Accounting Accruals, Heterogeneous Investor beliefs, and Stock Returns
Emma Peng
An Yan
Meng Yan
Fordham University Gabelli Schools of Business
Oct 2015
Accounting Accruals, Heterogeneous Investor beliefs, and Stock Returns
Abstract: In the paper, we study how a firm’s accounting accruals affect the heterogeneity of
investor beliefs on the firm’s value and further affect the firm’s future stock returns. We
document three findings. First, we find that the level of the heterogeneity in investor beliefs on a
firm’s value is higher when the firm experiences a larger increase in its accounting accruals.
Second, we find that future stock returns following earnings announcement are lower when the
firm’s accounting accruals increases the heterogeneity of investor beliefs to a larger degree.
Finally, we also find that the effect of the accruals-induced heterogeneous investor beliefs on
future stock returns is more pronounced when short-sale constraints are more binding. Overall,
our empirical findings suggest that accounting accruals are a key determinant of the
heterogeneity of investor beliefs. They also suggest a channel of investor beliefs whereby
accruals affects future stock returns by affecting the heterogeneity of investor beliefs.
JEL Classification: G12; M41
Keywords: heterogeneous investor beliefs, accounting accruals, stock returns.
1
Accounting Accruals, Heterogeneous Investor beliefs, and Stock Returns
1.
Introduction
Investors have heterogeneous prior beliefs on a firm’s value. How the heterogeneity of
investor beliefs affects the valuation of the firm’s securities has been studied in depth in the
finance literature. This research dates back to Miller (1977) (and subsequently, Harrison and
Kreps (1978), Mayshar (1983), and Morris (1996)). Miller (1977) argues that, when investors
with heterogeneous beliefs are subject to short-sale constraints, stocks would sell at a premium
over their fundamental values. This is because short-sale constraints prevent pessimistic
investors from trading in the stock market so that stock prices only reflect the beliefs of
optimistic investors. Recently, Chen, Hong, and Stein (2002) and Diether, Malloy, and Scherbina
(2002) find empirical evidence supporting Miller’s predictions. However, it is still not well
understood what causes heterogeneous investor beliefs.
In this paper, we study one factor that could cause the heterogeneity of investor beliefs:
different interpretations of a firm’s accounting information in the presence of potential earnings
management. Specifically, we focus on accounting accruals. We study how the possible
management of accounting accruals affects the heterogeneity of investor beliefs. We also study
how the effect of accruals on investor beliefs could affect future stock returns. To the best of our
knowledge, our paper is the first to identify the impact of accounting accruals on the
heterogeneity of investor beliefs. It is also the first to study how this impact affects future stock
returns.
We first propose that high accounting accruals increase the heterogeneity of investor
beliefs on the firm value. The accrual process requires managers’ subjective estimates about
2
future events and these estimates cannot be objectively verified, thereby leaving managers
discretion to manipulate earnings through accruals. 1 Trustful investors would take the reported
accruals at face value while skeptical investors, concerned with the possibilities of earning
manipulation, would place a lower weight on the accrual component of earnings when valuing
the firm. In other words, investors’ different interpretations of the value implication of accruals
would cause heterogeneous beliefs on the firm’s value. When the firm reports a higher level of
accruals, investors would become more heterogeneous in their beliefs on the firm’s value. This is
the first hypothesis we test in the paper. 2
Next, we examine how the impact of accounting accruals on heterogeneous investor
beliefs could affect future stock returns. Following Miller (1977), we argue that the
heterogeneity of investor beliefs generated by the different interpretations of accounting accruals
would boost a firm’s contemporaneous stock price. Over time, as the uncertainty about the firm’s
future cash flows induced by accruals gradually resolves, the heterogeneity in investor beliefs on
the value implication of accruals will be reduced. The reduced heterogeneity will consequently
cause the firm’s equity value to converge to its fundamental value, resulting in a lower long-run
stock return. In other words, we propose an investor belief channel through which accounting
accruals could affect future stock returns. An increase in the level of accruals could increase the
heterogeneity of investor beliefs, which subsequently leads to a lower future stock return. The
higher the level of the accrual-induced heterogeneity is, the lower the future stock return is. This
is the second hypothesis we test in the paper.
1
Bernstein (1993) points out that the accrual system relies on “deferrals, allocations, and valuations, all of which
involve higher degree of subjectivity.” Francis and Krishnan (1999) suggest that accruals cannot be objectively
verified by auditors.
2
Here, we focus only on the income-inflating earnings management in our discussion. However, managers could
also manage earnings downward. We will discuss this possibility and its implication on hypothesis H1 in later
section.
3
Finally, we study how short-sale constraints play a role in the investor belief channel
proposed in hypothesis H2. In Miller’s (1977) framework, a key condition for heterogeneous
investor beliefs to affect stock pricing is that investors are subject to short-sale constraints. The
effect of heterogeneous investor beliefs on stock pricing is greater when short-sale constraints
are more binding. 3 Following Miller’s framework, we hypothesize that the effect of the accrualinduced heterogeneous investor beliefs on future stock returns is more pronounced when shortsale constraints are more binding. This is the third hypothesis we test in the paper.
A central variable in our test of the above three hypotheses is the level of investors’
heterogeneous beliefs. We follow the literature and use the dispersion in analysts’ earnings
forecasts to proxy for the degree of heterogeneous investor beliefs. A higher dispersion in analyst
forecasts indicates a higher level of heterogeneity in investor beliefs (see, e.g., Diether, Malloy,
and Scherbina (2002); Verardo (2009)). Using analyst dispersion as the heterogeneity variable,
we find evidence consistent with all three hypotheses. First, we find that financial analysts
disagree more on their earnings forecasts when accruals experience a larger increase from the
previous quarter. 4 This result is consistent with the notion that an increase in accruals induces
concerns on potential earnings management and consequently causes heterogeneous beliefs on
the firm’s value.
Second, we find that the lower future stock return experienced by a firm with increased
accruals is more pronounced if the firm faces a higher level of dispersion in analysts’ earnings
forecasts in the month following the announcement of increased accruals. We also show that this
result is unlikely to be driven by the common return predictors, such as size, book-to-market,
3
See Boehme, Danielsen, and Sorescu (2006), Sadka and Scherbina (2007), and Hirshleifer, Teoh, and Yu (2011)
for the empirical findings.
4
The majority of our empirical tests are based on the change in accruals rather than the level of accruals. A firm’s
use of accruals could be an outcome of certain firm characteristics (Chan, Chan, Jegadeesh and Lakonishok (2006)).
We use change in accruals to purge firm fixed effects. We will discuss this in detail in Section 3.2.
4
historical return, illiquidity, as well as the growth anomaly (Fairfield, Whisenant, and Yohn
(2003)) and the post-announcement earnings drift. These results suggest that accounting accruals
could affect future stock returns through the investor belief channel by affecting the
heterogeneity of investor beliefs, as proposed in our second hypothesis.
To test the third hypothesis, we use stock holdings by institutional investors and
Amihud’s (2002) illiquidity measure to proxy for how tightly short-sales constraints bind. Prior
studies show that the stocks with more institutional investor holdings and higher liquidity are
easier to short (Nagel (2005), Berkman, Dimitrov, Jain, Koch, and Tice (2009), Sadka and
Scherbina (2007), and Banerjee and Graveline (2012)). Using these two proxies, we find that the
accrual-induced heterogeneous investor beliefs affect future stock returns to a larger degree for
stocks with lower institutional investor holdings and for stocks with lower stock liquidity,
presumably those stocks facing tighter short-sale constraints.
We also run several other robustness tests. In the paper, we use a proprietary sample
consisting of firms that disclose net operating cash flows in their preliminary earnings
announcements. By using this proprietary sample, we ensure that investors are able to infer the
amount of accruals from earnings and operating cash flows at the earnings announcement date.
However, this sample is only a subset of the universe of firms, since many firms do not announce
operating cash flows at earnings announcements. To check whether or not our sample selectivity
affects our empirical results, we run Heckman’s (1979) selection model. Our results from the
selection model are consistent with our earlier results. Moreover, we focus on total accruals
instead of discretionary accruals in our main tests since sample firms have all information needed
to infer the amount of total accruals at the earnings announcement, but not necessarily
information to infer the amount of discretionary accruals. When we use the discretionary
5
accruals in our robustness checks, our inferences do not change. The results are also robust to
different sample compositions, different model specifications, and various stock return windows.
Overall, our results suggest that accounting accruals are a key determinant of the
heterogeneity of investor beliefs. They also suggest that accounting accruals could affect future
stock returns by affecting the heterogeneity of investor beliefs. These results extend the literature
on heterogeneous investor beliefs and stock pricing. As we discussed earlier, the literature was
set forth originally by Miller (1977). 5 However, the literature has not provided any insight on
whether and how potential manipulation of accounting accruals affects the heterogeneity of
investor beliefs. Our paper fills the void.
By linking the impact of accruals on investors’ heterogeneous beliefs to future stock
returns, our paper also extends the literature on the accrual anomaly. The accrual anomaly is first
documented by Sloan (1996), who shows that the stocks of high accrual firms earn negative
abnormal returns in the future. Sloan (1996) argues that the accrual anomaly occurs since
investors naïvely fixate on accounting earnings and overestimate the persistence of accruals. 6
Bradshaw, Richardson, and Sloan (2001) further show that sell-side analysts overestimate the
persistence of accruals and fail to anticipate the subsequent earnings declines for firms reporting
high accruals. Our paper identifies a different channel through which accruals could affect future
stock returns. We propose that an increase in accruals could cause lower future stock returns
because
it
increases
the
heterogeneity
of
investor
beliefs
regarding
firm
value
contemporaneously in the period of the increased accruals. Thus, unlike the fixation explanation,
5
Several papers incorporate Miller’s insight in more formal and refined models. For example, Scheinkman and
Xiong (2003) and Hong, Scheinkman, and Xiong (2006) further develop dynamic models with heterogeneous
beliefs and shorting constraints to study the joint behavior of volume and overpricing.
6
In recent years, alternative explanations on the accrual anomaly emerge in the literature. For instance, researchers
suggest that the accrual anomaly can be a special case of the growth anomaly (e.g., Fairfield et al. (2003)). Other
studies on the accrual anomaly include Hirshleifer, Hou, Teoh, and Zhang (2004), and Dechow, Richardson, and
Sloan (2008).
6
which focuses on investors’ average (naïve and biased) beliefs in response to the accruals
information, our paper focuses on the heterogeneity or the dispersion of investors’ beliefs. We
find that the negative stock return following an increase in accruals is related to a higher degree
of investors’ heterogeneous beliefs even after we control for signed forecast errors, presumably a
proxy for the average level of analyst beliefs as suggested by the fixation explanation. Thus, it is
our view that, while the consideration of the average investor beliefs is important in determining
the accrual anomaly, the heterogeneity in investor beliefs characterizing the stock market may be
equally (if not more) important. 7
The remainder of the paper is organized as follows. Section 2 develops the hypotheses
on accruals, the heterogeneity of investor beliefs, and ex-post stock returns. Section 3 describes
the sample selection and variable construction. Section 4 reports the results from our empirical
tests. Section 5 discusses the other potential explanations on our findings. Section 6 concludes.
2. Hypothesis Development
The literature on heterogeneous investor beliefs originates from the work of Miller (1977)
who considers two realities of the stock market. First, investors have heterogeneous beliefs
regarding a stock’s intrinsic value, and second, there exist short-sale constraints. He argues that
when pessimistic investors are prevented from selling short, stock prices reflect the beliefs of
optimistic investors and securities would sell at a premium over their fundamental values. When
the heterogeneity of investor beliefs on a stock’s value increases, the stock will be purchased by
investors with higher valuations and therefore is priced contemporaneously at a higher level. In
7
Our findings that accruals affect future stock returns through affecting the heterogeneity of investor beliefs are
based on the change in accruals, while the accrual anomaly literature is mostly based on the level of accruals. Thus,
our findings only suggest that the heterogeneity of investor beliefs can explain the part of the accrual anomaly that is
caused by the change in accruals. Nevertheless, our paper still complements the literature by showing that the
heterogeneity in investor beliefs is another important channel in explaining the accrual-driven future stock returns.
7
this paper, we extend this heterogeneous belief theory by studying the effect of accounting
accruals on the heterogeneity of investor beliefs and further on future stock returns. 8
Accounting accruals include revenues and expenses recognized in a period of time either
before or after when cash is received and paid. For instance, managers can advance recognition
of revenue with credit sales, a type of income-increasing accruals. The credit sales will be
counted towards current earnings although cash will not be received until later periods. As a
result, credit sales increase reported earnings but have no effect on current cash flows. On the
other hand, depreciation expenses, a type of income-decreasing accruals that record the
allocation of the acquisition cost of plant assets, are deducted from revenue, although
depreciation entails no cash outflows. In this case, depreciation expenses decrease reported
earnings without decreasing current cash flow.
The recognition of accruals relies on managerial judgments and assumptions. 9 Thus,
accruals are difficult to be completely verified and need investors’ discretion to interpret. We
argue that larger increase in accruals lead to a higher level of the heterogeneity in investor beliefs.
For instance, an increase in accounting accruals could result from an increase in incomeincreasing earnings management with the purpose of beating earnings thresholds (Graham,
Harvey and Rajgopal (2005)). Prior literature shows that managers could use income-inflating
accruals management when they are in anticipation of certain corporate events (e.g., Teoh,
8
Researchers also examined the effect of the heterogeneity of investor beliefs beyond the stock market. For instance,
Janus, Jinjarak, and Uruyos (2013) suggest that agents’ heterogeneous beliefs regarding sovereign default risk is the
reason they trade on credit default swaps (CDS). Evidence from Zhang and Zhang (2013) indicates that one
contributing factor that the CDS market responds to earnings surprises more efficiently than the stock market is the
absence of short-sale restrictions in the derivatives market.
9
For instance, companies making credit sales are expected to recognize bad debts expense in each accounting period,
but how much to recognize depends on managers’ estimates about future uncollectible accounts. In another example,
for a long-term contract, managers can choose to recognize revenue when the contract is completed, or in interim
periods based on the progress toward completion. Further judgment is required in terms of how to measure progress
at a particular interim date.
8
Welch, and Wong (1998a and 1998b)). Concerned with these possibilities, the skeptical investors
would associate higher accruals with income-inflating earnings management and place a lower
weight on accruals when valuing the firm. 10 In contrast, the trustful investors could perceive
accruals as a signal of managers’ private information about the firm’s future cash flows and take
accruals at face value when valuing the firm. In other words, the skeptical investors would
disagree more with the trustful investors on the value implication of accruals when accruals
increase to a larger extent. Put shortly, we expect that an increase in accruals would increase the
heterogeneity of investor beliefs among investors. This is our first hypothesis (H1) to test.
Next, we examine whether the impact of accruals on heterogeneous investor beliefs could
affect future stock returns. As discussed earlier, investors could be more heterogeneous in their
valuations of a firm’s stock when the firm announces a higher level of accruals. According to
Miller (1977), this higher level of the heterogeneity of investor beliefs would cause the firm’s
stock to be valued contemporaneously at a higher level. Over time, as the uncertainty about the
firm’s future economic events associated with the accruals gradually disappears, the
heterogeneity in investor beliefs will decrease as well. Consequently, the firm’s equity value will
converge to its fundamental value, causing a negative ex-post future stock return. In this way, the
high level of investors’ heterogeneous beliefs caused by high accruals is followed by a negative
future stock return. In consideration of the above argument, we predict that the negative relation
between future stock returns and accruals is more pronounced if accruals contemporaneously
cause a higher level of heterogeneous investor beliefs. This is our second hypothesis (H2) to test.
10
For instance, firms can recognize too little bad-debt reserves. They can reduce the amount of depreciation expense
by modify depreciation life and modify method used for depreciation. They can also record sales for products not
shipped yet, or time the recognition of realized or unrealized gains or losses on investment (Nelson, Elliott, and
Tarpley 2003).
9
Finally, we examine whether or not the accrual-induced investor belief channel as
proposed in H2 is more effective when short-sale constraints are more binding. One necessary
condition in Miller’s (1977) framework is the existence of short-sale constraints. A high level of
the heterogeneity of investor beliefs would cause a high level of contemporaneous price and be
followed by a low ex-post future stock return only when the existence of short-sale constraints
prevents pessimistic investors from selling short the high-heterogeneity stock. The relation
between the heterogeneity of investor beliefs and future stock returns would be more pronounced
if short-sale constraints are more binding. Thus, our third hypothesis (H3) is that the investor
belief channel, i.e., the effect of accruals on future stock returns through affecting the
heterogeneity of investor beliefs, is more pronounced if the stock faces more binding short-sale
constraints.
3. Sample Selection and Variable Construction
3.1. Sample Selection
We obtain a proprietary database of firms that voluntarily disclose operating cash flows
in their preliminary earnings announcements. 11 Our empirical studies focus on investors’
responses to the accrual information subsequent to the earnings announcement date. Using this
proprietary sample ensures that investors have sufficient information on earnings and operating
cash flows to infer firms’ accruals amount at the earnings announcement date. 12
11
We thank Joshua Livnat for providing us with the proprietary database.
For firms without such voluntary disclosures, investors have to find out about the amount of operating cash flows
and hence the amount of accruals based on quarterly filings. Quarterly fillings are usually filed within a month after
earnings announcements (Easton and Zmijiewski, 1993). In an unreported robustness check with the whole universe
of firms, we assume that firms file their 10-Q (K) reports within two month subsequent to the fiscal quarter end. We
rerun all tests with the event windows on future stock returns starting from 60 days subsequent to the fiscal quarter
end. The results based on this new sample are qualitatively the same. They are available upon request from readers.
12
10
Our proprietary sample covers years 1994 to 2007. We extract stock prices from the
Center for Research in Securities Prices (CRSP), and financial analysts’ forecasts from I/B/E/S.
We exclude utilities and financial services firms (two-digit SIC codes 49 and 60-67). We exclude
firms with stock prices less than $1 per share. We also exclude firms with no information
available on I/B/E/S. Our final sample consists of 1,116 firms and 9,569 firm-quarters. In the
following empirical analysis, there may be sample attrition due to incomplete information from
missing lagged variables. Table 1 reports the annual breakdown of our sample as well as the
average and the median market capitalization every year.
3.2. Measures of Accruals
We follow the literature and calculate total accruals (ACCA) as firms’ quarterly net
income before extraordinary items and discontinued operations minus quarterly net operating
cash flows, scaled by the average total assets during the quarter. We calculate the change in total
accruals (ΔACCA) as the change from the previous quarter q-1 to the current quarter q.
In the paper, we focus mainly on the change in total accruals rather than the level of total
accruals in an attempt to purge firm fixed effects. First, the effect of accruals on the
heterogeneity of investor beliefs could vary among various firms. For example, consider a firm
with a high reputation among investors on its infrequent use of earnings management and
another firm with a bad reputation on its frequent use of earnings management. The highreputation firm with a high level of accounting accruals could still enjoy a lower level of
heterogeneity of investor beliefs compared to a firm with a bad reputation and a low level of
accruals. Second, the use of accruals could be an outcome of certain firm characteristics. For
example, high level of accruals may be “a reflection of strong past growth in sales” (Chan, Chan,
11
Jegadeesh, and Lakonishok (2006)). In unreported results, we also find that small firms, growth
firms, firms with high prior operating performance, and firms with high prior stock return
performance are more likely to have high accruals (see, e.g., Fairfield et al. (2003)). In an effort
to purge the above and the other unobserved firm fixed effects, we focus on the change in total
accruals ΔACCA rather than the level of total accruals ACCA in our empirical tests.
We also calculate change in discretionary accruals in the paper based on our proprietary
database. In particular, we use the modified Jones (1991) model to calculate discretionary
accruals (DACC):
ACCAq
Assetsq −1
= α 0 + β1
∆Salesq − ∆ Re cq
Assetsq −1
+ β2
PPEq
Assetsq −1
+ εq
(1)
where q indexes for quarters, ACCA is total accruals, Assets is the book value of assets, ΔSales is
current sales less prior-quarter sales, ΔRec is current accounts receivables less prior-quarter
accounts receivables, and PPE is gross property, plant and equipment. We run the above
regression for each industry quarter with at least 10 observations, where the industries are
defined by two-digit SIC codes. We calculate discretionary accruals (DACC) as the residuals
from equation (1). We calculate the change in discretionary accruals (ΔDACC) as the change
from the previous quarter q-1 to the current quarter q.
In our empirical tests, we will primarily focus on the change in total accruals rather than
the change in discretionary accruals. We do so to ensure that investors have all information to
infer the accrual amount at the earnings announcement day. This requirement is especially
important in our study on stock returns since our event window of stock returns starts from the
earnings announcement date. Due to this consideration, we use the change in total accruals to test
12
our hypotheses, while we use the change in discretionary accruals only in our robustness
checks. 13
3.3. Proxies for Heterogeneous Investor Beliefs
We proxy for the degree of heterogeneous investor beliefs on a firm’s value by the
dispersion of financial analysts’ forecasts on the firm’s one-year-ahead earnings (see Diether,
Malloy, and Scherbina (2002)). 14 The higher the dispersion in analysts’ earnings forecasts, the
higher the level of heterogeneity in investor beliefs. We calculate analyst forecast dispersion
(Dispersion) as the standard deviation of analysts’ earnings forecasts in the month subsequent to
the earnings announcement date, scaled by the absolute value of the firm’s actual earnings. We
code Dispersion as missing if there are less than three financial analysts covering the firm.
In the main tests, we focus on the level of analyst dispersion and study how the change in
accruals affects analyst dispersion (and further future stock returns). In several robustness checks,
we also examine the change in analyst dispersion and study how the change in accruals affects
the change in analyst dispersion. It is worth noting that with the control of lagged values, the
regression of the change in analyst dispersion against the change in accruals is equivalent to the
regression of the level of analyst dispersion against the level of accruals.
3.4. Measures of Future Stock Returns
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In another robustness check, we also calculate performance-adjusted discretionary accruals. We follow Kothari,
Leone, and Wasley (2005) to adjust discretionary accruals by matching firm-years annually on industry and return
on assets. We calculate performance-adjusted discretionary accruals as the difference between a firm’s DACC and
the corresponding DACC for the matched firm. The results based on performance-adjusted discretionary accruals are
similar to those based on DACC. Due to space constraints, we choose not to report the results in the paper. These
results are available upon request from readers.
14
The data we use in the calculation of earnings forecasts come from the Summary History file of I/B/E/S. Diether
et al. (2002) report a rounding bias due to stock splits, but they find that the bias does not affect their results.
13
We measure future stock returns in various trading day event windows. We first measure
two-month, three-month, and six-month stock returns starting from the earnings announcement
date: [0, 42], [0, 63], and [0, 126], where 0 denotes the earnings announcement date, 42 denotes
the 42nd trading day, i.e., two months, subsequent to the earnings announcement date, etc. We
also measure future stock returns excluding the period around the earnings announcement date:
[6, 42], [6, 63], and [6, 126], where 6 denotes the sixth trading day subsequent to the earnings
announcement date, i.e., the day after the first week of earnings announcement. We study these
three trading day windows to ensure that our results are not driven by the announcement period
return.
Finally, we also measure future stock returns after financial analysts report their earnings
forecasts to I/B/E/S: [a, 42], [a, 63], and [a, 126], where ‘a’ denotes the date subsequent to the
first reporting date of analysts’ forecasts after earnings are announced. One potential concern for
the windows starting from day 0 or day 6 is that these windows could overlap with the
measurement window of analyst dispersion, which is in the first month right after earnings
announcement. This potential overlapping would cause ambiguity on the causality between
analyst dispersion and stock returns. Specifically, this ambiguity could arise in the case of
overlapping windows, since analysts’ disagreement on their earnings forecasts could cause a
certain pattern of stock returns, and a certain pattern of stock returns could also cause analysts to
disagree with each other. In the paper, we intend to study how the accrual-induced analyst
dispersion affects stock returns in the future. Thus, to ensure the causality goes from analyst
dispersion to stock returns and not the other way around, we also measure future stock returns
starting subsequent to the report date of analysts’ earnings forecasts.
14
3.5. Measures of Short-sale Constraints
We use two proxies to capture how tightly short-sale constraints bind. The first one is the
fraction of stock holdings by institutional investors. Institutional investors lend shares in the
stock lending markets, from which short-sellers borrow to sell short. In contrast, retail investors
do not directly participate in stock lending. Thus, stocks with low institutional investor
ownership are hard to be located in the stock lending market and thus hard to sell short (Nagel
(2005) and Berkman et al. (2009)). The second proxy for short-sale constraints is the level of
stock illiquidity (Amihud (2002)). Stock illiquidity (Illiquidity) is calculated as the ratio of the
absolute value of daily return to the value of daily trading volume, averaged in the quarter prior
to day -6. Prior literature suggests that illiquid stocks are more costly to sell short (see, Sadka
and Scherbina (2007) and Banerjee and Graveline (2012)).
3.6. Construction of Other Variables
We calculate the following control variables. Firm size (Size) is the log of the market
value of equity at the end of the previous quarter, i.e., quarter q-1. Book-to-market ratio (BM) is
the ratio of the book value to the market value of equity at the end of quarter q-1. Historical stock
return (Historical Return) is the historical cumulative stock return in the three months prior to
announcement date. Stock beta (Beta) is estimated based on a period of 200 days ending 6 days
prior to the earnings announcement date. We will control for Size, BM, Beta, Historical Return,
as well as Illiquidity, in our empirical studies since these variables are the common return
predictors as documented in the literature.
To control for a firm’s growth potential, we use both book-to-market ratio (BM) and
growth in long-term net operating assets (GrLTNOA). We calculate GrLTNOA as the growth in
15
non-accrual net operating assets scaled by the average total assets (Fairfield et al. (2003)). We
also calculate two earnings variables. We calculate standardized unexpected earnings (SUE) as
(Eq – Eq-4 – cq)/sq, where Eq and Eq-4 are earnings in the current quarter and in the quarter a year
ago, respectively; and cq and sq are the mean and standard deviation, respectively, of (Eq – Eq−4)
over the preceding eight quarters. We calculate return on assets (ROA) as the ratio of net income
to total assets in quarter q-1. Finally, we calculate two variables based on the information from
I/B/E/S. We calculate the number of analysts' one-year-ahead earnings forecasts reported in
I/B/E/S (NForecast). We also calculate signed forecast error (Error) as the difference between
the average earnings forecast and the actual earnings per share, scaled by the absolute value of
the actual earnings per share. It is worth noting that our forecast error measure is based on the
signed difference between the forecasted EPS and the actual EPS, rather than the unsigned
difference as in many previous studies. Our results would remain qualitatively the same if we use
unsigned forecast error. In the paper, we choose to use signed forecast error since it better
proxies for the average of analyst beliefs. If analysts on average are more optimistic, signed
forecast error would be more positive. If analysts on average are more pessimistic, signed
forecast error would be more negative. Table 2 provides the sample statistics on the key variables
in our study. To minimize the influence of outliers, we winsorize all variables at the top and
bottom 1 percent of the distribution.
4. Empirical Findings
In this section, we study the impacts of accruals on the heterogeneity of investor beliefs
and further on future stock returns by testing hypotheses H1-H3.
16
4.1. Accruals and Investors’ Heterogeneous Beliefs
Our first hypothesis (H1) is that an increase in accruals causes a higher level of
heterogeneous beliefs among investors on the value of the firm. We test H1 by running the
following regression:
Dispersion = α0 + α1ΔACCA + α2 Control variables + ε.
(2)
In regression (2), the dependent variable is Dispersion, our proxy for the level of
heterogeneous beliefs. We measure Dispersion based on analysts’ forecasts in the first month
subsequent to the earnings announcement date. In doing so, we ensure the causality is from
ΔACCA to Dispersion, not the other way around. The control variables consist of ROA, SUE,
GrLTNOA, Error, NForecast, Size, BM, Beta, Illiquidity, and Historical Return. Both number of
analysts following (NForecast) and Forecast error (Error) are measured in the current quarter q.
We control for NForecast since many studies show that analyst dispersion is affected by the
number of analyst following. We control for Error to purge the effect of the average level of
analyst beliefs on investor’s heterogeneous beliefs. Return on assets (ROA) and earnings surprise
(SUE) are measured in the current quarter q as well. We use these two variables to control for the
effect of reported earnings on investors’ heterogeneous beliefs. Finally, we control for growth in
long-term net operating assets (GrLTNOA) and other return predictors (BM, Beta, Illiquidity, and
Historical Return) to be consistent with our controls in the later regressions on stock returns.
According to hypothesis H1, we expect α1 to be positive.
We try various econometric techniques for regression (2) to ensure the robustness of our
results. In particular, we run ordinary least square regressions (OLS), Fama-MacBeth regressions,
and fixed effect regressions. In OLS regressions, we include year dummies to control for year
effects. We also allow correlated residuals within each firm in all OLS regressions. Significance
17
tests are conducted based on heteroskedasticity-consistent standard errors following HuberWhite procedure. We use Fama-MacBeth regressions because they provide standard errors
corrected for cross-sectional correlation. In particular, we first run separate regressions for each
year, and then average the regression coefficients across years as in Fama and MacBeth (1973)
and estimate the statistical inference based on the Newey-West standard errors. Finally, we run
fixed effects models to control for stable firm attributes that cause autocorrelation.
We report the results in Table 3. In columns (1) to (3), we report the results from FamaMacBeth regressions. We first control for the two earnings variables ROA and SUE in column
(1), followed by the regressions gradually adding more controls in columns (2) and (3). In
columns (4) and (5), we report results from OLS regressions without and with time dummies,
respectively. Finally, in column (6), we report the results from a fixed-effect regression.
As can be seen, α1, the coefficient of ΔACCA, is positive in all six columns. It is
significant at 1% in five of the six columns and significant at 5% in the other column. These
results in Table 3 show that an increase in accruals is associated with a higher level of analyst
dispersion. They also show that the effect of accruals on analyst dispersion is incremental to the
earnings effect, i.e., the effect of the reported earnings on analyst dispersion. Overall, our results
support hypothesis H1. They suggest that an increase in accruals causes investors to be more
heterogeneous in their beliefs on the value of the firm. 15
4.2. Robustness Checks on Accruals and Investors’ Heterogeneous Beliefs
We run four robustness tests. First, we run regressions against the change in discretionary
accruals (ΔDACC) rather than the change in total accruals (ΔACCA). As discussed earlier, we use
15
We note that omitted variables could affect heterogeneity in investor beliefs. To the extent that we do not control
for all determinants of belief divergence in the Table 3 tests, correlated omitted variables could bias the results.
18
the change in total accruals in our main tests, since investors can infer the value of the variable at
the earnings announcement date for the firms in our proprietary database. To demonstrate the
robustness of our results, we also use discretionary accruals here. We present the regression
based on ΔDACC in Panel A of Table 4, with the specifications similar to those in Table 3. As
can be seen, the coefficients of ΔDACC are positive and significant at the 1% level in all
columns. These results support hypothesis H1 as well.
In the second robustness check, we run regressions on the change in analyst dispersion,
∆Dispersion, rather than on the level of dispersion as in Table 3. In these regressions where the
dependent variable is ∆Dispersion, we choose to control for the change variables ∆Error and
∆NForecast rather than the level variables Error and NForecast. In some regressions, we also
control for Lagged ACCA (or Lagged DACC), Lagged Dispersion, and Lagged Error. The other
control variables are the same as in regression (2). We report the results from this robustness
check in Panel B of Table 4. In the first four columns, the accrual variable is the change in total
accruals (ΔACCA). In the next four columns, it is the change in discretionary accruals (ΔDACC).
For each accrual variable, we run regressions with the control variables gradually included. For
all the regression specifications, we run Fama-MacBeth regressions. As predicted, α1, the
coefficient of ΔACCA or ΔDACC, remains positive and significant in all columns. The evidence
suggests that our results on the positive relation between the change in accruals and analyst
dispersion are robust to the alterative change specification on analyst dispersion. Also as we
discussed earlier, the specification of regressing ∆Dispersion against ΔACCA (or ΔDACC) and
Lagged ACCA (or Lagged DACC) is equivalent to the specification of regressing Dispersion
against ACCA (or DACC), all level variables.
19
In the third robustness check, we address the concern of sample selectivity. Our sample
consists of the firms disclosing both the earnings and the operating cash flow information at the
earnings announcement date. However, many firms do not report the operating cash flow
information at the earnings announcement date. Thus, our sample is only a subset of the universe
of Compustat firms. If our sample is not a truly random sample, then the estimates from the
above regressions could be biased. To address the potential sample selection concern, we
estimate Heckman's (1979) selection model. The Heckman selection model consists of a
selection equation and a dispersion equation. To estimate the selection equation, we run a probit
model on whether or not a firm reports the operating cash flow information at the earnings
announcement date. The sample in the estimation of the selection equation consists of all firms
that are covered by Compustat and I/B/E/S. The independent variables in the selection equation
include ACCAq-1, ACCAq-2 (or DACCq-1 and DACCq-2 in the case of DACC as the accrual
variable), lagged Error, lagged NForecast, lagged Beta, lagged Size, lagged Illiquidity, lagged
Historical Return, lagged capital expenditures scaled by assets, and lagged stock trading turnover.
The sample in the estimation of the dispersion equation consists of the firms disclosing both the
earnings and the cash flow information at the earnings announcement date. The specification of
the dispersion equation is the same as in the previous regressions.
We report the results from the Heckman selection model in Panel C of Table 4. Due to
space constraint, we report only the results on the dispersion equation. The dependent variable in
the first five columns is the level of analyst dispersion (Dispersion); and it is the change in
analyst dispersion (∆Dispersion) in columns (6) to (9). For each analyst dispersion variable, we
first run regressions against ΔACCA, followed by regressions against ΔDACC. In general, the
results from the Heckman model are similar to those reported in the previous tables. The
20
coefficients of ΔACCA and ΔDACC are positive. They are also significant at either 1% or the 5%
level in all columns. Thus, it is evident that our results on accruals and analyst dispersion are
unlikely to be driven by the factors that cause the selectivity of our sample.
4.3. Income-inflating versus Income-deflating Earnings Management
Both increases in income-inflating accruals manipulation and decreases in incomedeflating accruals manipulation can give rise to increases in accruals. Our earlier argument on
the relation between accruals and the heterogeneity of investor beliefs focuses only on the
income-inflating earnings management. This focus is based on an assumption that on average,
managers face more pressures to boost reported earnings to meet the market’s expectations than
to defer current earnings to the future (Chan, Chan, Jegadeesh, and Lakonishok 2006). 16
Consequently, investors are more concerned with income-inflating manipulation than with
income-deflating manipulation. Our test results also confirm that concern with income-inflating
manipulation dominates the relation between accruals and the heterogeneity of investor beliefs.
However, investors are probably aware that managers also manage accruals downward to deflate
the current income, in order to create cookie jar reserves, to minimize political costs, or to
depress share prices. 17 If skeptical investors have been concerned about possibility of incomedeflating earnings management, would the positive relation between accruals and the
heterogeneity of investor beliefs be weakened?
To understand the implication of concerns with income-deflating manipulation, we study
the relation between the change in accruals and analyst dispersion in subsamples with various
16
Consistently, Nelson, Elliott, and Tarpley (2003) show more incidences of the income-increasing earnings
management than the income-decreasing earnings management.
17
For example, Gong, Louis, and Song (2008) document evidence that managers use the income-deflating earnings
management to depress share prices prior to stock repurchases.
21
levels of ∆ACCA. First, we create a subsample of high ΔACCA (consisting of firms with ΔACCA
higher than the sample median) and a subsample of low ΔACCA (consisting of firms with
ΔACCA higher than the sample median). Firms in these two subsamples have either increases or
modest decreases in accruals, and investors are mainly concerned about income-inflating
accruals manipulation. As a result, we expect strong positive relation between accruals and
dispersion. Next, we create subsamples of firms with ΔACCA in the bottom 25% and bottom 10%
of the sample distribution, respectively. We are interested in the extreme accruals decreases
because it is where we expect to find the most concern with income-deflating accruals
manipulation. Specifically, some suspicious investors would interpret a substantial accruals
decrease as increased level of income-deflating accruals manipulation and disagree more with
the trustful investors on the value implication of accruals, predicting a negative relation between
increases in accruals and the heterogeneity of investor beliefs. On the other hand, those
suspicious investors mainly concerned with income-increasing would interpret the accrual
decreases as reflecting large decreases in income-increasing earnings management and disagree
less with the trustful investors, which predicts a positive relation. The two effects would offset
each other, so the positive relation between accruals change and the heterogeneity of investor
beliefs would be at least weakened.
We present the results from this robustness check in Table 5. The coefficient of ΔACCA
is positive and significant in both columns (1) and (2), when we focus on accruals increases or
slight decreases. As we move onto the substantial accruals decrease, the coefficient of ΔACCA is
still positive in column (3) but statistically insignificant. It is negative and insignificant in
column (4). The results in (3) and (4) are consistent with the increased concern among investors
22
with the income-deflating earnings management and the consequent offsetting effect from the
income-deflating and the income-inflating earnings management.
In columns (5) – (8) of Table 5, we use the similar subsamples as in columns (1) – (4) but
with ΔDACC as the accrual variable. The coefficients of ΔDACC demonstrate a similar pattern as
the coefficients of ΔACCA. Overall, our results in Table 5 suggest that the positive relation
between the change in accruals and analyst dispersion holds for most scenarios of accrual
changes because investors are mostly concerned about managers using accruals to boost earnings.
4.4. Accruals, Investors’ Heterogeneous Beliefs, and Future Stock Returns
In hypothesis H2, we predict a negative future stock return following an increase in
accruals. We also predict that the negative relation between future stock returns and increased
accruals is more pronounced if the increase in accruals causes a higher level of heterogeneous
investor beliefs. We run the following regression to test this hypothesis:
Ret = β0 + β1ΔACCA + β2Dispersion +β3ΔACCA×
Dispersion + β4 Control variables + ε.
(3)
The dependent variable in regression (3) is future stock return (Ret). We first measure
future stock return in two trading day windows: [0, 63] and [6, 63], starting from either the
earnings announcement date or one week after the earnings announcement date. However, as we
discussed earlier, these two stock return windows could overlap in month 1 with the
measurement window of our analyst dispersion variable. To eliminate this overlapping, we also
measure future stock returns starting after the first report date of analysts’ earnings forecasts, in
window [a, 63]. By using window [a, 63], we ensure that the causality is from analyst dispersion
23
to ex-post stock returns. In the paper, we use all three event windows for future stock returns to
demonstrate the robustness of our results.
In regression (3), we interact Dispersion, the proxy for the heterogeneity of investor
beliefs, with ΔACCA. The control variables include the well-documented return predictors: Size,
BM, Beta, Historical Return, and Illiquidity. We also control for the earnings variable SUE, ROA,
and GrLTNOA to control for other stock anomalies such as the post-earnings announcement drift
and the growth anomaly. Finally, we control for Error, as well as NForecast, to purge the effect
from average analyst beliefs (as implied by the fixation argument), so that we can focus on the
effect from the heterogeneity of analyst forecasts. According to hypothesis H2, we expect the
coefficient of the interaction term ΔACCA × Dispersion to be negative.
We present the results in Table 6, with the first three columns based on future stock
returns in window [0, 63], the next three columns based on future stock returns in window [6, 63],
and the last three columns based on future stock returns in window [a, 63]. In columns (1), (4),
and (7), we first run Fama-MacBeth regressions on future stock returns against ΔACCA. As can
be seen, the coefficients of ΔACCA in these three columns are negative and significant. These
results show that an increase in accruals is followed by lower stock returns in the future. They
are consistent with the previous findings in the literature on the accrual anomaly.
In columns (2), (5), (8), we report results with the interaction term ΔACCA × Dispersion
as one of the independent variables in the Fama-MacBeth regressions. The coefficients of the
interaction term are negative and significant in all three columns. In columns (3), (6), and (9), we
further present the results based on OLS regressions with year dummies as additional control
variables. Again, the coefficients of the interaction term are negative and they are significant (at
either the 1% or the 5% level).
24
Overall, our results in Table 6 show that the negative relation between an increase in
accruals and future stock returns is more pronounced if financial analysts disagree more with one
another in the month following the increase in accruals. These results do not seem to be driven
by the predictive powers of the other common return predictors, such as firm size, historical
return, illiquidity, and the difference between value and glamour stocks. They are also robust to
different econometric techniques and different measurement windows of stock returns. Thus, our
results are consistent with hypothesis H2, suggesting that the stock price reversal following an
increase in accruals is more pronounced when the heterogeneity of investor beliefs increases to a
larger degree in response to the increase in accruals. In other words, our results suggest a channel
of investor beliefs on the pricing effect of accounting accruals.
4.5. Robustness Checks on Accruals, Heterogeneous Beliefs, and Future Stock Returns
We run several robustness checks on the investor belief channel. First, we address the
concern on the potential sample selection bias by running the Heckman selection model. The
Heckman selection model consists of a selection equation and a return equation. The selection
equation is the same as that discussed in Section 4.2 and the return equation is similar to that
reported in Table 6. We report the results in Table 7. To conserve space, we only report the
results from the return equation. In columns (1) and (2), we report results with future stock
returns measured in window [0, 63]; in columns (3) and (4), the return window is [6, 63]; and in
columns (5) and (6), the return window is [a, 63]. For each future stock return window, we run
regressions with control variables introduced gradually. As can be seen, the coefficients of the
interaction variable between ΔACCA and Dispersion are negative and highly significant in all
columns. These results support hypothesis H2. They also show that our results on analyst
25
dispersion, the change in accruals, and future stock returns are unlikely to be driven by the
factors that cause the selectivity of our sample.
In the second robustness check, we use discretionary accruals as the accrual measure. The
specification of the regression is similar to that of regression (3). Similar to the earlier results, the
coefficients of the interaction term, ΔDACC × Dispersion, are negative and significant in all six
columns, for all three stock return event windows and for both Fama-MacBeth and OLS
regressions. These results again provide support to hypothesis H2.
In the third robustness check, we run regression (3) in two subsamples: the subsample
with a high level of analyst dispersion and the subsample with a low level of dispersion. We
include in the high-dispersion subsample those firms with analyst dispersion above the median of
the whole sample. We include in the low-dispersion subsample those firms with analyst
dispersion below the sample median. As we discussed earlier, if the investor belief channel on
the pricing effect of accruals is consistent with Miller’s (1977) framework, then we expect the
channel to be stronger in the subsample of high analyst dispersion, compared to the subsample of
low analyst dispersion.
We present the results based on these two subsamples in Panel C of Table 7, with the first
three columns based on the high-dispersion subsample and the latter three columns based on the
low-dispersion subsample. As can be seen, the coefficient of the interaction variable, ΔACCA ×
Dispersion, is negative and significant only in the high-dispersion subsample. It is generally
insignificant in the low-dispersion subsample. Thus, our results suggest that the investor belief
channel as hypothesized in H2 is more effective for the high-heterogeneity firms than for the
low- heterogeneity firms. They are also consistent with Miller’s framework on the relation
between the heterogeneity of investor beliefs and stock pricing.
26
In the fourth robustness check, we use the change in analyst dispersion, ∆Dispersion,
rather than the level of dispersion to proxy for the heterogeneity of investor beliefs. In particular,
we regress future stock return against ΔACCA, ΔDispersion, the interaction term between
ΔACCA and ΔDispersion, and control variables. The control variables are mostly the same as
those in the regressions presented in Table 6. The only exception is that we also include both
lagged Dispersion and the interaction term between ΔACCA and Lagged Dispersion as additional
control variables. We do so to ensure that the effect of ΔACCA × ΔDispersion on future stock
returns is through analyst dispersion in the current quarter rather than analyst dispersion in the
previous quarter. From hypothesis H2, we expect the coefficient of ΔACCA × ΔDispersion to be
negative.
We present the results in Panel D of Table 7. The first two columns are based on future
stock returns measured in window [0, 63], the next two columns are based on window [6, 63],
and the last two columns are based on window [a, 63]. For each future stock return, we first run
Fama-MacBeth regressions, followed by OLS regressions with year dummies as additional
control variables. As predicted, the coefficients of ΔACCA × ΔDispersion are negative and
significant in all six columns. Thus, our earlier results presented in Table 6 are robust to the
alternative change specification on analyst dispersion.
In the fifth robustness check, we add additional control variables to make sure our
findings are not driven by alternative explanations. It is possible that earnings surprise could
increase the heterogeneity of investor beliefs and consequently affect future stock returns. In
consideration of this possibility, we include the interaction term between ∆ACCA and SUE as an
additional independent variable to control for the effect of earnings surprise on future stock
returns. We further control for the interaction term between ∆ACCA and GrLTNOA. Since
27
earnings growth is often associated with increases in accruals, controlling for ΔACCA ×
GrLTNOA ensures that our results are not simply a special case of the growth anomaly as in
Fairfield et al. (2003). Finally, the fixation explanation in the accounting literature attributes the
relation between accruals and future stock returns (i.e., the accrual anomaly) to investors’ overly
optimistic reaction to accruals. In the paper, we use signed forecast error (Error) to proxy for the
average belief among all market participants. We include as independent variables both Error
and the interaction term between ΔACCA and Error to control for the fixation explanation.
We present the results with these additional controls in Panle E of Table 7. We gradually
introduce the three interaction variables, ΔACCA × SUE, ΔACCA × GrLTNOA, and ΔACCA ×
Error. As can be seen, the coefficient of the interaction variable between ΔACCA and Dispersion
(ΔACCA × Dispersion) remains negative and highly significant with all these new controls.
These results demonstrate that our findings on analyst dispersion, accruals, and future stock
returns are unlikely to be driven by the fixation explanation, the earnings effect, or the growth
anomaly.
In the final robustness check, we run Fama-MacBeth regressions with the alternative
measurement windows for future stock returns. In Table 6 and Panels A through E of Table 7,
we report results based on event windows ending at the third month subsequent to the earnings
announcement date. Here, we measure future stock returns in the alternative windows that end at
either the second month or the sixth month subsequent to the earnings announcement date: [0,
42], [6, 42], [a, 42], [0, 126], [6, 126], and [a, 126]. We present the results in Panel F of Table 7.
We find that the coefficient of the variable interacting between Dispersion and ΔACCA is
negative and significant across all event windows. These results support hypothesis H2 as well.
28
4.6. The Role of Short-sale Constraints
In hypothesis H3, we predict that the investor belief channel as hypothesized in H2 is
stronger for firms facing a higher degree of short-selling constraints. To test hypothesis H3, we
use two proxies for the degree of short-sale constraints: institutional investor holdings and
Amihud’s (2002) illiquidity measure. We expect the investor belief channel to be stronger for
stocks with low institutional investor holdings and for illiquid stocks.
First, we divide the sample into the subsamples with high and low institutional investor
holdings based on the level of institutional holdings at the end of the previous quarter. We
include in the subsample with high (low) institutional holdings those firms with the level of
institutional holdings above (below) the median level of the whole sample. We run regression (3)
separately for both subsamples and present the results in Panel A of Table 8. The first three
columns are based on the subsample with high institutional holdings and the latter three columns
are based on the subsample with low institutional holdings. As can be seen, the coefficient of the
interaction variable, ΔACCA × Dispersion, is negative and significant only in the subsample with
low institutional holdings, presumably those firms facing a higher degree of short-sale
constraints. In the subsample with high institutional holdings, the coefficient of the interaction
variable is negative but insignificant.
Next, we divide the sample into the subsamples of liquid and illiquid stocks based on
Amihud’s illiquidity measure in the quarter prior to the earnings announcement date. We define
liquid stocks as those with the level of Amihud’s illiquidity measure below the median of the
whole sample and illiquid stocks as those above the sample median. We report the results based
on these two subsamples in Panel B of Table 8, with the first three columns based on the
subsample of illiquid stocks and the latter three based on the subsample of liquid stocks. Our
29
results show that the coefficients of ΔACCA × Dispersion are negative and significant only in the
subsample of illiquid stocks, presumably the stocks facing a high level of short-sale constraints.
In contrast, the coefficients of ΔACCA × Dispersion are negative but insignificant in the
subsample of liquid stocks. Overall, our results in Table 8 support hypothesis H3. They suggest
short-sale constraints play an important role in explaining the relation between the accrualinduced heterogeneity of investor beliefs and future stock returns. 18
5. Other Explanations on the Relation between Accruals, Analyst Dispersion, and Future
Stock Returns
In this section, we discuss other potential explanations for our empirical findings. Many
studies in the literature also use dispersion of analysts’ earnings forecasts to proxy for the degree
of asymmetric information (e.g., see Thomas, 2002). They argue that the disagreement among
financial analysts could be induced by information asymmetry. A higher level of analyst
dispersion can be viewed as indicating an increased degree of information asymmetry. Using
analyst dispersion as the proxy, the asymmetric information theory would predict that an increase
in accruals increases information asymmetry, thereby affecting stock pricing. However,
information asymmetry, by itself, cannot generate a long run drift in stock prices in the context
of any corporate event. This is because rational investors will learn instantaneously the
information conveyed by the corporate event, so that asymmetric information models cannot
generate a systematic bias in the long-run stock prices (either upward or downward) subsequent
18
In an unreported test, we use another proxy for the degree of short-sale constraints, i.e., the percentage of each
firm's shares that are held short. Following Boehme, Danielsen, and Sorescu (2006), we scale each short interest
observation by the number of shares outstanding and form two subsamples with high versus low short interest. The
results are stronger for the subsample with high short interest. It confirms once again that the documented effect is
stronger for firms facing a higher degree of short-selling constraints.
30
to any corporate event. Thus, the impact of the accrual-driven analyst dispersion on future stock
returns is clearly not driven by the information asymmetry theory.
Easley and O’Hara (2004) suggest that uninformed investors could face information
uncertainty since they could be less informed or slowly informed about new information
compared to informed investors. This information uncertainty could be a non-diversifiable risk
factor, thereby affecting stock returns. A higher level of analyst dispersion can be viewed as
indicating an increased degree of information uncertainty. This information risk argument would
predict that firms with higher information risk, such as those reporting higher accruals and
experiencing higher analyst dispersion, would experience a decrease in contemporaneous stock
price and higher long-term stock return. However, if market underreact to the increase in information
risk (e.g., for smaller or illiquid stocks), stock price could gradually incorporate the shock to
information uncertainty. In other words, our results could be consistent with the information risk
argument if the market underreacts contemporaneously to an unexpected increase in information risk
and if the under-reaction lasts for three months. 19
6. Conclusion
It has been established that firms with high heterogeneity of investor beliefs experience
more negative future stock returns. However, little is known about what causes the heterogeneity
of investor beliefs. We propose that the difficulty in interpreting accounting accruals in the
presence of potential earnings management could lead to heterogeneous investor beliefs
regarding the firm value. We also propose that accruals could affect future stock returns by
affecting investors’ heterogeneous beliefs.
19
We thank an anonymous referee for this point.
31
We document three findings. First, we find that the level of heterogeneity in investor
beliefs on a firm’s value is higher when the firm experiences a larger increase in its accounting
accruals, which may indicate income-increasing earnings management. Second, we find that
future stock returns following earnings announcement are lower when the firm’s accounting
accruals increase the heterogeneity of investor beliefs to a larger degree. Finally, we also find
that the effect of the accruals-induced heterogeneous investor beliefs on future stock returns is
more pronounced when short-sale constraints are more binding. Overall, our empirical findings
suggest accounting accruals are a key determinant of the heterogeneity of investor beliefs. They
also suggest a channel of investor beliefs in which accruals affect future stock returns by
affecting the heterogeneity of investor beliefs.
32
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Teoh, S, H., I. Welch, and T.J. Wong, 1998a. Earnings Management and the Long-run
Underperformance of Initial Public Equity Offerings, Journal of Finance 53, 1935-1974.
Teoh, S, H., I. Welch, and T.J. Wong, 1998b. Earnings Management and the Underperformance
of Seasoned Equity Offerings, Journal of Financial Economics 50, 63-99.
Thomas, S. 2002. Firm Diversification and Asymmetric Information: Evidence from Analysts’
Forecasts and Earnings announcements. Journal of Financial Economics 64, 373-396.
Verardo, M. 2009. Heterogeneous Beliefs and Momentum Profits. Journal of Financial and
Quantitative Analysis 44, 796-822.
Zhang, G., and S. Zhang. 2013. Information Efficiency of the U.S. Credit Default Swap Market:
Evidence from Earnings Surprises. Journal of Financial Stability 9, 720-730.
35
Table 1: Distribution of Sample across Years
Year
Number of Number of
Average market
Median market
firms
firm-quarters capitalization ($ thousands) capitalization ($ thousands)
1994
64
103
3394.15
1915.52
1995
75
111
3201.22
1701.31
1996
125
208
6426.33
1942.34
1997
129
258
4382.50
2012.57
1998
159
377
5240.56
1941.96
1999
66
83
3812.38
1577.45
2000
173
401
6704.86
1557.05
2001
204
544
8333.55
1851.88
2002
289
711
11159.93
1974.98
2003
450
1,222
9232.61
2076.82
2004
548
1,563
10358.13
2477.43
2005
609
1,757
9424.86
2337.06
2006
652
1,824
10043.79
2529.81
2007
404
407
10356.66
2610.86
Total
1,116
9,569
9111.48
2210.15
36
Table 2: Sample Statistics
Variable
Ret [0, 63]
Ret [6, 63]
Ret [a, 63]
ACCA
ΔACCA
Institutional
holdings
Beta
BM
Size
Illiquidity
Historical
Return
SUE
ROA
GrLTNOA
Dispersion
NForecast
Error
Number of
observations
9,569
9,569
9,543
9,569
9,569
Mean
0.042
0.038
0.035
-0.016
0.000
Median
0.036
0.032
0.030
-0.014
-0.001
Min
-0.816
-0.819
-0.841
-0.610
-0.601
Max
1.910
1.750
1.446
0.500
1.288
Skewness
0.631
0.581
0.553
-1.449
0.871
Kurtosis
7.027
6.526
6.622
27.391
33.587
9,569
0.708
0.732
0.038
3.302
-0.147
6.064
9,569
9,569
9,569
9,569
1.140
0.414
7.350
0.003
1.053
0.345
7.228
0.000
-2.844
0.035
2.479
0.000
5.339
1.761
12.697
0.964
0.671
7.470
0.459
27.286
4.453
1.806
3.270
974.598
9,569
0.019
0.015
-0.731
2.047
1.148
18.946
9,569
9,569
9,367
9,569
9,569
9,569
0.000
0.013
0.012
0.113
10.465
0.346
0.002
0.015
0.001
0.032
8.000
0.079
-1.000
-0.260
-11668
0.000
3.000
0.000
1.000
0.083
133447
2.500
45.000
10.000
-0.746
-3.479
61
5.910
1.294
6.769
142.126
29.195
4705
43.001
4.573
54.525
Ret is raw stock return measured in various event windows. [0, 63] stands for a three-month window starting from
the earnings announcement date. [6, 63] covers a period starting from the sixth trading day to three months
subsequent to the earnings announcement date. [a, 63] covers a period starting from the IBES earnings forecast
report date to three months subsequent to the earnings announcement date. ACCA is the amount of total accruals,
calculated as the difference between earnings before extraordinary items and the operating cash flows. ΔACCA is
the changes in total accruals from the previous quarter to the current quarter. Institutional investor holding is the
fraction of stock held by institutional investors. Beta is estimated from the capital market model, based on a period
of 200 days prior to the earnings announcement date. BM is the ratio of the book value to the market value of equity
at the beginning of the quarter. Size is the log of market value of equity at the beginning of the quarter. Illiquidity
is the average ratio of the absolute value of daily return to the value of daily trading volume in the year prior to the
earnings announcement date. Historical Return is the historical cumulative stock return in the three months prior to
announcement date. SUE is standardized unexpected earnings, calculated as (Eq − Eq-4 − cq)/sq, where Eq and Eq4 are earnings in the current quarter and in the same quarter a year ago, respectively; and cq and sq are the mean and
standard deviation, respectively, of (Eq − Eq−4) over the preceding eight quarters. ROA is net income divided by
total assets at the beginning of the quarter. GrLTNOA is growth in long-term net operating assets, defined as growth
in net operating assets other than accruals scaled by average total assets. Dispersion is the standard deviation of
analysts' one-year-ahead earnings forecasts made in the month following the earnings announcement date, scaled by
the absolute value of the average earnings forecast. NForecast is the number of analysts' one-year-ahead earnings
forecasts reported in I/B/E/S. Error is analyst forecast error, calculated as the average earnings forecast minus the
actual EPS, scaled by absolute value of the actual EPS.
37
Table 3: Total Accruals and Analyst Dispersion
VARIABLES
(1)
(2)
(3)
Constant
0.165***
0.383***
0.323***
[0.014]
[0.074]
[0.075]
∆ACCA
0.304***
0.256***
0.200**
[0.099]
[0.092]
[0.080]
NForecast
0.001
0.008***
0.008***
[0.001]
[0.002]
[0.002]
SUE
0.032
0.085
0.474
[0.380]
[0.324]
[0.345]
ROA
-4.528***
-3.673***
-2.849***
[0.646]
[0.712]
[0.487]
GrLTNOA
0.325
0.495
[0.812]
[1.300]
Beta
-0.009
-0.004
[0.016]
[0.012]
BM
0.034
0.021
[0.042]
[0.044]
Size
-0.046***
-0.042***
[0.010]
[0.011]
Illiquidity
7.496***
6.557***
[2.126]
[1.911]
Historical
Return
-0.096
-0.114
[0.098]
[0.134]
Error
0.028
[0.038]
Observations
R-squared
Regression
Type
9,569
0.190
FamaMacBeth
9,367
0.278
FamaMacBeth
9,046
0.362
FamaMacBeth
(4)
0.309***
[0.038]
0.161***
[0.054]
0.006***
[0.001]
0.008
[0.099]
-2.051***
[0.196]
0.004
[0.006]
0.008
[0.006]
0.078***
[0.023]
-0.039***
[0.005]
0.202
[0.171]
(5)
0.320***
[0.039]
0.156***
[0.055]
0.006***
[0.001]
0.014
[0.098]
-2.019***
[0.195]
0.002
[0.005]
0.009
[0.006]
0.083***
[0.022]
-0.039***
[0.005]
0.193
[0.172]
(6)
0.519***
[0.063]
0.121***
[0.041]
0.001
[0.001]
-0.033
[0.047]
-1.136***
[0.136]
0.004
[0.018]
-0.002
[0.005]
0.077***
[0.016]
-0.059***
[0.008]
0.032
[0.178]
0.000
[0.041]
0.058***
[0.010]
0.007
[0.041]
0.058***
[0.010]
-0.034
[0.024]
0.007
[0.005]
9,360
9,360
9,360
0.136
0.142
0.041
OLS without
OLS with
year dummies year dummies Fixed effect
The dependent variable is analyst forecast dispersion, calculated as the standard deviation of analysts’ earnings
forecasts in the month subsequent to the earnings announcement date, scaled by the absolute value of the firm’s actual
earnings. ∆ACCA is the change in total accruals from the previous quarter to the current quarter, where total accruals
are calculated as the difference between earnings before extraordinary items and the operating cash flows. NForecast is
the number of analysts' one-year-ahead earnings forecasts reported in I/B/E/S. SUE is standardized unexpected earnings,
calculated as (Eq − Eq-4 − cq)/sq, where Eq and Eq-4 are earnings in the current quarter and in the same quarter a year ago,
respectively; and cq and sq are the mean and standard deviation, respectively, of (Eq − Eq−4) over the preceding eight
quarters. ROA is net income divided by total assets at the beginning of the quarter. GrLTNOA is growth in long-term
net operating assets, defined as growth in net operating assets other than accruals scaled by average total assets. Beta is
estimated from the capital market model, based on a period of 200 days prior to the earnings announcement date. BM
is the ratio of the book value to the market value of equity at the beginning of the quarter. Size is the log of market
value of equity at the beginning of the quarter. Illiquidity is the average ratio of the absolute value of daily return to the
value of daily trading volume in the year prior to the earnings announcement date. Historical Return is the historical
cumulative stock return in the three months prior to announcement date. Error is analyst forecast error, calculated as the
average earnings forecast minus the actual EPS, scaled by absolute value of the actual EPS. The robust standard errors
are in brackets; *** p<0.01, ** p<0.05, * p<0.1.
38
Table 4: Accruals and Analyst Dispersion - Robustness Tests
Panel A: Accruals Measured as Discretionary Accruals
VARIABLES
(1)
(2)
(3)
Constant
0.164***
0.377***
0.305***
[0.013]
[0.075]
[0.067]
0.410***
0.322***
0.425***
∆DACC
[0.116]
[0.084]
[0.138]
NForecast
0.001
0.009***
0.009***
[0.001]
[0.002]
[0.002]
SUE
0.411
0.650
1.148*
[0.537]
[0.494]
[0.652]
ROA
-4.540***
-3.441***
-2.653***
[0.614]
[0.644]
[0.512]
Error
0.011
[0.045]
Other Controls
N
Y
Y
Observations
8,955
8,769
8,458
R-squared
0.181
0.268
0.362
Regression
FamaFamaFamaType
MacBeth
MacBeth
MacBeth
Panel B: Regressions using Change Variables
(1)
(2)
VARIABLES
Constant
0.012*
0.016**
[0.007]
[0.008]
∆ACCA
0.311**
0.257*
[0.153]
[0.150]
∆NForecast
0.002
0.003
[0.013]
[0.015]
∆SUE
-0.489*
-0.284
[0.247]
[0.242]
∆ROA
0.631
-0.486
[0.745]
[0.453]
∆GrLTNOA
0
[0.000]
∆Beta
-0.011*
[0.006]
∆BM
-0.2
[0.166]
∆Size
-0.127
[0.079]
∆Illiquidity
-0.703
[2.450]
∆ Historical
Return
0.133
[0.151]
39
(4)
(5)
0.307***
0.329***
[0.040]
[0.051]
0.188***
0.185***
[0.061]
[0.060]
0.006***
0.006***
[0.001]
[0.001]
0.008
0.014
[0.111]
[0.110]
-2.091***
-2.056***
[0.213]
[0.211]
0.055***
0.055***
[0.010]
[0.010]
Y
Y
8,762
8,762
0.135
0.142
OLS without
OLS with
year dummies year dummies
(6)
0.545***
[0.066]
0.155***
[0.051]
0.001
[0.001]
-0.001
[0.050]
-1.259***
[0.145]
0.002
[0.005]
Y
8,762
0.044
Fixed effect
(3)
(4)
(5)
0.002
[0.007]
0.192**
[0.079]
0.014
[0.010]
-0.273
[0.188]
-0.213
[0.165]
0
[0.000]
-0.003
[0.006]
-0.074
[0.078]
-0.058
[0.048]
-1.18
[2.738]
0.006
[0.004]
0.213**
[0.088]
0.014
[0.010]
-0.287**
[0.135]
-0.251
[0.160]
0
[0.000]
0.008*
[0.004]
-0.136
[0.101]
-0.011
[0.036]
-1.34
[1.675]
0.130*
[0.067]
0.261**
[0.126]
0.009*
[0.005]
-0.339
[0.221]
-0.416
[0.318]
-0.001
[0.001]
0.002
[0.007]
0.023
[0.096]
0.055
[0.055]
0.452
[1.520]
0.024
[0.033]
0.008
[0.016]
0.043
[0.048]
∆Error
0.229***
[0.029]
Lagged ACCA
Lagged
Dispersion
0.220***
[0.032]
0.073
[0.109]
0.198***
[0.021]
0.112
[0.195]
-0.117**
[0.054]
-0.293***
[0.087]
0.003**
[0.001]
-0.21
[0.314]
-0.472
[0.373]
Lagged NForecast
Lagged SUE
Lagged ROA
Lagged
GrLTNOA
-0.001
[0.001]
-0.004
[0.006]
-0.057*
[0.030]
-0.016*
[0.009]
-0.463
[1.646]
Lagged Beta
Lagged BM
Lagged Size
Lagged Illiquidity
Lagged Historical
Return
0.019
[0.063]
0.065***
[0.022]
6707
0.863
Lagged Error
Observations
R-squared
6707
0.247
6707
0.377
6707
0.704
6707
0.795
Panel C: Accruals and Analyst Dispersion: Heckman Selection Model
Constant
∆ACCA
∆DACC
NForecast
The dependent variable is Dispersion
(1)
(2)
(3)
(4)
(5)
-0.300*** -0.405* -0.465** -0.277*** -0.708***
[0.030] [0.211] [0.223] [0.044] [0.243]
0.248*** 0.227*** 0.213***
[0.049] [0.051] [0.052]
0.307*** 0.318***
[0.062] [0.068]
0.006*** 0.006*** 0.006*** 0.007*** 0.007***
[0.001] [0.001] [0.001] [0.001] [0.001]
∆NForecast
The dependent variable is ∆Dispersion
(6)
(7)
(8)
(9)
-0.022
-0.193
0.033 -0.324**
[0.075] [0.690] [0.034] [0.159]
0.434** 0.365**
[0.169] [0.174]
0.114** 0.121**
[0.055] [0.057]
0.005
40
0.007
0.005** 0.006***
SUE
ROA
Error
Inverse
Mills Ratio
Other
controls
Obs.
[0.008] [0.008] [0.002] [0.002]
-0.008
0.037
0.028
-0.017
0.023 -0.362** -0.275
-0.055
-0.050
[0.050] [0.050] [0.051] [0.053] [0.054] [0.184] [0.187] [0.051] [0.052]
-2.247*** -1.945*** -1.903*** -2.330*** -1.969*** -2.382*** -2.028*** -0.620*** -0.439***
[0.116] [0.121] [0.124] [0.124] [0.132] [0.408] [0.433] [0.114] [0.120]
-0.022***
-0.033***
-0.092***
-0.006
[0.005]
[0.006]
[0.019]
[0.005]
0.254*** 0.257*** 0.277*** 0.262*** 0.364*** 0.091** 0.134
0.013 0.131**
[0.014] [0.069] [0.073] [0.015] [0.079] [0.036] [0.225] [0.010] [0.054]
N
79,055
Y
78,863
Y
78,569
N
75,669
Y
75,207
N
78,606
Y
78,424
N
75,242
Y
61,885
In Panel A, Dispersion is the analyst forecast dispersion, measured as standard deviation of analysts' one-year-ahead
earnings forecasts scaled by the absolute value of the average earnings forecast. ∆DACC is the change in discretionary
accruals, where we calculate discretionary accruals based on modified Jones model. In Panel B, the dependent variable
is change in analyst dispersion, where analyst dispersion is the standard deviation of earnings forecasts scaled by the
absolute value of the average forecast. In Panel C, Inverse Mills Ratio is computed from the first-stage probit
regression on the likelihood of disclosing operating cash flow in the preliminary earnings announcement. The
independent variables in the first stage consist of ACCA lagged by one and two quarters, beta, size, BM, lagged cash
flow ((Net income +Depreciation)/ Assets), lagged profitability (EBIT/Assets), lagged Capital Expenditures/Sales. The
results from the first stage are not reported. We also controlled for lagged dispersion, lagged error, and lagged ACCA
in columns (7) and (9). The coefficients of these three variables are not reported. In all Panels, ACCA (total accruals)
is earnings before extraordinary items minus operating cash flows. NForecast is the number of analysts' one-yearahead earnings forecasts reported in I/B/E/S. SUE is standardized unexpected earnings, calculated as (Eq − Eq-4 −
cq)/sq, where Eq and Eq-4 are earnings in the current quarter and in the same quarter a year ago, respectively; and cq and
sq are the mean and standard deviation, respectively, of (Eq − Eq−4) over the preceding eight quarters. ROA is net
income divided by total assets at the beginning of the quarter. GrLTNOA is growth in long-term net operating assets,
defined as growth in net operating assets other than accruals scaled by average total assets. Beta is estimated from the
capital market model, based on a period of 200 days prior to the earnings announcement date. BM is the ratio of the
book value to the market value of equity at the beginning of the quarter. Size is the log of market value of equity at
the beginning of the quarter. Illiquidity is the average ratio of the absolute value of daily return to the value of daily
trading volume in the quarter prior to the earnings announcement date. Historical Return is the historical cumulative
stock return in the three months prior to announcement date. Error is analyst forecast error, calculated as the average
earnings forecast minus the actual EPS, scaled by absolute value of the actual EPS. The change variables are from the
previous to the current quarter. The robust standard errors are in brackets; *** p<0.01, ** p<0.05, * p<0.1.
41
Table 5: Accruals and Analyst Dispersion, Subsample Tests
Bottom
Bottom
High
Low
quartile
decile
High
Sample
∆ACCA ∆ACCA ∆ACCA ∆ACCA ∆DACC
(1)
(2)
(3)
(4)
(5)
Constant
0.230**
0.386**
*
0.206***
0.042
0.216***
[0.155]
[0.064]
[0.077]
[0.089]
[0.056]
∆ACCA
0.208** 0.395**
0.125
-0.397
[0.099]
[0.177]
[0.303]
[0.344]
∆DACC
0.521***
[0.159]
0.010**
NForecast
*
0.008** 0.007***
0.007
0.008***
[0.003]
[0.003]
[0.002]
[0.005]
[0.002]
SUE
-0.179
0.069
-0.066
-0.303
0.504
[0.739]
[0.211]
[0.208]
[0.422]
[0.538]
ROA
-1.561*** -1.950*** -1.005*** -0.700** -2.544***
[0.389]
[0.269]
[0.170]
[0.267]
[0.346]
GrLTNOA
-0.550
0.265
-1.228
-0.478
-0.066
[0.537]
[0.457]
[1.271]
[0.596]
[0.795]
Beta
-0.003
0.032
0.008
0.019*
-0.008
[0.022]
[0.020]
[0.014]
[0.011]
[0.019]
0.123**
BM
0.012
*
0.081** 0.143*** 0.076***
[0.047]
[0.043]
[0.031]
[0.041]
[0.028]
Size
-0.058** -0.037*** -0.032**
-0.020 -0.032***
[0.024]
[0.012]
[0.012]
[0.015]
[0.008]
Illiquidity
0.137
2.321
5.277
-2.210
4.147**
[3.541]
[3.097]
[5.187]
[3.598]
[1.704]
Historical
0.127**
Return
-0.073
*
0.124
-0.066
0.088
[0.129]
[0.044]
[0.080]
[0.081]
[0.053]
0.151** 0.084**
Error
*
*
0.076***
0.045
0.069**
[0.031]
[0.020]
[0.018]
[0.035]
[0.034]
Observations
4,698
4,669
2,218
853
4,398
R-squared
0.514
0.529
0.542
0.700
0.346
Low
∆DACC
(6)
Bottom
quartile
∆DACC
(7)
Bottom
decile
∆DACC
(8)
0.580**
[0.275]
0.314**
[0.123]
0.006
[0.143]
0.586**
[0.284]
-0.710
[0.753]
-0.234
[0.283]
0.011*** 0.008***
[0.004]
[0.003]
0.863
0.057
[0.641]
[0.673]
-2.335*** -1.051**
[0.560]
[0.507]
0.076
3.759
[0.765]
[2.739]
-0.017
-0.027
[0.022]
[0.032]
0.002
[0.003]
-1.266*
[0.742]
-0.395
[0.319]
-1.142*
[0.574]
0.023
[0.025]
0.067
[0.052]
-0.082**
[0.040]
1.171
[3.896]
0.053
[0.047]
-0.046**
[0.020]
6.391
[8.201]
0.050
[0.061]
-0.001
[0.018]
0.015
[3.653]
-0.278
[0.302]
-0.070
[0.261]
0.071
[0.120]
0.032*
[0.016]
4,364
0.321
0.028
[0.020]
2,081
0.390
0.069
[0.049]
808
0.484
The dependent variable is analyst forecast dispersion, calculated as the standard deviation of analysts' one-year-ahead
earnings forecasts scaled by the absolute value of the average earnings forecast. ∆ACCA is the change in total accruals
from the previous quarter to the current quarter, where total accruals are calculated as the difference between earnings
before extraordinary items and the operating cash flows. ∆DACC is the change in discretionary accruals, where we
calculate discretionary accruals based on modified Jones model. Subsamples of high ∆ACCA and high ∆DACC consist
of those firms with ACCA or DACC above the sample median, respectively. Bottom quartile and decile consists of
those in the bottom 25% or 10% of the distribution. NForecast is the number of analysts' one-year-ahead earnings
forecasts reported in I/B/E/S. SUE is standardized unexpected earnings. ROA is net income divided by total assets.
GrLTNOA is growth in long-term net operating assets, defined as growth in net operating assets other than accruals
scaled by average total assets. Beta is estimated from the capital market model. BM is the ratio of the book value to the
market value of equity at the beginning of the quarter. Size is the log of market value of equity at the beginning of the
quarter. Illiquidity is the average ratio of the absolute value of daily return to the value of daily trading volume in the
prior quarter. Historical Return is the historical cumulative stock return in the three months prior to announcement date.
Error is analyst forecast error, calculated as the average earnings forecast minus the actual EPS, scaled by absolute
value of the actual EPS. The robust standard errors are in brackets; *** p<0.01, ** p<0.05, * p<0.1.
42
Table 6: Total Accruals, Analyst Dispersion, and Stock Returns
VARIABLES
Ret [0,63]
Ret [6,63]
(1)
(2)
(3)
(4)
(5)
(6)
Constant
0.004
0.007 0.111*** -0.015
-0.012 0.129***
[0.029] [0.056] [0.017] [0.030] [0.063] [0.017]
∆ACCA
-0.146** -0.069 -0.071** -0.127** -0.077 -0.072**
[0.064] [0.118] [0.034] [0.059] [0.114] [0.033]
Beta
0.016
0.014
0.007**
0.015
0.016
0.005*
[0.010] [0.011] [0.003] [0.010] [0.012] [0.003]
BM
0.029** 0.066*** 0.050*** 0.029** 0.063*** 0.047***
[0.012] [0.018] [0.007] [0.011] [0.018] [0.007]
Size
0.001
-0.001 -0.003*
0.003
0.001
-0.003
[0.003] [0.006] [0.002] [0.003] [0.007] [0.002]
Illiquidity
-18.458 -19.749 -0.084 -18.539 -18.924 -0.054
[15.341] [17.664] [0.085] [16.349] [17.915] [0.084]
Historical
Return
-0.134*** -0.167*** -0.137*** -0.125*** -0.146*** -0.147***
[0.042] [0.053] [0.017] [0.040] [0.053] [0.017]
SUE
0.179
0.032
0.108
0.050
[0.177] [0.034]
[0.200] [0.033]
ROA
0.260
-0.100
0.231
-0.071
[0.371] [0.079]
[0.329] [0.078]
GrLTNOA
-0.956
-0.003
-0.872
-0.005
[0.785] [0.011]
[0.713] [0.011]
Error
-0.081*** -0.072***
-0.077*** -0.071***
[0.020] [0.003]
[0.019] [0.003]
NForecast
0.000
0.000
0.000
0.000
[0.001] [0.000]
[0.001] [0.000]
Dispersion
0.059
0.011
0.058
0.013*
[0.058] [0.007]
[0.057] [0.007]
∆ACCA
-1.932** -0.230***
-1.623* -0.220***
×Dispersion
[0.893] [0.082]
[0.940] [0.081]
Observations 9,569
9,360
9,360
9,569
9,360
9,360
R-squared
0.085
0.188
0.117
0.086
0.189
0.113
Reg. Type
Fama-MacBeth
OLS
Fama-MacBeth
OLS
(7)
0.0002
[0.025]
-0.126*
[0.074]
0.014
[0.008]
0.022*
[0.013]
0.001
[0.003]
-16.855
[15.193]
Ret [a,63]
(8)
-0.024
[0.059]
-0.024
[0.121]
0.013
[0.010]
0.066***
[0.024]
0.002
[0.006]
-16.393
[15.757]
(9)
0.132***
[0.015]
-0.028
[0.030]
0.004
[0.003]
0.034***
[0.006]
-0.004**
[0.002]
0.077
[0.076]
-0.083** -0.082 -0.125***
[0.032] [0.061] [0.016]
0.181 0.115***
[0.160] [0.030]
0.417
-0.107
[0.483] [0.071]
-1.357
-0.007
[0.958] [0.010]
-0.077*** -0.060***
[0.027] [0.003]
0.000
0.000
[0.001] [0.000]
0.085
0.009
[0.062] [0.006]
-1.843** -0.184**
[0.899] [0.074]
9,543
9,334
9,334
0.078
0.185
0.097
Fama-MacBeth
OLS
The dependent variable, Ret, is raw stock return in various trading day windows. [0,63], [6,63], and [a,63] are threemonth windows starting from earnings announcement date, the sixth trading day after earnings announcement, and
IBES earnings forecast report date after earnings announcement, respectively. ∆ACCA is the change in total accruals
from the previous quarter to the current quarter, where total accruals are calculated as the difference between earnings
before extraordinary items and the operating cash flows. BM is quarter-beginning book-to-market ratio. Size is the log
of market value at quarter beginning. Illiquidity is the average ratio of the absolute value of daily return to the value of
daily trading volume in the prior quarter. Historical Return is the historical cumulative stock return in the three months
prior to announcement date. SUE is standardized unexpected earnings. ROA is net income divided by total assets.
GrLTNOA is growth in net operating assets other than accruals scaled by average total assets. Error is the average
earnings forecast minus the actual EPS, scaled by absolute value of the actual EPS. NForecast is the number of
analysts' one-year-ahead earnings forecasts reported in I/B/E/S. Dispersion is the standard deviation of analysts' oneyear-ahead earnings forecasts scaled by the absolute value of the average earnings forecast. Standard errors are in
brackets; *** p<0.01, ** p<0.05, * p<0.1.
43
Table 7: Total Accruals, Analyst Dispersion, and Stock Returns - Robustness Tests
Panel A: Heckman Selection Model
Variables
Ret [0,63]
Ret [0,63]
Ret [6,63]
Ret [6,63]
Ret [a,63]
(1)
(2)
(3)
(4)
(5)
Constant
0.582***
0.664***
0.638***
0.739***
0.598***
[0.103]
[0.143]
[0.102]
[0.144]
[0.101]
∆ACCA
-0.191***
-0.133***
-0.193***
-0.139***
-0.136***
[0.031]
[0.037]
[0.031]
[0.037]
[0.028]
∆ACCA
-0.300***
-0.269***
×Dispersion
[0.088]
[0.086]
Inverse Mills
-0.194***
-0.184***
-0.210***
-0.203***
-0.190***
Ratio
[0.039]
[0.047]
[0.039]
[0.047]
[0.037]
Observations
81,638
78,859
81,638
78,859
80,942
Other controls
N
Y
N
Y
N
Panel B: Discretionary Accruals, Analyst Dispersion, and Stock Returns
VARIABLES
Ret [0,63]
Ret [0,63]
Ret [6,63]
Ret [6,63]
(1)
(2)
(3)
(4)
Constant
-0.043
0.004
-0.042
-0.000
[0.066]
[0.024]
[0.060]
[0.024]
∆DACC
0.257
-0.026
0.223
-0.026
[0.191]
[0.043]
[0.167]
[0.042]
∆DACC
-4.027**
-0.283**
-3.038**
-0.232**
×Dispersion
[1.932]
[0.111]
[1.455]
[0.110]
Observations
8,461
8,451
8,461
8,451
Other controls
Y
Y
Y
Y
R-squared
0.190
0.080
0.192
0.071
FamaFamaReg. Type
MacBeth
OLS
MacBeth
OLS
Ret [a,63]
(5)
-0.062
[0.067]
0.280
[0.199]
-4.408*
[2.277]
8,436
Y
0.167
FamaMacBeth
Ret [a,63]
(6)
0.741***
[0.132]
-0.102***
[0.034]
-0.231***
[0.078]
-0.202***
[0.043]
78,833
Y
Ret [a,63]
(6)
0.028**
[0.014]
-0.009
[0.040]
-0.163*
[0.099]
8,426
Y
0.057
OLS
Panel C: Total Accruals, Analyst Dispersion, and Stock Returns – Subsample Test
VARIABLES
Ret [0,63]
(1)
Constant
0.124
[0.117]
∆ACCA
0.226
[0.263]
-3.390**
[1.426]
4,522
Y
0.237
∆ACCA
x Dispersion
Observations
Other controls
R-squared
Ret [6,63]
Ret [a,63]
(2)
(3)
High Dispersion
0.137
0.105
[0.135]
[0.093]
0.179
[0.229]
-3.125**
[1.366]
4,522
Y
0.242
0.113
[0.204]
-2.331**
[1.041]
4,507
Y
0.209
44
Ret [0,63]
(4)
0.990
[0.949]
1.733
[1.718]
-56.120
[63.222]
4,524
Y
0.188
Ret [6,63]
Ret [a,63]
(5)
(6)
Low Dispersion
2.403
-0.608
[2.307]
[0.644]
4.023
[3.884]
-127.049
[130.890]
4,524
Y
0.178
-0.821
[0.920]
23.571
[24.747]
4,513
Y
0.132
Panel D: Total Accruals, Analyst Dispersion, and Stock Returns, Alternative Specification
VARIABLES
Ret [0,63] Ret [0,63] Ret [6,63] Ret [6,63] Ret [a,63]
(1)
(2)
(3)
(4)
(5)
Constant
0.079**
0.116***
0.072**
0.134***
0.079**
[0.035]
[0.018]
[0.033]
[0.018]
[0.034]
∆ACCA
0.260
-0.074
0.230
-0.073
0.260
[0.195]
[0.047]
[0.179]
[0.048]
[0.190]
Lagged Dispersion
-0.061
0.013
-0.060
0.019*
-0.061
[0.050]
[0.010]
[0.042]
[0.010]
[0.048]
∆Dispersion
0.117
0.012
0.090
0.010
0.117
[0.145]
[0.011]
[0.145]
[0.010]
[0.142]
∆ACCA×Lagged
Dispersion
-10.205
-0.451***
-9.613
-0.450***
-10.205
[6.315]
[0.124]
[6.038]
[0.122]
[6.277]
∆ACCA×∆Dispersion
-3.527** -0.366***
-2.841*
-0.317**
-3.527**
[1.718]
[0.121]
[1.567]
[0.128]
[1.663]
Observations
8,886
8,886
8,886
8,886
8,886
Other controls
Y
Y
Y
Y
Y
R-squared
0.204
0.119
0.209
0.114
0.204
FamaFamaFamaRegression Type
MacBeth
OLS
MacBeth
OLS
MacBeth
Ret [a,63]
(6)
0.131***
[0.016]
-0.036
[0.046]
0.014
[0.009]
0.007
[0.011]
-0.359***
[0.110]
-0.261**
[0.122]
8,860
Y
0.098
OLS
Panel E: Total Accruals, Analyst Dispersion, and Stock Returns, Additional Controls
VARIABLES
Ret [0,63]
Ret [6,63]
Ret [a,63]
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Constant
-0.015 -0.022 -0.043 -0.026 -0.039 -0.066 -0.035 -0.041 -0.073
[0.045] [0.051] [0.065] [0.051] [0.057] [0.066] [0.048] [0.053] [0.074]
∆ACCA
-0.018
0.081
0.220
-0.025
0.065
0.196
-0.044 -0.007
0.078
[0.088] [0.125] [0.162] [0.072] [0.102] [0.146] [0.111] [0.119] [0.110]
∆ACCA × SUE
6.866
5.304
-5.616
5.855
4.110
-6.187
5.487
4.279
-2.320
[6.991] [7.419] [11.075] [7.897] [8.351] [10.101] [6.273] [6.213] [8.300]
-23.615* -20.022*
-22.458** -19.799*
-7.412 -4.578
∆ACCA ×
[12.111] [11.014]
[10.906] [10.599]
[9.673] [10.229]
GrLTNOA
∆ACCA× Error
-1.056
-1.275
-0.395
[0.824]
[0.875]
[0.413]
-2.429** -2.340** -2.449*** -2.204** -2.086** -2.006*** -1.935** -1.792** -1.811**
∆ACCA
[0.975] [0.986] [0.876] [0.873] [0.884] [0.739] [0.868] [0.804] [0.891]
×Dispersion
Observations
9,049
9,049
9,049
9,049
9,049
9,049
9,023
9,023
9,008
Other controls
Y
Y
Y
Y
Y
Y
Y
Y
Y
R-squared
0.194
0.179
0.187
0.194
0.178
0.186
0.178
0.153
0.132
Regression Type
FM
FM
FM
FM
FM
FM
FM
FM
FM
45
Panel F: Total Accruals, Analyst Dispersion, and Stock Returns, Alternative Event Windows
VARIABLES
Ret [0,42]
Ret [6,42]
Ret [a,42]
Ret [0,126]
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Constant
0.079** 0.046*** 0.091*** 0.059*** 0.052** 0.044*** 0.057 0.126***
[0.034] [0.013] [0.031] [0.015] [0.022] [0.011] [0.048] [0.018]
∆ACCA
0.041
-0.053
0.052
-0.050
0.079
-0.018
-0.003
-0.073
[0.073] [0.034] [0.085] [0.035] [0.068] [0.029] [0.086] [0.045]
∆ACCA
-2.087** -0.236** -2.414** -0.239** -1.713* -0.173** -3.383*** -0.248*
×Dispersion
[0.884] [0.093] [1.035] [0.105] [0.966] [0.069] [1.252] [0.128]
Observations
9,089
9,089
9,089
9,089
9,089
9,089
9,089
9,089
Other controls
Y
R-squared
0.201
0.087
0.198
0.086
0.206
0.063
0.204
0.117
Regression
FamaOLS
FamaOLS
FamaOLS
FamaOLS
Type
MacBeth
MacBeth
MacBeth
MacBeth
Ret [6,126]
(9)
(10)
0.046 0.144***
[0.043] [0.018]
-0.018
-0.074
[0.085] [0.046]
-3.018** -0.238**
[1.139] [0.121]
9,089
9,089
Ret [a,126]
(11)
(12)
0.032
0.147***
[0.042] [0.016]
0.031
-0.038
[0.085] [0.043]
-3.112** -0.200*
[1.354] [0.112]
9,089
9,089
0.210
FamaMacBeth
0.189
FamaMacBeth
0.112
OLS
0.095
OLS
For Panels A-E, the dependent variable is raw stock return (Ret) in trading day window [0,63], [6,63], or [a,63], which is a three-month window starting from the
earnings announcement date, the sixth trading day or the IBES earnings forecast report date after earnings announcement, respectively. ∆ACCA is the change in
total accruals from the previous quarter to the current quarter, where total accruals are earnings before extraordinary items minus the operating cash flows.
∆DACC is the change in discretionary accruals from the previous quarter to the current quarter, where discretionary accruals are calculated based on modified
Jones model. Beta is estimated from the capital market model. Beta is estimated from the capital market model, based on a period of 200 days prior to the
earnings announcement date. BM is the ratio of the book value to the market value of equity at the beginning of the quarter. Size is the log of market value of
equity at the beginning of the quarter. Illiquidity is the average ratio of the absolute value of daily return to the value of daily trading volume in the prior quarter.
Historical Return is the historical cumulative stock return in the three months prior to announcement date. SUE is standardized unexpected earnings, calculated
as (Eq − Eq-4 − cq)/sq, where Eq and Eq-4 are earnings in the current quarter and in the same quarter a year ago, respectively; and cq and sq are the mean and
standard deviation, respectively, of (Eq − Eq−4) over the preceding eight quarters. ROA is net income/total assets. GrLTNOA is growth in net operating assets
other than accruals scaled by average total assets. Error is calculated as the average earnings forecast minus the actual EPS, scaled by absolute value of the actual
EPS. NForecast is the number of earnings forecasts. Dispersion is the standard deviation of analysts' one-year-ahead earnings forecasts scaled by the absolute
value of the average earnings forecast. In Panel A, Inverse Mills Ratio is computed from the first-stage probit regression on the likelihood of disclosing operating
cash flows in the preliminary earnings announcement. The independent variables in the first stage consist of ACCA lagged by one and two quarters, beta, size,
BM, lagged cash flow ((NI+depreciation)/assets), lagged profitability (EBIT/assets), lagged capital expenditures/sales. The results from the first stage regression
are not reported. For Panel C, High (low) dispersion subsample includes all firms with dispersions higher (lower) than the sample median. In Panel F, the
dependent variable, Ret, is raw stock return in various trading day windows. [0,42] and [0,126] stand for two and six month window, respectively, starting from
earnings announcement date. [6,42] and [6,126] stand for two and six month window, respectively, starting from the sixth trading day after earnings
announcement. [a,42] and [a,126] stand for two and six month window, respectively, starting from IBES earnings forecast report date after earnings
announcement. Standard errors are in brackets; *** p<0.01, ** p<0.05, * p<0.1.
46
Table 8: Accrual, Analyst Dispersion, and Stock Return – by Degree of Short-Sale Constraints
Panel A: Institutional Holdings as Proxy for the Short-Sales Constraints
Ret
Ret [0,42]
Ret [6,42] Ret [a,42] Ret [0,42] Ret [6,42]
[a,42]
VARIABLES
(1)
(2)
(3)
(4)
(5)
(6)
High Institutional Holding
Low Institutional Holding
Constant
0.067
0.109
0.091
0.138
0.114
0.128
[0.107]
[0.121]
[0.123]
[0.096]
[0.079]
[0.098]
∆ACCA
0.819
0.768
0.807
-0.104
-0.094
-0.033
[0.589]
[0.578]
[0.566]
[0.120]
[0.100]
[0.084]
∆ACCA x Dispersion
-41.496
-38.916
-36.026
-2.559**
-2.222**
-1.979**
[37.973]
[36.769]
[32.403]
[1.104]
[1.033]
[0.789]
Observations
4,528
4,528
4,505
4,518
4,518
4,515
Other controls
Y
Y
Y
Y
Y
Y
R-squared
0.187
0.183
0.172
0.217
0.219
0.196
Number of groups
51
51
51
53
53
53
Panel B: Illiquidity as Proxy for the Short-Sales Constraints
Ret [0,42] Ret [6,42] Ret [a,42]
VARIABLES
(1)
(2)
(3)
High Level of Illiquidity
Constant
0.285**
0.212**
0.204**
[0.115]
[0.093]
[0.080]
∆ACCA
0.058
0.006
0.017
[0.194]
[0.153]
[0.147]
∆ACCA x Dispersion -4.091*** -3.433*** -3.117***
[1.492]
[1.171]
[1.127]
Observations
4,503
4,503
4,496
Other controls
Y
Y
Y
R-squared
0.188
0.195
0.193
Number of groups
53
53
53
Ret [0,42] Ret [6,42] Ret [a,42]
(4)
(5)
(6)
Low Level of Illiquidity
0.148
0.184
0.058
[0.216]
[0.211]
[0.115]
-0.080
-0.074
0.019
[0.170]
[0.168]
[0.091]
-0.050
-0.229
-0.509
[2.866]
[2.779]
[3.416]
4,543
4,543
4,524
Y
Y
Y
0.155
0.142
0.141
53
53
53
The dependent variable, Ret, is raw stock return in various trading day windows. [0,63], [6,63], and [a,63] are threemonth windows starting from the earnings announcement date, the sixth trading day after earnings announcement,
and the IBES earnings forecast report date after earnings announcement, respectively. ∆ACCA is the change in total
accruals from the previous quarter to the current quarter, where total accruals are calculated as the difference
between earnings before extraordinary items and the operating cash flows. Beta is estimated from the capital market
model, based on a period of 200 days prior to the earnings announcement date. BM is the ratio of the book value to
the market value of equity at the beginning of the quarter. Size is the log of market value of equity at the beginning
of the quarter. Illiquidity is the average ratio of the absolute value of daily return to the value of daily trading
volume in the prior quarter. Historical Return is the historical cumulative stock return in the three months prior to
announcement date. Error is the average earnings forecast minus the actual EPS, scaled by absolute value of the
actual EPS. NForecast is the number of analysts' one-year-ahead earnings forecasts reported in I/B/E/S. SUE is
standardized unexpected earnings, calculated as (Eq − Eq-4 − cq)/sq, where Eq and Eq-4 are earnings in the current
quarter and in the same quarter a year ago, respectively; and cq and sq are the mean and standard deviation,
respectively, of (Eq − Eq−4) over the preceding eight quarters. is net income divided by total assets at the beginning
of the quarter. ROA is net income divided by total assets. GrLTNOA is growth in net operating assets other than
accruals scaled by average total assets. Dispersion is the standard deviation of analysts' one-year-ahead earnings
forecasts scaled by the absolute value of the average earnings forecast. In panel A, the subsample of high (low)
institutional investor holdings consists of firms with the fraction of stock held by institutional investors in the quarter
prior to the earnings announcement date above (below) the sample median. In panel B, the subsample of high (low)
level of illiquidity consists of firms with their levels of illiquidity in the quarter prior to the earnings announcement
47
date above (below) the sample median. Illiquidity is the average ratio of the absolute value of daily return to the
value of daily trading volume. Standard errors are in brackets; *** p<0.01, ** p<0.05, * p<0.1.
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