC COM and DAC COMR is quite different.
Table 2 presents the correlations among those return factors. Panel A of Table 2 reports the
(pairwise) contemporaneous correlations between the accrual-measure based return factors and the
Fama-French four factors. As a comparison, we also report the correlations of the value-weighted
aggregate accrual measure (AAC) and the aggregate discretionary accrual measure (ADAC) to
the Fama-French factors. As shown in Panel A, neither AAC nor ADAC is significantly correlated
with the Fama-French factors. AC COM is significantly correlated with Rm−Rf (positive), SMB
(positive) and HML (negative), while AC RES is significantly correlated with SMB (positive)
10
and HML (negative). In the case of return factors based on discretionary accrual components, it
is interesting that DAC COMR — the factor constructed based on the market-wide component of
discretionary accruals (R2) — is significantly correlated with all Fama-French factors. DAC RES
is significantly correlated with SMB (positive), HML (negative), and UMD (positive).
Panel B of Table 2 reports the pairwise correlations among the return factors constructed based
on the (discretionary) accrual components. AC RES is only weakly correlated with AC COM
but not with AC COMR, seemingly suggesting that the return factors based on the market-wide
and firm-specific components of accruals are likely to be orthogonal. In the case of discretionary
accruals, neither DAC COM nor DAC COMR is correlated with DAC RES — their correlation
levels are quite low and are not significant at conventional significance levels either. This again
is not surprising as DAC RES and DAC COMR (DAC COM) are constructed to capture the
potential impact of the discretionary accruals on stock returns from different angles (firm-specific
vs. market-wide).
3 There Are More Than One Accrual Anomalies
The accrual anomaly documents that firm-level accruals negatively predict next-period firm-level
stock returns. Both Hirshleifer et al. (2008) and Kang et al. (2008) find that the aggregate accrual
and the aggregate discretionary accrual are able to positively predict next-period aggregate stock
market returns. Their findings point to another potential anomaly, i.e., an accrual anomaly at the
aggregate level. It is possible that the two return effects of the (discretionary) accrual measures
may co-exist in a unified empirical framework. More important, the two return effects of accruals
may capture distinctly different accrual-return relations. We set out to explore these issues in this
section.
3.1 Motivation
To motivate our investigation of a potential second accrual anomaly, we first study whether the
aggregate (discretionary) accrual measures, together with firm-level (discretionary) accruals, also
affect firm-level stock returns. We run the following predictive regressions, for each firm, of the firm’s
stock returns against its one-year-lagged accruals ACit−1 (discretionary accruals DACit−1) and/or
11
one-year-lagged value-weighted aggregate accruals AACt−1 (aggregate discretionary accruals
ADACt−1) over the 1965-2005 period:
Rit −Rft = a+mACit−1 + lAACt−1 + εit, or (5)
Rit −Rft = a+mDACit−1 + lADACt−1 + εit, (6)
where Rit is firm i’s annual stock returns compounded from April of year t to March of year t+ 1;
and Rft is the annual risk-free rate compounded from April of year t to March of year t + 1. We
run a time-series regression of Equation (5) or Equation (6) for each firm in our sample with at
least ten observations of data in the sample period. We summarize and report the cross-sectional
statistics for the estimates.
In Equations (5) or (6), a negative m, i.e., the estimated coefficient of firm-level (discretionary)
accruals, indicates the existence of the conventional accrual anomaly as the accrual literature shows
that firms with higher (discretionary) accruals tend to yield lower future returns than firms with
lower accruals (see, e.g., Sloan, 1996; Collins and Hribar, 2000; and Xie, 2001). A positive l, i.e.,
the estimated coefficient of aggregate (discretionary) accruals, suggests that the return-predicability
with aggregate (discretionary) accrual as identified in Hirshleifer et al. (2008) and Kang et al. (2008)
applies to the firm-level as well.
Table 3 reports the cross-sectional averages, t-values of the cross-sectional averages, and the
cross-sectional medians of the estimation results from the firm-level predictive regressions as in
Equation (5). In Model (1), only firm-level accruals, ACit, are included as the independent variable,
the cross-sectional average value of this predictive coefficient, m, is negative at -0.212 with a t-
value of -2.796, and the value of the cross-sectional median is -0.180. This finding confirms the
conventional accrual anomaly that firm-level accruals negatively relate to next-period stock returns.
In Model (2), we use the value-weighted aggregate accruals (AACt) as the sole return predictor.
The cross-sectional average value of this predictive coefficient is positive at 5.932 with a t-value of
17.357, and the value of the cross-sectional median is 4.559. The positive sign of l indicates that the
aggregate accruals positively predicts firm-level stock returns, which constitutes a potential second
accrual anomaly.
In Model (3) we include both ACit and AACt as return predictors, and find that m is still
12
significantly negative and l is significantly positive. The firm-level stock return predicability of ACit
and ACt co-exists in our predictive regression. The co-existence is also reflected in the adjusted
R2 from the regressions. When the aggregate accruals (AACt) is added as a regressor, the cross-
sectional average of adjusted R2 increases from 0.6% to 2.2%. The return predictive power of AACt
is distinct and it is also different from that of ACit.
Models (4) to (6) replicate the same regressions for discretionary accrual measures. We take
Model (6) as the example, where both firm-level discretionary accruals (DACit) and the value-
weighted aggregate discretionary accruals (ADACt) are included. We find strong evidence that
m is significantly negative and l is significantly positive, suggesting the cohabitation of the two
distinct return-predicability with the two different discretionary accrual measures.
The empirical evidence in Table 3 implies that there might be a second accrual anomaly.
The contrast in the return effects of the firm-level (discretionary) accruals versus the aggregate
(discretionary) accruals also suggests that investors respond asymmetrically to the firm-level and
the aggregate (discretionary) accruals.
3.2 Co-movement in Firm-level (Discretionary) Accruals
Given the return predicability with the firm-level (discretionary) accruals and the aggregate
(discretionary) accruals, one may conjecture that (discretionary) accruals may affect stock returns
through both a firm-specific channel (i.e., the conventional accrual anomaly) and a market-wide
channel (i.e., the second accrual anomaly). To test this conjecture, we first establish in this section
the evidence that there is a considerable amount of co-movement in firm-level (discretionary)
accruals. That is, firm-level (discretionary) accruals co-move with the aggregate (discretionary)
accruals which serves as a market-wide measure.
We estimate Equation (3), where individual firm’s accrual (ACit) is regressed against
contemporaneous value-weighted aggregate accruals (AACt), for each firm in our sample. We
then compute the cross-sectional average coefficient estimates, t-statistics, average adjusted R2,
percentage of positive coefficients, and percentage of positive significant coefficient (with t-statistics
larger than 1.645 in absolute value). We report the results in Panel A of Table 4. We replicate
the same analysis by estimating Equation (4), in which firm-level discretionary accruals (DACit)
is regressed against the value-weighted aggregate discretionary accruals (ADACt). We report the
13
results in Panel B of Table 4.
We examine the results in Panel A first. For the pooled sample, the estimated coefficient on
AACt is 0.709 and it is statistically significant (average t-statistics is 5.99). The average adjusted
R2 is 6% and about 73% of firms have positive β. The evidence suggests that firm-level accruals
exhibits a considerable co-movement with a market-wide factor (AACt here). Panel A also shows
that as firm size increases and the estimated coefficient, adjusted R2 from the regression all increase
monotonically, suggesting that larger firms demonstrate a higher degree of co-movement. Results
reported in Panel B show the same patterns. We observe a considerable co-movement in firm-level
discretionary accruals (DACit) and the degree of such co-movement increases with firm size.
3.3 Portfolio Tests: Existence of Two Accrual Anomalies
The finding from Table 4 suggests another way to decompose firm-level (discretionary) accrual
measures — they can be decomposed into a market-wide component and a firm-specific component.
As we explain in Section 2, the former can be captured by either β or adjusted R2 from the
co-movement regressions, and the latter by the residuals from Equations (3) or (4). Note that
aggregating the fitted values (excluding the intercepts) from the decomposition equation across
firms yields the aggregate (discretionary) accrual measure. Thus, the aggregate (discretionary)
accrual measures, by ways of construction and by their very nature, correspond to the market-wide
component of firm-level (discretionary) accruals. We thus conjecture that the conventional accrual
anomaly is mainly due to the firm-specific component of accruals, and the return-predicability with
the aggregate (discretionary) accrual measures is largely driven by the market-wide component of
accruals.
We test the conjecture by applying the standard hedge portfolio test, which evaluates abnormal
returns to hedge portfolios formed on the basis of accrual measures such as the market-wide
component of (discretionary) accruals and the firm-specific component of (discretionary) accruals.
We construct the hedge portfolio following the way the Fama-French factors such as SMB, HML,
and UMD are constructed. Specifically, we sort the stocks into the top 30%, the middle 40%,
and the bottom 30% based on a certain (discretionary) accrual measure, then we compute the
equal-weighted raw return and the Fama-French four-factor-adjusted return to a standard zero-
investment strategy with a long position on stocks in the bottom group and a short position on
14
stocks in the top group.
Panel A of Table 5 reports the results of hedge portfolio tests using accrual measures. When
we sort the stocks based on firm-level accruals (ACit), we find that the hedge portfolio yields
an average monthly Fama-French-four-factor adjusted abnormal return of 0.267%, confirming the
existence of the accrual anomaly. When we sort the stocks by accrual β from the estimation of
Equation (3), we document the average monthly Fama-French-four-factor adjusted abnormal return
to the hedge portfolio is 0.105%. And when we sort the stocks based on R2 from the estimation of
Equation (3), we find that the hedge portfolio yields an average monthly Fama-French-four-factor
adjusted abnormal return of 0.159%. In the case of sorting stocks using β and R2, we find a
different accrual anomaly because the stocks are sorted based on the market-wide component of
accruals, but not by accruals. We also find that when we sort stocks based on the residual from
Equation (3), the hedge portfolio yields an average monthly abnormal return of 0.271%, which is
in line with the magnitude of the conventional accrual anomaly (0.267%) when stocks are sorted
by firm-level accruals.
Panel B of Table 5 reports the results of using discretionary accrual measures. Specifically,
when we sort the stocks into portfolios by firm-level discretionary accruals, we find that a standard
zero-investment strategy with a long position on stocks with a low level of DACit and a short
position on stocks with a high level of DACit yields an average monthly Fama-French-four-factor
adjusted abnormal return of 0.302%. When we sort stocks into portfolios based on the residuals
from Equation 4, we find that the hedge portfolio yields an abnormal return of -0.264%. Its
magnitude is similar to that of the conventional accrual anomaly. However, when we sort stocks
into portfolio based on β from Equation 4, the hedge portfolio with a long position on stocks with a
high level of β and a short position on stocks with a low level of β yields an monthly average Fama-
French-four-factor adjusted abnormal return of 0.232% (t-statistics = 3.04). Sorting stocks based
on R2 from Equation 4, the hedge portfolio also yields a statistically significant abnormal return
of 0.153% (t-statistic = 1.79). The market-wide component of discretionary accruals, captured by
either β or adjusted R2 from Equation (4), causes an accrual-related anomaly that is different from
the one driven by the firm-specific component of discretionary accruals.
Panel C of Table 5 reports the results of using normal accrual measures. We do not observe
either the conventional accrual anomaly or the two anomalies due to different components of normal
15
accruals. We thus conclude that the conventional accrual anomaly and the two accrual anomalies
due to firm-specific component and market-wide component of (discretionary) accruals only apply
to accruals and/or discretionary accruals but not on normal accruals.
4 Regression Analysis: Relations Among Different Accrual
Anomalies
Our analysis so far establishes the dichotomy of the (discretionary) accrual-return relations, which
represents two different accrual anomalies — one is driven by the firm-specific component and the
other is driven by the market-wide component of (discretionary) accruals. By construction, the two
accruals anomalies are distinct and are likely to be orthogonal to each other. Notably, the hedge
portfolio sorted by the residuals from either Equation (3) or Equation (4) yields an abnormal return
that is in a similar magnitude to the hedge portfolio sorted by firm-level (discretionary) accruals,
implying that the accrual anomaly due to the firm-specific component of (discretionary) accruals
may supersede the conventional accrual anomaly. We explore the relations among the two accrual
anomalies and the conventional accrual anomaly in this section.
4.1 Time-series Regressions
To study the relations among the different types of accrual anomalies, we employ the return
factors constructed in Section 2. Recall that we construct four return factors based on the total
accrual measures, AC factor, AC RES, AC COM and AC COMR, and another set of four return
factors based on the discretionary accrual measures, DAC factor, DAC RES, DAC COM and
DAC COMR.7
Panel A of Table 6 replicates analysis of the conventional accrual anomaly in Sloan (1996) and
Xie (2001). We first sort the stocks into deciles by firm-level accruals (ACit) and then regress the
returns to portfolios against the Fama-French four factors. The estimated coefficient of the intercept
(α) thus measure the monthly abnormal returns after adjusting for the Fama-French four factors.7Note that in our notations, AC factor and DAC factor correspond to the conventional accrual anomaly;
AC COM , AC COMR, DAC COM and DAC COMR are all related to the accrual anomaly due to the market-wide component of total accruals or discretionary accruals; and finally, AC RES and DAC RES reflect the accrualanomaly due to the firm-specific component of total accruals or discretionary accruals.
16
As shown in Panel A, the hedge portfolio with a long position on stocks in the bottom accrual decile
and a short position on stocks in the top accrual decile yields a monthly Fama-French-four-factor
adjusted abnormal return of 0.351% (t-statistic = 2.08). The second part of Panel A shows that the
hedge portfolio with a long position on stocks in the bottom discretionary accrual decile and a short
position on stocks in the top discretionary accrual decile yields a monthly Fama-French-four-factor
adjusted abnormal return of 0.575% (t-statistic = 3.91).
The results in Panel A are retained for the purpose of comparison. In Panel B, in addition
to the Fama-French four factors, we include the returns to the factor-mimicking portfolio
constructed based on the firm-specific (discretionary) accrual component (AC RES andDAC RES
respectively) as explanatory variable. We regress the excess returns to (discretionary) accrual
deciles (Rpt −Rft) on the five return factors. As shown in the first part of Panel B, the estimated
coefficients of AC RES across all accrual deciles are statistically significant. More interestingly,
the hedge portfolio constructed based on the firm-level accruals (ACit) no longer generates an
abnormal return after controlling for the return factor based on the firm-specific accrual component
(AC RESt). That is, after controlling for AC RES, the conventional accrual anomaly disappears.
The evidence suggests that the firm-specific accrual component explains stock returns that cannot
be accounted for by the Fama-French four factors, and provides a direct support for the argument
that the accrual anomaly due to the firm-specific component of accruals supersedes the conventional
accrual anomaly.
The second part of Panel B report the results using the return factor based on the firm-specific
component of discretionary accruals, DAC RES. The loadings on this factor are statistically
significant in almost all discretionary accrual deciles. We also find that when this factor is added,
the conventional accrual anomaly becomes much weaker — the hedge portfolio that is long on
stocks in the bottom discretionary accrual decile and short on stocks in the top discretionary
accrual decile yields an abnormal return of 0.250%, which is less than half of the abnormal return
without controlling for DAC RES (which equals 0.575%). Clearly, a large part of the conventional
accrual anomaly can be accounted for by the firm-specific component of the discretionary accruals.
In Panels C and D, we include the return factors constructed based on the market-wide
(discretionary) accrual components to the regressions. Two findings surface immediately. First,
the estimated coefficients on those return factors, e.g., AC COM , DAC COM , AC COMR,
17
DAC COMR, are statistically significant in most (discretionary) accrual deciles. The evidence
indicates that there is considerable return co-movement associated with the market-wide component
of (discretionary) accruals as well. In addition, the return effect of the market-wide (discretionary)
accrual component is robust to the Fama-French four factors, signaling the existence of a second
accrual anomaly.
Second, we find that the hedge portfolio based on firm-level (discretionary) accruals still
yields significant abnormal returns after controlling for the returns to factor-mimicking portfolio
constructed based on the market-wide component of (discretionary) accruals. For example, the
standard zero-investment hedge portfolio with a long position on stocks in the bottom accrual
decile and a short position on stocks in the top accrual decile yields an average monthly abnormal
return of 0.367% (t-statistics = 2.17) after adding AC COM . While AC COM is priced, the
abnormal return to the hedge portfolio is at par with that of the conventional accrual anomaly
which, as reported in Panel A, has the abnormal return of 0.351%. That is, the conventional accrual
anomaly still holds after controlling for the return effect of the market-wide accrual component,
suggesting that there are two different types of accrual anomalies.
In summary, the findings in Table 6 lead to two conclusions. First of all, the two accrual
anomalies, which are driven by different components of (discretionary) accruals, co-exist and are
likely orthogonal to each other. Second, the accrual anomaly driven by the firm-specific component
of (discretionary) accruals largely supersedes the conventional accrual anomaly. Therefore, the two
accrual anomalies can be interchangeably classified as the conventional accrual anomaly in the sense
of Sloan (1996) and Xie (2001), and a new accrual anomaly driven by the market-wide component
of (discretionary) accruals.8
4.2 Relating the Accrual Based Factors to Fama-French Factors
We further examine whether the various return factors constructed based on different
(discretionary) accrual components reflect known factors commonly used in empirical studies such
as the market, size, book-to-market, and momentum. If true, the intercepts from the regressions of8The two accrual anomalies in our paper thus have two combinations: one is the conventional accrual anomaly
plus the accrual anomaly based on the market-wide component of (discretionary) accruals; and the other is theaccrual anomaly due to the firm-specific component of (discretionary) accruals plus the accrual anomaly due to themarket-wide component of (discretionary) accruals.
18
the (discretionary) accrual based factors against the set of known factors should be zero, and the
R2 of these regressions should be high.
Table 7 reports such regression results. In those regressions, each of the eight return factors
based on different (discretionary) accruals are used as the dependent variable and the Fama-French
four factors are used as the independent variables. The estimated intercepts are statistically
significant for all (discretionary) accrual based factors except for AC COM , which has a t-statistics
of 1.15; all the other t-statistics lie between 1.77 and 4.25. Moreover, the R2s of the regressions
are quite low, ranging between 0.5% and 16.7%. The two pieces of evidence combined indicate
that the Fama-French four factors cannot explain the various factors constructed based on different
(discretionary) accrual components. This result is important inasmuch as a finding of a high R2
would suggest little independent role for our (discretionary) accrual-based factors in explaining
asset returns.
4.3 Cross-sectional Regressions
We provide further evidence on the existence and orthogonality of the two accrual anomalies using
Fama and French’s 10 × 10 size/book-to-market portfolios as test assets. We follow Fama and
MacBeth’s (1973) approach to conduct the two-pass cross-sectional testing. Specifically, in the first
pass, for each portfolio at each time t, we run a time-series regression of its monthly excess returns
against the Fama-French four factors and the various (discretionary) accrual-based factors over the
past 60 months from t− 60 to t− 1. In the second pass, we run a cross-sectional regression of the
100 portfolio returns at time t against the portfolios’ factor loadings estimated from the first-pass
time-series regressions to obtain the premiums associated with the loadings. We then repeat the
two-path regressions for each month t and use the Fama-MacBeth method to compute the average
premiums and their t-statistics. We report the results in Table 8.
In Model 1 of Table 8, we use the Fama-French four factors and AC factor in the two-path
regression. The coefficient estimate on the loading of AC factor is significantly positive at 0.981
(with a t-statistics of 3.52). The finding demonstrates the return effect of firm-level accruals and
corroborates the existence of the conventional accrual anomaly. In Models 2 and 3, we respectively
use AC COMR and AC RES, along with the Fama-French four factors, in the two-path regression.
The coefficient estimates on loadings of both AC COMR and AC RES are significant and positive,
19
indicating the existence of two accrual-return relations — one is due to the market-wide component
of firm-level accruals, and the other to the firm-specific component of firm-level accruals.
In Model 4, we use both AC factor and AC RES, together with the Fama-French four factors,
in the two-path regression. Interestingly, the coefficient estimate on the loading of AC factor
remains significantly positive, and the estimate on the loading of AC RES becomes statistically
insignificant. This result suggests that the two factors might capture similar information and that
the information content of AC factor swamps the information content of AC RES. In Model
5, we include both AC COMR and AC RES, plus the Fama-French four factors, in the two-
path regression. The coefficient estimates on loadings of both factors are positive and statistically
significant. This result shows that the two factors based respectively on the market-wide component
and the firm-specific component of firm-level accruals contain distinct information that both affect
the cross-sectional variations in stock returns, providing a strong support for the orthogonality of
the two accrual-return relations.
If we use the various factors constructed on the basis of discretionary accruals in the two-path
regression (Models 6 to 10 in Table 8), we obtain similar results. Notably, when both DAC COMR
and DAC RES are present (Model 10), the coefficient estimate on the loading of DAC COMR
is still significantly positive, indicating the robustness of the accrual anomaly due to the market-
wide component of firm-level discretionary accruals. The estimate of the loading on DAC RES is
positive and insignificant, though. It seems that the two accrual anomalies are less robust in the
case of the discretionary accruals.
5 Further Evidence and Discussions
5.1 The Economic Magnitude of the Two Accrual Anomalies
We have so far established robust evidence that there are two accrual anomalies, and that the accrual
anomaly due to firm-specific component of (discretionary) accruals supersedes the conventional
accrual anomaly. We also show evidence that two accrual anomalies are largely orthogonal to each
other. In this section, we study the economic magnitude of the two accrual anomalies. Specifically,
we examine the abnormal returns to a hedge portfolio constructed based on a conditional two-way
sort: first by (discretionary) accruals or the firm-specific (discretionary) accrual component and
20
then by the market-wide (discretionary) accrual component.9 We form those portfolios at each
year-end of year t− 1 and hold the portfolios from April of year t to March of year t+ 1. We then
compute the average monthly Fama-French-four-factor adjusted returns to each portfolio over the
1980-2005 sample period. We report the results in Table 9.
In Panel A of Table 9, we sort the stocks into 3 × 3 portfolios first by the firm-level accruals
(ACit) and then by the market-wide component of accruals (β and R2 from Equation (3)). That
is, we first sort the stocks into three equal-sized groups based on ACit, and within each group we
further sort the stocks into three equal-sized subgroups based on either β or R2 from Equation (3).
As shown in Panel A, the hedge portfolio taking a long position on stocks with low accruals (ACit)
and a short position on stocks with high accruals yields an average monthly abnormal return of
0.280% (t-statistic = 2.81), which also shows the magnitude of the conventional accrual anomaly in
our sample period. In contrast, the hedge strategy that exploits the two accrual anomalies — a long
position on stocks with a low level of accruals and a high level of β and a short position on stock
with a high level of accruals and a low level of β — yields an average monthly abnormal return
of 0.277% (t-statistic = 2.00). However, the conventional accrual strategy, if limited to the stocks
with a high level of β only, yields an average monthly abnormal return of 0.468%, representing a
67% increase from that of the conventional accrual strategy applied to all firms. Further, another
hedge strategy exploiting the two accrual anomalies — a long position on stocks with a low level of
accruals and a high level of R2 and a short position on stock with a high level of accruals and a low
level of R2 — yields an average monthly abnormal return of 0.453%, representing a 62% increase
relative to the payoffs of the conventional accrual strategy. Obviously, the economic magnitude
of the second accrual anomaly is significant when R2 from Equation (3) is used to capture the
market-wide component of firm-level accruals.
In Panel B, we first sort stocks into three groups based on the discretionary accruals (DACit),
and then within each group we further sort stocks into three equal-sized subgroups based on either
β or R2 from Equation (4). The pure discretionary accrual hedge strategy (Xie, 2001) yields an
average monthly abnormal return of 0.273% (t-statistic = 4.12). The enhanced hedge strategy,9We sort the stocks by accruals or discretionary accruals first for two reasons: 1), we have shown above that the
return effect due to firm-specific component of (discretionary) accruals supersedes the return effect of (discretionary)accruals; and 2), with the sorting of stocks by (discretionary) accruals, we have a benchmark to show the economicmagnitude of the conventional accrual anomaly.
21
which take advantages of the return effect due to the market-wide component of discretionary
accruals, yields a much larger abnormal return. Specifically, the hedge portfolio taking a long
position on stocks with low discretionary accruals and high βs and a short position on stock with
high discretionary accruals and low βs yields an abnormal return of 0.513% (t-statistic =4.29),
representing an 88% increase from that of a pure discretionary accrual strategy. The similar
enhanced hedge strategy yields an abnormal return of 0.362% when R2 is used to measure the
market-wide component of discretionary accruals.
The two-way sort used in Panel C of Table 9 deviates slightly from those in Panel A. Here we
sort the stocks into 3 × 3 portfolios first by the firm-specific accrual component (residuals from
Equation (3)) and then by the market-wide accrual component (β or R2). As shown in Panel C,
a hedge strategy with a long position on stocks with a low level of residuals and a short position
on stocks with a high level of residuals yields an average monthly abnormal return of 0.320% (t-
statistic = 4.36), and the magnitude is comparable to that of the conventional accrual strategy.
When we sort the stocks by both residuals and β from Equation (3), the hedge strategy taking a
long position on stocks with a low level of residuals and a high level of β and taking a short position
on stocks with a high level of residuals and a low level of β yields an average monthly abnormal
return of 0.455% (t-statistic = 3.52), representing a 42% improvement from the hedge strategy
built solely on residuals. When we sort the stocks by both residuals and R2 from Equation (3), the
hedge strategy taking a long position on stocks with a low level of residuals but a high level of R2
and taking a short position on stocks with a high level of residuals but a low level of R2 yields an
average monthly abnormal return of 0.506% (t-statistic = 3.96), which represents a 58% increase.
Finally, in Panel D, we sort the stocks into 3×3 portfolios first by the firm-specific discretionary
accrual component (residuals from Equation (4)) and then by the market-wide discretionary accrual
component (β or R2). Panel D shows that a hedge strategy taking a long position on stocks with a
low level of residuals and a short position on stocks with a high level of residuals yields an average
abnormal return of 0.275% (t-statistic = 3.94), and the magnitude is comparable to that of a pure
hedge strategy sorting stocks by discretionary accruals only. When we sort the stocks by both
residuals and β from Equation (4), the hedge strategy holding a long position on stocks with a low
level of residuals but a high level of β and holding a short position on stocks with a high level of
residuals but a low level of β yields an average monthly abnormal return of 0.571% (t-statistic
22
= 4.59), representing a 108% improvement from the hedge strategy built solely on discretionary
accrual residuals. When we sort the stocks by both residuals and R2, the hedge strategy yields a
moderate abnormal return of 0.317%, which also represents a 16% increase from the pure hedge
strategy built on residuals only.
5.2 Discussions
Our analysis shows that there are more than just one accrual anomalies, and that the firm-
specific and market-wide components of (discretionary) accruals affect stock returns in distinct
ways. However, our results are silent about the economic rationales behind each of the two
accrual anomalies. Here we discuss various plausible economic rationales underling the two accrual
anomalies without offering substantive empirical evidence.
The coexistence of the two qualitatively opposite accrual anomalies — one is driven by the
firm-specific component of (discretionary) accruals and the other by the market-wide component
of (discretionary) accruals — suggests that accounting information such as total accruals and
discretionary accruals may affect stock return through different channels. The underlying incentives
behind the two (discretionary) accrual components are likely to be very different. If we interpret
firm-level (discretionary) accruals as a proxy for firm-level earnings management, then our results
imply that firms may manage earnings in response to both firm-specific shocks and market-wide
shocks. Further research along this line may greatly improve our understanding of the nature
of (discretionary) accruals’ return effects. Here we discuss the extant research and explore what
incentives motivate firm managers to manage earnings in response to both firm-specific shocks and
market-wide shocks.
On the firm-specific shocks, a large literature discusses the managerial incentives to manage
earnings as a response to firm-level shocks. For example, Dye (1988) and Trueman and
Titman (1988) develop analytical models that illustrate contracting frictions can lead to earnings
management intended to influence the decisions of external capital providers. Burgstahler and
Dichev (1997), and Degeorge et al. (1999) report evidence that firms use earnings management
to avoid reporting negative earnings, earnings declines, or falling short of market expectations.
Teoh et al. (1998) find that firms report positive discretionary accruals prior to initial public offers.
Graham et al. (2005) survey Chief Financial Officers (CFOs) and report that CFOs indicate they
23
manage earnings to maintain or increase the stock price of their firms. Kothari, Loutskina, and
Nikolaev (2006) argue that managers of overvalued firms are likely to manage their firms’ accruals
upwards to prolong the overvaluation.
In terms of market-wide shocks, we first use the modern managerial compensation schemes as
an example. To ameliorate the agency problem facing modern firms, managerial compensation
schemes rely on accounting earnings and stock returns as their basis. Given the mix of accounting
earnings and stock returns as determinants of managerial compensation, managers have incentives
to manage earnings to shield themselves from aggregate market shocks. For example, Watts and
Zimmerman (1978), Healy (1985), McNochols and Wilson (1988), and Defeo et al. (1989) all find
that CEOs report accounting income so as to increase their compensation and that the relation is
causal. Sloan (1993) shows that accounting earnings are much less sensitive to macroeconomic risk
than stock returns and accounting profits are more closely correlated with market-adjusted stock
returns than with raw returns. Recently, Kothari, Shu, and Wysocki (2006) provide systematic
evidence that managers delay the dissemination of bad news. Given the contractual arrangement,
the incentive of earnings management is likely to be stronger when the aggregate market is perceived
to be weak. If a negative shock hits the stock market and causes a gap between firm performance
and analyst or investor expectations, such capital market incentives to manage earnings are likely
to be higher. It is also worth noting that earnings management is potentially costly to firms
and managers. The increased worries about potential litigation related to financial reporting may
place constraints on the exercise of managerial opportunism — firm managers thus may choose to
time the aggregate equity market rather than their own stock performance to manage earnings.
If a negative shock hits the stock market and causes a gap between firm performance and capital
market expectations, such incentives to manage earnings are likely to be high. This explains why
we find the market-wide component of (discretionary) accruals affect stock returns.
6 Conclusion
In this paper, we motivate our empirical analysis by the findings that the aggregate (discretionary)
accruals positively predict one-year-ahead firm-level stock returns, and that there is a considerable
amount of co-movement in firm-level (discretionary) accruals. We introduce a novel way to
24
decompose firm-level (discretionary) accruals into a market-wide component and a firm-specific
component. We provide robust empirical evidence that the two different components affect
stock returns in different ways and drive two different accrual anomalies. While the firm-specific
component negatively predicts next-period stock returns, firms with a higher level of the market-
wide component have on average higher next-period stock returns. We show that the two accrual
anomalies co-exist and the accrual anomaly due to the firm-specific component of (discretionary)
accruals largely supersedes the conventional accrual anomaly documented in Sloan (1996) and
Xie (2001). We offer further evidence that the two accrual anomalies are distinct and likely
orthogonal to each other. Given the potential orthogonality of the two accrual anomalies, we
design a hedge strategy that explicitly exploits the different roles of the two (discretionary) accrual
components (firm-specific versus market-wide) in affecting stock returns. We find that the hedge
portfolio yields an abnormal return significantly higher than that of a typical accrual strategy built
only on firm-level (discretionary) accruals.
We also briefly discuss potential economic rationales behind the two accrual anomalies. Our
preliminary analysis appears to suggest that firm managers manage earnings in response to both
market-wide shocks and firm-specific shocks. Further research is called for to examine which firms
are more likely to manage earnings in response to market-wide shocks and which firms are more
likely to manage earnings in response to firm-specific shocks. Our paper shows that accounting
information such as (discretionary) accruals impacts on the stock market through both market-
wide and firm-specific channels.
25
References
[1] Burgstahler, D., Dichev, I., 1997. Earnings management to avoid earnings decreases and losses.Journal of Accounting and Economics, 24, 99126.
[2] Collins, D.W., Hribar, P., 2000. Earnings-based and accrual-based market anomalies: Oneeffect or two? Journal of Accounting and Economics, 29, 101-123.
[3] Dechow, P., Sloan, R., Sweeney, A., 1995. Detecting earnings management, The AccountingReview, 70 (2), 193-225.
[4] Degeorge, F., Patel, J., and Zeckhauser, R., 1999. Earnings management to exceed thresholds.Journal of Business, 72, 1-33.
[5] Defeo, V.J., Lambert, R.A., Larcker, D.F., 1989. The executive compensation effects of equity-for-debt swaps, The Accounting Review, 64, 201-227.
[6] Dye, R. 1988. Earnings management in an overlapping generations model. Journal ofAccounting Research, 26, 195-235.
[7] Fama, E., MacBeth, J., 1973. Risk, return, and equilibrium: empirical results. Journal ofPolitical Economy, 81, 607-636.
[8] Fama, Eugene F., Kenneth R. French, 1992. The cross-section of expected stock returns.Journal of Finance, 47, 427-465.
[9] Fama, Eugene F., Kenneth R. French, 1993. Common risk factors in the returns on stocks andbonds, Journal of Financial Economics, 33, 3-56.
[10] Graham, J., Harvey C., and Rajgopal, S., 2005. The economic implications of corporatefinancial reporting. Journal of Accounting and Economics, 40, 3-73.
[11] Hirshleifer, David, Kewei Hou, Siew Hong Teoh, 2008, Accruals and aggregate stock marketreturns. Journal of Financial Economics, forthcoming.
[12] Jones, J. 1991. Earnings management during import relief investigations. Journal of AccountingResearch, 29, 193-228.
[13] Khan, M., 2008. Are accruals mispriced? Evidence from tests of an intertemporal capital assetpricing model. Journal of Accounting and Economics, 45, 55-77.
[14] Kang, Qiang, Qiao Liu, Rong Qi, 2008. Predicting stock market returns with aggregatediscretionary accruals, working paper, University of Hong Kong.
[15] Kothari, S., Shanken, J., 1997. Book-to-market, dividend yield, and expected market returns:a time-series analysis. Journal of Financial Economics, 44, 169-203.
[16] Kothari, S., Lewellen, J., Warner, J., 2005. Stock returns, aggregate earnings surprise, andbehavioral finance. Journal of Financial Economics, forthcoming.
[17] Kothari, S., Shu, S., Wysocki, P., 2006. Do managers withhold bad news? Working paper,MIT Sloan School of Management.
26
[18] McNichlos, M., Wilson, G.P., 1988. Evidence of earnings management from the provisions forbad debts. Journal of Accounting Research, 26, 1-31.
[19] Ng, J., 2005. Distress risk informaiton in accruals, working paper, The Wharton School.
[20] Richardson, Scott A., Richard G. Sloan, Mark T. Soliman, and Irem Tuna, 2005. Accrualreliability, earnings persistence, and stock prices. Journal of Accounting and Economics, 39,437485.
[21] Sloan, R. 1993. Accounting earnings and top executive compensation. Journal of Accountingand Economics, 16, 55-100.
[22] Sloan, R. 1996. Do stock prices fully reflect information in accruals and cash flows about futureearnings? The Accounting Review, 71, 289-315.
[23] Teoh, S., Welch, I., Wong, T., 1998. Earnings management and the long-run marketperformance of initial public offerings. Journal of Finance, 53, 1935-1974.
[24] Trueman, B., Titman, S., 1988. An explanation for accounting income smoothing. Journal ofAccounting Research, 26, 127-139.
[25] Watts, R., Zimmerman, J., 1986. Positive Accounting Theory, Englewood Cliffs, NJ: Prentice-Hall.
[26] Wu, Ginger, Lu Zhang, and Frank X. Zhang, 2008. Struggling to understand the accrualanomaly. Working paper, University of Michigan.
[27] Xie, H., 2001. The mispricing of abnormal accruals, Accounting Review, 76, 357-373.
[28] Zhang, Frank X., 2007. Accruals, investment, and the accrual anomaly. The AccountingReview, 82, 1333-1363.
27
28
Table 1 Summary Statistics of Main Variables 1965 – 2005 For all U.S. firms (excluding financial firms – firms with SIC code between 6000 and 6999) on NYSE, AMEX, and NASDAQ with December fiscal year end and coverage on both CRSP and Compustat, we compute their accruals scaled by average total assets (ACi t) as in Sloan (1996). The total number of observation is 36,585 for the period from 1965 to 2005. We also compute the value weighted aggregate accruals in year t for the firms in our sample (AACt). Using the Jones’ (1991) model to decompose accruals into discretionary accruals (DACi,,t) and normal accruals (NACi,t), we compute value-weighted aggregate discretionary accruals (ADACt) and value-weighted normal accruals (ANACt). We also construct eight accrual based factor-mimicking portfolios. For each firm at each portfolio-formation year-end in year t-1, we run the co-movement regression of firm-level accruals or discretionary accruals (ACi,t, or DACi,t) against their corresponding aggregate variables (AACt or ADACt,) over the period from years t-10 to t-1: ACi,s = αi + βi AACs + εis, DACi,s = αi + βi ADACs + εis. We sort the sample firms into three portfolios (top 30%, medium 40%, and bottom 30%) based on respective β values, R squares, and residuals from the above regressions. The first two measures capture the market-wide component of accruals (discretionary accruals) and the last one captures the firm-specific component of accruals (discretionary accruals). We compute the monthly equal-weighted returns on each portfolio over the holding period from April of year t to March of year t+1. We then calculate the returns on the accrual-based factor-mimicking portfolio, AC_factor (the spread of the returns on a portfolio of stocks with low accruals over the returns on a portfolio of stocks with high accruals), AC_COMt (the difference between the returns on a portfolio of stocks with high βs and the returns on a portfolio of stocks with low βs); AC_COMRt (the definition is similar to that of AC_COMt, but stocks are sorted by R2); and AC_RESt (the definition is similar to that of AC_factor,, but stocks are sorted by residuals). DAC_factor, DAC_COM, DAC_COMR, and DAC_RES are constructed in the same way using different terms from the comovement regression based on the discretionary accruals. We also use the monthly Fama-French four factors obtained from Ken French’s website: Rmt-Rft is the return on the CRSP value-weighted market index over the risk-free rate, SMBt, HMLt, and UMDt are the factors measuring size, value, and momentum effects, respectively. All the numbers in the table are quoted in percentage. The sample period for various accrual measures is 1965-2005, and the sample period for various factor returns is 1980-2005.
Variable Definition
Mean Median Std. Dev. Min. Max.
ACit Accruals -3.575 -3.879 7.596 -54.038 67.890 DACit discretionary accruals -0.151 -0.141 5.937 -42.926 57.821 NACit normal accruals -3.425 -3.425 4.994 -34.281 60.627 AACt value weighted accruals -4.129 -4.519 1.643 -6.725 -0.277 ADACt value-weighted dis. Accruals -0.521 -0.580 0.515 -1.668 0.842 ANACt value-weighted nor. Accruals -3.603 -4.118 1.386 -5.961 0.035 AC_factor factor based on total accruals 0.370 0.296 1.754 -4.659 7.827 AC_COMt co-move. factor of accruals (β ) 0.126 0.149 1.645 -6.473 6.295 AC_COMRt co-move. factor of accruals (R2) 0.086 0.157 1.302 -4.261 4.051 AC_RESt residual factor of accruals 0.274 0.277 1.316 -3.837 4.932 DAC_factor factor based on dis. Accruals 0.372 -0.298 1.218 -3.265 4.821 DAC_COMt co-move. factor of dis. accruals (β ) 0.179 0.221 1.278 -5.189 5.351 DAC_COMRt co-move. factor of dis. accruals (R2) 0.021 0.064 1.230 -4.383 3.872 DAC_RESt residual factor of dis. Accruals 0.278 0.229 1.270 -4.509 6.124 Rmt-Rft market risk premium 0.637 1.060 4.459 -23.130 12.430 SMLt Fama-French size factor 0.153 0.050 3.296 -16.700 22.180 HMLt Fama-French book-market factor 0.413 0.380 3.193 -12.800 13.800 UMDt Fama-French momentum factor 0.847 1.040 4.377 -25.050 18.400
29
Table 2 Correlations among the Return Factors The table reports the correlations among various (discretionary) accrual-based factors and the Fama-French four factors. Table 1 defines the factors. The p-values are reported in parentheses. ***, **, and ** represent significance level at 1%, 5%, and 10% respectively. Panel A: Correlations among the (discretionary) accrual-based return factors and the Fama-French factors Rmt -Rft
SMBt HMLt UMDt
AC_factor 0.138** (0.015)
0.070 (0.214)
-0.040 (0.482)
0.065 (0.253)
AC_COMt 0.270*** (<0.001)
0.329*** (<0.001)
-0.281*** (<0.001)
0.005 (0.935)
AC_COMRt -0.133** (0.018)
-0.289*** (<0.001)
0.118** (0.036)
-0.034 (0.545)
AC_RESt 0.001 (0.991)
0.169*** (0.003)
-0.051 (0.367)
-0.002 (0.970)
DAC_factor 0.238*** (<0.001)
0.176*** (0.002)
-0.197*** (<0.001)
0.097* (0.087)
DAC_COMt -0.094* (0.094)
-0.057 (0.317)
0.012 (0.838)
-0.055 (0.332)
DAC_COMRt -0.176*** (0.002)
-0.405*** (<0.001)
0.197*** (<0.001)
-0.112* (0.047)
DAC_RESt 0.189*** (0.001)
0.104* (0.066)
-0.171*** (0.002)
0.007 (0.907)
Panel B: Correlations among the (discretionary) accrual-based return factors
AC_factor AC_COMt
AC_COMRt AC_RESt DAC_factor DAC_COMt
DAC_COMRt DAC_RESt
AC_factor 1 0.042 (0.463)
-0.034 (0.548)
0.525*** (<0.001)
0.458*** (<0.001)
-0.083 (0.143)
-0.029 (0.604)
0.334*** (<0.001)
AC_COMt 1 0.309*** (<0.001)
0.106* (0.060)
0.099* (0.079)
0.285*** (<0.001)
-0.216*** (<0.001)
0.071 (0.210)
AC_COMRt 1 0.008 (0.882)
-0.028 (0.620)
0.191*** (<0.001)
0.214*** (<0.001)
-0.061 (0.280)
AC_RESt
1 0.515*** (<0.001)
-0.042 (0.452)
-0.032 (0.573)
0.528*** (<0.001)
DAC_factor 1 -0.107* (0.057)
-0.110* (0.051)
0.731*** (<0.001)
DAC_COMt 1 0.063 (0.267)
-0.126* (0.026)
DAC_COMRt 1 -0.127* (0.024)
DAC_RESt 1
30
Table 3 Two Accrual Anomalies: Return-accrual Relations at The Macro- and Micro-level For all US firms (excluding financial firms, that is, firms with SIC code between 6000 and 6999) on NYSE, AMEX, and NASDAQ with December fiscal year end and coverage on both CRSP and Compustat, we compute their accruals scaled by average total assets (ACi t) as in Sloan (1996). The total number of observation is 36,585 for the period from 1965 to 2005. We compute the value weighted aggregate accruals in year t for the firms in our sample (AACt). Besides the accrual measures, we also use the Jones’ (1991) model to decompose the firm level accruals into discretionary accruals (DACit) and normal accruals. We compute the value weighted aggregate discretionary accruals (ADACt) accordingly. We regress each firm’s annual stock returns (compounded from April of year t to March of year t+1) against ACi t (DACit) and AACt (ADACt) as follows: Ri,t-Rft= a+ m ACi,,t-1 +l AACt-1 +εi,t or Ri,t-Rft= a+ m DACi,,t-1 +l ADACt-1 +εi,t We require a firm to have at least 10 observations of data throughout the sample period 1965-2005. We report the cross-sectional means, t-values of the cross-sectional means, and cross-sectional medians of the firm-level regression results in the first, second (i.e., in parentheses), and third rows of each cell of this table.
Model
Intercept (a)
ACi,t (m)
AACt (l)
DACit
(m) ADACt
(l) Adj.R2
(1) 14.411 -0.212 0.006
(31.776) (-2.796) (2.271) 14.918 -0.180 -0.020
(2) 42.851 5.932 0.022 (24.809) (17.357) (7.551) 34.582 4.559 -0.011
(3) 44.671 -0.650 6.848 0.034 (24.944) (-8.140) (19.116) (8.277) 36.498 -0.568 5.399 0.002
(4) 18.801 -1.689 0.009 (51.29) (-3.79) (2.911) 16.715 -1.228 -0.019
(5) 18.011 7.835 0.027 (41.12) (8.39) (3.78) 15.781 5.991 0.003
(6) 18.542 -2.165 8.152 0.039 (38.19) (-5.04) (9.23) (4.56) 16.631 -1.956 6.604 0.007
31
Table 4 Evidence on Comovement in Firm-level (Discretionary) Accruals This table reports the univariate regression results of individual firm’s (discretionary) accruals against the contemporaneous value-weighted aggregate (discretionary) accruals. Firms are sorted by size into quintiles from the smallest to the largest ones. In each cell, we report the average coefficient estimates, t-statistics, average adjusted R2, percentage of positive coefficients and percentage of positive significant coefficient (with t-statistics larger than 1.645) in the first, second , third, fourth and fifth rows. The sample period is 1980 – 2005. Panel A: Co-movement in firm-level total accruals Smallest 2 3 4 Largest Pooled Coeff. (t-stst.) Adj. R2 % +positive %+significant
0.556 (3.22) 0.030 60.27 18.91
0.622 (3.62) 0.050 68.56 23.65
0.685 (3.78) 0.067 74.85 30.54
0.771 (4.02) 0.068 79.34 37.13
0.912 (4.65) 0.083 81.74 36.83
0.709 (5.99) 0.060 72.90 29.42
Panle B: Co-movement in firm-level discretionary accruals Smallest 2 3 4 Largest Pooled Coeff. (t-stst.) Adj. R2 % +positive %+significant
0.397 (2.37) 0.005 59.62 18.59
0.431 (2.74) 0.016 61.09 19.55
0.465 (4.36) 0.016 65.06 20.51
0.619 (3.63) 0.021 68.27 24.68
0.728 (6.59) 0.026 77.24 27.01
0.528 (8.13) 0.017 66.26 22.07
32
Table 5 Characteristics and Returns to Portfolios Sorted by Various Accrual Measures The sample contains all US firms (excluding financial firms, that is, firms with SIC code between 6000 and 6999) on NYSE, AMEX, and NASDAQ with December fiscal year end and coverage on both CRSP and Compustat. We sort stocks into various portfolios based on the results of co-movement regressions: ACi,t = αi,t + βi,t AACt + εi,t, (1) DACi,t = αi,t + βi,t ADACt + εi,t (2) NACi,t = αi,t + βi,t ANACt + εi,t, (3) ACi,t is firm i’s accruals at year t. AACt is the value-weighted aggregate accruals at year t. DACi,t is firm i’s discretionary accruals at time t, and ADACt is the value-weighted discretionary accruals. NACi,t is firm i’s normal accruals at time t, and ANACt is the value-weighted normal accruals. The first, second and third cells of the table report for each equal-weighted portfolio the characteristics, raw returns (Rp,t), and abnormal returns (i.e., Jensen’s alpha, SARp,t) adjusted by Fama-French four factors (including the momentum factor), respectively. The t-statistics are reported in parentheses. The sample period is 1980 – 2005. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. Low
(30%) Med. (40%)
High (30%)
Panel A: Portfolio based on accrual-related measures By accruals (ACit) AC -9.530***
(-182.48) -4.148*** (-221.05)
1.032*** (38.82)
High-Low
Rp,t 1.562*** (5.56)
1.368*** (6.04)
1.192*** (4.56)
-0.370*** (3.73)
SARp,t 0.261** (2.31)
0.118 (1.47)
-0.007 (-0.07)
-0.267*** (-2.56)
By accrual beta β it -0.864***
(-52.24) 0.819*** (120.44)
3.476*** (104.19)
High-Low
Rp,t 1.319*** (5.30)
1.360*** (5.78)
1.445*** (5.19)
0.126* (1.75)
SARp,t 0.093 (1.02)
0.089 (1.07)
0.198* (1.90)
0.105* (1.95)
By R2 from Equation (1) above R2 0.035***
(23.88) 0.162*** (89.92)
0.460*** (155.04)
High-Low
Rp,t 1.354*** (5.39)
1.374*** (5.44)
1.479*** (5.93)
0.125* (1.66)
SARp,t 0.070 (0.083)
0.092 (0.91)
0.229** (2.21)
0.159* (1.77)
By accrual residuals from equation (1) above
Residuals -4.351*** (-108.78)
-0.220*** (-22.25)
3.660*** (94.63)
High-Low
Rp,t 1.524*** (5.56)
1.351*** (6.04)
1.250*** (4.60)
-0.274*** (-3.68)
SARp,t 0.262*** (2.63)
0.117 (1.48)
-0.008 (-0.08)
-0.271*** (-3.45)
33
Panel B: Portfolios based on discretionary accrual – related measures By discretionary accruals DAC -4.694***
(-121.61) -0.134*** (-15.12)
3.961*** (111.46)
High-Low
Rp,t 1.560*** (5.65)
1.370*** (6.02)
1.189*** (4.56)
-0.372*** (-5.39)
SARp,t 0.279*** (2.82)
0.117 (1.52)
-0.024 (-0.24)
-0.302*** (-4.25)
By discretionary accrual beta from equation (2) above β it -3.624***
(-93.39) 0.105*** (14.89)
4.231*** (105.45)
High-Low
Rp,t 1.272*** (4.63)
1.388*** (6.17)
1.452*** (5.43)
0.179*** (2.48)
SARp,t -0.004 (-0.04)
0.138* (1.67)
0.229** (2.32)
0.232*** (3.04)
By R2 from equation (2) above R2 -0.027***
(-65.22) 0.069*** (77.20)
0.359*** (129.51)
High-Low
Rp,t 1.395*** (5.50)
1.365*** (5.49)
1.457*** (6.10)
0.062* (1.72)
SARp,t 0.096 (1.09)
0.117 (1.26)
0.249*** (2.48)
0.153* (1.79)
By residuals from equation (2) above
Residuals -3.880*** (-117.01)
-0.067*** (-7.65)
3.619*** (116.94)
High-Low
Rp,t 1.515*** (5.44)
1.366*** (6.19)
1.238*** (4.63)
-0.278*** (-3.86)
SARp,t 0.245*** (2.46)
0.137* (1.83)
-0.019 (-0.18)
-0.264*** (-3.53)
Panel C Portfolios based on normal accrual-related measures By normal accruals NAC -7.576***
(-187.58) -3.717*** (-246.54)
-0.576*** (9.96)
High-Low
Rp,t 1.385*** (4.99)
1.398*** (6.21)
1.325*** (4.84)
-0.060 (-0.51)
SARp,t 0.064 (0.51)
0.160* (1.85)
0.131 (1.35)
0.068 (0.55)
By normal accrual beta β it -0.214***
(-29.36) 1.050*** (166.41)
3.269*** (93.77)
High-Low
Rp,t 1.386*** (6.00)
1.346*** (5.51)
1.395*** (4.77)
0.009 (0.06)
SARp,t 0.194** (2.04)
0.074 (0.82)
0.116 (1.02)
-0.078 (-0.62)
34
By R2 from equation (3) above R2 0.173***
(50.80) 0.302*** (110.65)
0.566*** (186.90)
High-Low
Rp,t 1.372*** (5.40)
1.331*** (5.53)
1.381*** (5.59)
0.010 (0.11)
SARp,t 0.063 (0.70)
0.098 (1.14)
0.163 (1.56)
0.100 (1.06)
By residuals from Equation (3)
Residuals -2.252*** (-92.02)
-0.190*** (-31.69)
1.878*** (78.17)
High-Low
Rp,t 1.365*** (4.90)
1.363*** (6.23)
1.393*** (5.02)
0.028 (0.28)
SARp,t 0.090 (0.83)
0.168** (2.14)
0.094 (0.83)
0.004 (0.03)
35
Table 6 Time-series Regression for Monthly Returns on Portfolios Sorted by (Discretionary) Accruals: 1980 – 2005 At the end of each fiscal year t, we sort the sample firms on ACi t, or DACi t into ten equal-weighted portfolios, and we hold the portfolios over the period from April of year t+1 through March of year t+2. Here, AC D1 (D10) refers to the portfolio with the lowest (highest) decile of accruals, and DAC D1 (D10) refers to the portfolio with the lowest (highest) decile of discretionary accruals. In Panel A, we run the time-series regression on the following baseline model:
Rp,t – Rft = ap + bp(rmt-rft)+sp SMBt+hpHMLt+dpUMDt+εpt, where Rp,t – Rft is the monthly return on the (discretionary) accrual portfolio p in excess of the one-month Treasury bill rate in month t, and Rmt-Rft, SMBt, HMLt, and UMDt are the Fama and French four factors. In Panels B, C and D, we add into the baseline model respectively AC_RES, AC_COM, AC_COMR,,DAC_RES, DAC_COM, and DAC_COMR – the six return factors constructed based on (discretionary) accrual measures (see Table 1 for definitions). The sample period is from 1980 to 2005. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. Panel A: Baseline Model – Replication of the Accrual Anomaly in Sloan (1996) Rp,t – Rft = ap + bp(Rmt-Rft)+sp SMBt+hpHMLt+dpUMDt + εpt, Portfolio
a
t(a)
b
t(b)
s
t(s)
h
t(h)
d
t(d)
R2
AC D1 0.251 1.51 1.087*** 26.57 0.666*** 12.86 0.467*** 7.64 -0.127*** -3.52 0.768 AC D10 -0.100 -0.70 1.073*** 30.69 0.606*** 13.71 0.320*** 6.13 -0.200*** -6.47 0.824 Hedge D1-D10
0.351**
2.08 0.014 0.34 0.059 1.13 0.147*** 2.36 0.073** 1.98 0.018
Baseline Model – Replication of the Accrual Anomaly in Xie (2001) Rp,t – Rft = ap + bp(Rmt-Rft)+sp SMBt+hpHMLt+dpUMDt + εpt, Portfolio
a
t(a)
b
t(b)
s
t(s)
h
t(h)
d
t(d)
R2
DAC D1 0.433*** 3.05 1.073*** 30.64 0.647*** 14.60 0.339*** 6.48 -0.134*** -4.32 0.823 DAC D10 -0.142 -0.99 1.078*** 30.53 0.613*** 13.72 0.403*** 7.63 -0.176*** -5.64 0.816 Hedge D1-D10
0.575*** 3.91 -0.006 -0.16 0.033 0.73 -0.064 -1.17 0.042 1.32 0.006
36
Panel B: Adding Residual-based Factor (AC_RES, DAC_RES) Rp,t – Rft = ap + bp(Rmt-Rft)+sp SMBt+hpHMLt+dpUMDt +lpAC_RESt+ εpt, Portfolio
a
t(a)
B
t(b)
s
t(s)
h
t(h)
d
t(d)
l
t(l)
R2
AC D1 0.126 0.76 1.092*** 27.30 0.633*** 12.34 0.468*** 7.83 -0.124*** -3.50 0.464*** 3.94 0.779 AC D10 0.048 0.35 1.066*** 31.92 0.645*** 15.07 0.320*** 6.41 -0.204*** -6.90 -0.544*** -5.54 0.839 Hedge D1-D10
0.078 0.51 0.026 0.70 -0.012 -0.26 0.148*** 2.68 0.080*** 2.45 1.008*** 9.29 0.229
Rp,t – Rft = ap + bp(Rmt-Rft)+sp SMBt+hpHMLt+dpUMDt +lpDAC_RESt+ εpt, Portfolio
a
t(a)
b
t(b)
s
t(s)
h
t(h)
d
t(d)
l
t(l)
R2
DAC D1 0.258* 1.90 1.047*** 31.63 0.636*** 15.29 0.362*** 7.35 -0.133*** -4.57 0.662*** 6.54 0.844 DAC D10 0.008 0.06 1.100*** 32.34 0.621*** 14.55 0.384*** 7.58 -0.177*** -5.92 -0.568*** -5.47 0.831 Hedge D1-D10
0.250** 2.13 -0.053* -1.87 0.014 0.39 -0.022 -0.51 0.044* 1.76 1.231*** 14.08 0.393
Panel C: Adding Beta-based Factor (AC_COM, DAC_COM) Rp,t – Rft = ap + bp(Rmt-Rft)+sp SMBt+hpHMLt+dpUMDt +lpAC_COMt+ εpt, Portfolio
a
t(a)
b
t(b)
s
t(s)
h
t(h)
d
t(d)
l
t(l)
R2
AC D1 0.232 1.40 1.076*** 26.08 0.642*** 12.06 0.476*** 7.79 -0.125*** -3.47 0.183* 1.77 0.770 AC D10 -0.134 -0.97 1.052*** 30.42 0.563*** 12.61 0.336*** 6.56 -0.196*** -6.48 0.334*** 3.86 0.832 Hedge D1-D10
0.367** 2.17 0.023 0.55 0.079 1.45 0.140** 2.24 0.071* 1.93 -0.151 -1.43 0.021
37
Rp,t – Rft = ap + bp(Rmt-Rft)+sp SMBt+hpHMLt+dpUMDt +lpDAC_COMt+ εpt, Portfolio
a
t(a)
b
t(b)
s
t(s)
h
t(h)
d
t(d)
l
t(l)
R2
DAC D1 0.428*** 2.97 1.073*** 30.43 0.647*** 14.57 0.340*** 6.47 -0.133*** -4.29 0.021 0.20 0.823 DAC D10 -0.194 -1.34 1.087*** 30.74 0.618*** 13.89 0.410*** 7.80 -0.172*** -5.53 0.222** 2.10 0.818 Hedge D1-D10
0.622*** 4.18 -0.013 -0.36 0.029 0.64 -0.070 -1.30 0.039 1.21 -0.201* -1.85 0.014
Panel D: Adding R2-based Factor (AC_COMR, DAC_COMR) Rp,t – Rft = ap + bp(Rmt-Rft)+sp SMBt+hpHMLt+dpUMDt +lpAC_COMRt+ εpt, Portfolio
a
t(a)
b
t(b)
s
t(s)
h
t(h)
d
t(d)
l
t(l)
R2
AC D1 0.288* 1.74 1.079*** 26.44 0.635*** 11.90 0.462*** 7.59 -0.128*** -3.56 -0.271** -2.19 0.771 AC D10 -0.079 -0.55 1.068*** 30.50 0.589*** 12.87 0.317*** 6.08 -0.200*** -6.50 -0.151 -1.42 0.825 Hedge D1-D10
0.367** 2.16 0.011 0.26 0.046 0.84 0.145** 2.32 0.072** 1.97 -0.120 -0.94 0.017
Rp,t – Rft = ap + bp(Rmt-Rft)+sp SMBt+hpHMLt+dpUMDt +lpDAC_COMRt+ εpt, Portfolio
a
t(a)
b
t(b)
s
t(s)
h
t(h)
d
t(d)
l
t(l)
R2
DAC D1 0.451*** 3.18 1.065*** 30.44 0.611*** 12.95 0.337*** 6.48 -0.139*** -4.50 -0.249** -2.10 0.825 DAC D10 -0.125 -0.87 1.071*** 30.33 0.577*** 12.13 0.401*** 7.63 -0.181*** -5.82 -0.251** -2.12 0.818 Hedge D1-D10
0.575*** 3.89 -0.006 -0.16 0.034 0.69 -0.064 -1.17 0.042 1.31 0.002 0.02 0.003
38
Table 7 Relating the (Discretionary) Accrual-Based Factors to the Four Factors This table reports the estimates from regressing each of the various (discretionary) accrual-based factors against the Fama-French four factors (Table 1 defines those factors), with t-statistics reported in parentheses. The sample period is January 1980 to December 2005. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. Dependent Variables
constant rm –rf SMB HML UMD Adj.R2
AC_factor 0.267** (2.56)
0.066** (2.55)
0.031 (0.95)
0.043 (1.11)
0.029 (1.26)
0.016
AC_COMt 0.105 (1.15)
0.061*** (2.71)
0.129*** (4.54)
-0.049 (-1.47)
-0.012 (-0.62)
0.146
AC_COMRt 0.159* (1.77)
-0.029 (-1.54)
-0.114*** (-4.82)
-0.020 (-0.71)
-0.003 (-0.18)
0.079
AC_RESt 0.271*** (3.45)
-0.011 (-0.59)
0.071*** (2.92)
-0.001 (-0.03)
-0.007 (-0.42)
0.018
DAC_factor 0.302*** (4.25)
0.053*** (3.05)
0.040* (1.80)
-0.017 (-0.65)
0.023 (1.52)
0.070
DAC_COMt 0.233*** (3.04)
-0.036* (-1.93)
-0.022 (-0.91)
-0.033 (-1.19)
-0.018 (-1.08)
0.005
DAC_COMRt 0.153* (1.79)
-0.030* (-1.80)
-0.143*** (-6.77)
-0.008 (-0.32)
-0.021 (-1.41)
0.167
DAC_RESt 0.264*** (3.53)
0.039** (2.10)
0.016 (0.67)
-0.034 (-1.23)
-0.001 (-0.09)
0.032
39
Table 8 Fama-MacBeth Regressions at the Portfolio Level This table reports the Fama-MacBeth (1973) regression results using the Fama-French 10x10 size/book-to-market portfolios as testing assets. The factors used in the regressions are the Fama-French four factors plus various (discretionary) accrual-based factors (Table 1 defines the factors). We follow a two-pass approach. In the first pass, at each month t, we estimate for each portfolio the factor loadings from a time-series regression using monthly excess returns over the period from month t-60 to month t-1. In the second pass, for each month t, we estimate a cross-sectional regression using the estimated factor loadings as independent variables. We repeat the two-pass regression for each month, and we follow the Fama-MacBeth approach to report in the table the averages and t-statistics (in parentheses) from the cross-sectional regressions. For brevity, we only report the results of using AC_COMR and DAC_COMR as market-wide (discretionary) accrual factors (using AC_COM and DAC_COM yields similar results). The sample period is from January 1980 to December 2005. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.
Model 1
2 3 4 5 6 7 8 9 10
Rmt-Rft 0.613* (1.84)
0.812*** (2.58)
0.657** (1.98)
0.740** (2.28)
0.696** (2.12)
0.792** (2.42)
0.741** (2.36)
0.711** (2.21)
0.732** (2.26)
0.617*** (1.97)
SMB 0.731*** (2.80)
0.724** (2.38)
0.775*** (2.84)
0.697*** (2.72)
0.660** (2.44)
0.805*** (2.86)
0.606** (2.31)
0.815*** (2.91)
0.759*** (2.75)
0.597** (2.44)
HML 0.275 (1.16)
0.200 (0.94)
0.273 (1.11)
0.130 (0.56)
0.314 (1.32)
0.082 (0.37)
0.273 (1.26)
0.169 (0.73)
0.184 (0.82)
0.351 (1.54)
UMD 1.245*** (2.66)
1.948*** (3.70)
1.642*** (3.43)
1.381*** (3.10)
1.539*** (3.32)
1.935*** (3.85)
1.389*** (3.19)
1.794*** (3.82)
1.713*** (3.70)
1.008** (2.56)
AC_Factor 0.981*** (3.52)
1.106*** (3.99)
AC_COMRt 0.569*** (2.97)
0.525*** (3.01)
AC_RESt 0.436*** (2.81)
0.163 (1.27)
0.306** (2.14)
DAC_Factor 0.465*** (3.27)
0.413*** (3.13)
DAC_COMRt 0.547*** (2.61)
0.479*** (2.62)
DAC_RESt 0.484*** (2.72)
0.519*** (2.98)
0.171 (1.32)
Adj. R2 0.639 0.636 0.635 0.644 0.644 0.633 0.641 0.631 0.639 0.645
40
Table 9 Returns to the Hedge Portfolio Based on the Two Accrual Anomalies The sample contains all US firms (excluding financial firms, that is, firms with SIC code between 6000 and 6999) on NYSE, AMEX, and NASDAQ with December fiscal year end and coverage on both CRSP and Compustat. For each firm at each portfolio-formation year-end of year t-1, we run the co-movement regression of firm-level accruals (ACi,t) or discretionary accruals (DACi t) against the contemporaneous aggregate accruals (AACt) or aggregate discreationary accruals (ADACt) over the period from years t-10 to t-1. We use a conditional two-way sort to form 3x3 equal-weighted portfolios and hold the portfolios from April of year t to March of year t+1. We calculate and report for each portfolio the Fama-French four-factor-adjusted returns (i.e., Jensen’s α) and the corresponding t-statistics (in parentheses) in the table. In Panels A and B, we first sort the stocks into three equal-sized groups based on firm-level accruals (ACit) or discretionary accruals (DACi t), then within each group, we further sort the stocks into another three equal-sized subgroups based on either the estimated coefficients (β) or the R2 from the comovement regressions. In Panel C and D, we first sort the firms using the residuals from the comovement regression and then sort them either by β or the R2 from the comovement regressions. The sample period is 1980 to 2005. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. Panel A: Sort by accruals and the market-wide accrual component (beta and R2) ap The second sort By Beta
ap By R2 ap
Low 0.262* (1.92)
0.244* (1.82)
Medium 0.163 (1.32)
0.174 (1.24)
Low Accruals (P1)
0.270*** (2.46)
High 0.385*** (2.76)
0.390*** (3.28)
High-Low 0.123 (0.87)
0.146 (1.13)
Low 0.108 (0.99)
-0.063 (-0.52)
Medium -0.057 (-0.50)
-0.017 (-0.15)
High Accruals (P3)
-0.010 (-0.11)
High -0.082 (-0.66)
0.050 (0.48)
High-Low -0.191 (1.54)
0.113 (1.01)
P1-P3 (p1-p3) for Low 0.154 (1.10)
0.307** (2.10)
(p1-p3) for Medium
0.220 (1.55)
0.191 (1.38)
0.280*** (2.81)
(p1-p3) for High 0.468*** (3.50)
0.340*** (2.78)
P1/High-P3/Low 0.277** (2.00)
0.453*** (3.39)
41
Panel B: Sort by discretionary accruals and the market-wide discretionary accrual component ap The second sort By Beta
ap By R2 ap
Low 0.186 (1.50)
0.135 (1.14)
Medium 0.183* (1.67)
0.271** (2.21)
Low Discretionary Accruals (P1)
0.261*** (2.72)
High 0.417*** (3.51)
0.375*** (3.27)
High-Low 0.231* (1.91)
0.240** (2.04)
Low -0.095 (-0.75)
0.013 (0.10)
Medium 0.024 (0.23)
0.013 (0.12)
High Discretionary Accruals (P3)
-0.012 (-0.12)
High 0.039 (0.31)
-0.061 (-0.52)
High-Low 0.135 (1.04)
1.098 (0.39)
P1-P3 (p1-p3) for Low 0.282** (2.29)
0.122 (0.99)
(p1-p3) for Medium
0.158 (1.59)
0.258** (2.20)
0.273*** (4.12)
(p1-p3) for High 0.378*** (3.11)
0.436*** (3.77)
P1/High-P3/Low 0.513*** (4.29)
0.362*** (3.08)
Panel C: Sort by accrual residuals and the market-wide accrual component (beta and R2) Ap The second sort By Beta
ap By R2 ap
Low 0.236* (1.94)
0.171 (1.47)
Medium 0.223* (1.88)
0.263* (1.95)
Low Accruals Residuals (P1)
0.300*** (3.10)
High 0.444*** (3.44)
0.464*** (4.09)
High-Low 0.208 (1.56)
0.293*** (2.43)
Low -0.011 (-0.09)
-0.041 (-0.32)
Medium -0.050 (-0.45)
-0.100 (-0.87)
High Accruals Residuals (P3)
-0.020 (-0.20)
High -0.003 (-0.02)
0.078 (0.63)
High-Low 0.008 (0.06)
0.119 (1.03)
P1-P3 (p1-p3) for Low 0.247** (2.01)
0.213 (1.62)
(p1-p3) for Medium
0.274*** (2.45)
0.362*** (2.86)
0.320*** (4.36)
(p1-p3) for High 0.447*** (3.38)
0.386*** (3.41)
P1/High-P3/Low 0.455*** (3.52)
0.506*** (3.96)
42
Panel D: Sort by discretionary accrual residuals and the market-wide discretionary accrual component (beta and R2) Ap The second sort By Beta
ap By R2 ap
Low 0.078 (0.61)
0.150 (1.21)
Medium 0.264** (2.29)
0.269** (2.26)
Low Discretionary Residual (P1)
0.242*** (2.48)
High 0.385*** (3.22)
0.306*** (2.72)
High-Low 0.308*** (2.69)
0.156 (1.31)
Low -0.186 (-1.51)
-0.011 (-0.09)
Medium 0.075 (0.65)
-0.067 (-0.58)
High Discretionary Residual (P3)
-0.033 (-0.33)
High 0.011 (0.09)
-0.020 (-0.16)
High-Low 0.197 (1.56)
-0.009 (0.07)
P1-P3 (p1-p3) for Low 0.264** (2.32)
0.161 (1.30)
(p1-p3) for Medium
0.189* (1.73)
0.336*** (2.97)
0.275*** (3.94)
(p1-p3) for High 0.374*** (3.01)
0.326*** (2.76)
P1/High-P3/Low 0.571*** (4.59)
0.317*** (2.93)
43
Figure 1 Monthly Cumulative Returns to Total Accrual based Factors This figure plots the monthly cumulative equal-weighted returns to the four different total accrual based factors: AC_factor, AC_COM, AC_COMR, and AC_RES (see Table 1 for definitions of those factors). The sample period is January 1980 to December 2005.
-50
0
50
100
150
200
250
198001198009198105198201198209198305198401198409198505198601198609198705198801198809198905199001199009199105199201199209199305199401199409199505199601199609199705199801199809199905200001200009200105200201200209200305200401200409200505200601
Ret
urn
in P
erce
ntag
e
AC_factor AC_COM AC_RES AC_COMR
44
Figure 2 Monthly Cumulative Returns to Discretionary Accrual based Factors This figure plots the monthly cumulative equal-weighted returns to the four different discretionary accrual based factors: DAC_factor, DAC_COM, DAC_COMR, and DAC_RES (see Table 1 for definitions of those factors). The sample period is January 1980 to December 2005.
-50
0
50
100
150
200
250
198001198006198011198104198109198202198207198212198305198310198403198408198501198506198511198604198609198702198707198712198805198810198903198908199001199006199011199104199109199202199207199212199305199310199403199408199501199506199511199604199609199702199707199712199805199810199903199908200001200006200011200104200109200202200207200212200305200310200403200408200501200506200511
Ret
urn
in P
erce
ntag
e
DAC_factor DAC_COM DAC_RES DAC_COMR