Rounding of Earnings Per Share and Managerial Insider Trading*
Robert Kim, University of Massachusetts Boston
Yong Gyu Lee**, Sungkyunkwan University
Gerald Lobo, University of Houston
September 2015
Abstract: Prior research (e.g., Thomas 1989; Das and Zhang 2003) provides evidence of
managers “rounding” reported earnings per share (EPS). We explore whether managerial
trading incentives can help explain the rounding pattern of EPS. Specifically, we
hypothesize that managers anticipate a disproportionately larger price reaction to rounded
EPS and exert additional effort to round EPS when they plan to sell shares following the
earnings announcement. Consistent with this hypothesis, we find that managers who round
diluted EPS, but not basic EPS, have higher managerial insider sales following the earnings
announcement relative to managers who do not round diluted EPS. Furthermore, we find
that the positive association between rounding of diluted EPS and subsequent stock sales
undertaken by chief financial officers (CFOs) is stronger when the level of abnormal stock
repurchases is higher, consistent with managers’ strategic behavior rather than passive
insider trading in response to performance.
* Preliminary draft. Please do not cite.
** Corresponding author: Business School, Sungkyunkwan University, 25-2 Sungkyunkwan-ro,
Jongno-gu, Seoul 110-745, Korea, E-mail: yonglee@skku.edu
I. INTRODUCTION
Prior research provides evidence of managers “rounding” reported earnings per share (EPS).
Thomas (1989) shows that the last digit (in dollar and cent format) of reported EPS is more likely
to be zero and five and less likely to be nine for profit firms (hereafter, “second digit management”).
Further, Das and Zhang (2003) report that the one tenth of a cent of EPS is more likely between
five and nine for profit firms, and suggest that managers use rounding to report an additional cent
of EPS (hereafter, “third digit management”). A general reason for why managers engage in such
rounding behaviors relates to firm valuation. That is, if reported earnings affect firm value as
perceived by various financial statement users, and the rounding phenomenon describes managers’
perceptions of how stock is valued as well as users’ decision making, then small changes in
reported earnings near user reference points will have disproportionately large effects on perceived
firm value (Carslaw 1988; Thomas 1989).1
In this study, we explore whether managerial trading incentives can help explain these
previously documented irregularities in reported EPS. Given that a significant portion of
managerial compensation in the U.S. is in the form of stock-based compensation, a feasible way
for managers to realize benefits would be through insider stock sales. Specifically, we hypothesize
1
Another general reason for why managers have incentives to round earnings relates to the use of
accounting numbers in various contracts (the “contracting perspective”). If budgets or lending and
compensation contracts are denominated in round earnings numbers, small changes around such contractual
parameters may have large cash flow effects (Thomas 1989). While the valuation perspective relies on
cognitive limitations of human decision makers, the contracting perspective only presumes that key
contractual numbers are typically selected as round earnings numbers. Thomas (1989) calls for research to
investigate these perspectives by concluding that the evidence on rounding of certain earnings numbers that
are unlikely to be included as parameters in budgets and other contracts suggests that the contracting
perspective alone is unlikely to explain all rounding behavior. We respond to this call by focusing on the
valuation perspective and leave empirical investigation of the contracting perspective to future research.
1
that managers anticipate a disproportionately larger price reaction to rounded EPS and exert
additional effort to round EPS when they plan to sell shares following the earnings announcement.
Our analysis starts by confirming the irregularities in reported EPS after the mandatory
adoption of SFAS No. 128, which became effective for fiscal years ending after December 15,
1997.2 Using primary EPS reported prior to the adoption of SFAS No. 128, both Thomas (1989)
and Das and Zhang (2003) document unusual patterns of reported EPS, and Jorgensen et al. (2014)
confirm these patterns using annual diluted EPS reported under SFAS No. 128. Using quarterly
EPS numbers reported under SFAS No. 128, we complement these prior findings by first showing
that the irregularities in reported EPS manifest in diluted EPS, but not in basic EPS. This finding
suggests that managers have incentives to round only the EPS numbers that information users tend
to focus on.3
Next, we examine whether equity investors react to rounded EPS numbers. A positive
investor reaction to rounded EPS would create a favorable environment for managers planning to
sell their stock, thereby leading them to make additional effort to round reported EPS. We find that
equity investors react positively to the unusual digit patterns in diluted EPS but not to those in
basic EPS. These results complement prior findings that diluted EPS is more value-relevant than
basic EPS (Jennings et al. 1997; Core et al. 2002).
Having documented that only diluted EPS numbers exhibit irregularities and investors react
positively to these numbers in the short run, we then investigate whether managers sell their stock
following the rounding of diluted EPS. Based upon prior evidence showing the relative importance
2
Under the previous reporting standard, APB No. 15, firms reported primary EPS and fully-diluted EPS as
undiluted and diluted measures of EPS, respectively. Under SFAS No. 128, firms report basic EPS and
diluted EPS as such measures.
3
Jorgensen et al. (2014) suggest that the focal measure under SFAS No. 128 is diluted EPS. See Section II
for more discussion.
2
of CFOs vs. CEOs in corporate outcomes such as financial reporting (e.g., Jiang et al. 2010), we
focus on the managerial stock sales undertaken by CFOs and CEOs.
In our primary tests, we estimate regressions of managerial stock sales following the earnings
announcement on the indicator of both the second and third digit managements, using firm fixed
effects. For a sample of 12,108 firm-quarters from 1999 to 2012, we find that rounded diluted EPS,
but not basic EPS, is significantly associated with subsequent managerial stock sales. Specifically,
the second digit management accompanied by the third digit management exhibits a significantly
positive association with stock sales undertaken by both CFOs and CEOs, after controlling for
whether the manager beat the analyst forecast benchmark (McVay et al. 2006) and other
determinants of insider sales documented in the literature. Thus, our findings support the notion
that managers round diluted EPS in order to realize benefits through selling shares following the
earnings announcement.
While our findings are suggestive of managers making additional effort to round diluted EPS
in order to boost their proceeds from insider sales (hereafter, “active” trading), an alternative
explanation proposed by Heath et al. (1999), Sehyun (1998), and McVay et al. (2006) is that
insiders sell after good performance (hereafter, “passive” trading). If we could directly measure
the managerial intent to sell shares, our supposition of causality—that managers who intend to sell
shares are more likely to undertake actions to round diluted EPS—would be on much stronger
grounds. However, managerial intent is hard to measure directly and must be inferred from
observable managerial activities such as ex post managerial sales (McVay et al. 2006). We
therefore perform several additional tests to demonstrate that our main results do not simply reflect
passive insider trading in response to performance.
3
First, we conduct a “placebo” test after replacing diluted EPS with basic EPS in our analysis.
The aim of this test is to show that managerial stock sales are associated only with the EPS measure
that is more likely to be managed (because it is what investors focus more on) and thus exhibits
unusual patterns. Since each pair of diluted and basic EPS numbers is computed for the same firm
and quarter observations where the underlying transactions can be held constant, irregularities
found in the distribution of diluted EPS, but not in that of basic EPS, constitute powerful evidence
suggesting that the focal EPS measure is managed. Therefore, by showing a positive association
between rounded EPS and subsequent managerial stock sales only for diluted EPS, but not for
basic EPS, we can strengthen confidence in interpreting our findings in terms of active trading.
Second, we examine how managers planning to sell shares round diluted EPS. We posit that
under active trading, managers will exert effort to round diluted EPS through managing the
denominator (i.e., weighted average number of shares outstanding).4 Specifically, we build upon
Bens et al.’s (2003) evidence that executives’ stock repurchase decisions are driven by incentives
to manage diluted, but not basic EPS, and examine the measure of abnormal stock repurchases
developed in Hribar et al. (2006). The results indicate that the positive association between the
indicator of rounded diluted EPS and subsequent managerial stock sales is stronger when the level
of abnormal stock repurchases is higher. Importantly, this result holds only for the stock sales
undertaken by CFOs, who are expected to play a more prominent role in making decisions that
involve specialized knowledge in accounting and finance, such as stock repurchase decisions.
4
Regarding management of the numerator of EPS, the literature is replete with both academic and anecdotal
evidence that firms use a great variety of ways to manage the dollar amount of reported earnings, but it does
not seem to provide direct evidence as to whether managing the level of earnings leads to unusual digit
patterns in diluted EPS. In a context related to ours, however, McVay et al. (2006) find that firms where
managers sell more shares in the following quarter are significantly more likely to meet the analyst forecast
threshold using discretionary working capital accruals. Similarly, we examine whether the association
between rounding diluted EPS and subsequent managerial sales is stronger for firms with higher
discretionary working capital accruals, but do not find a significant result.
4
Taken together, these findings suggest that our main results are driven by CFOs strategically using
stock repurchases to round diluted EPS prior to selling their shares.
Third, we investigate whether our main results hold for other insiders, such as COOs,
presidents, and board chairs. These insiders, compared with CFOs or CEOs, are less likely to have
the ability to round EPS when they want to sell their stock, and thus we expect to find neither an
increase in their stock sales following the rounding of diluted EPS nor an incremental increase in
their subsequent sales following abnormal stock repurchases. The results are consistent with this
conjecture, thereby providing further assurance that our findings are driven by managers’ strategic
behavior, rather than the passive performance alternative.
Finally, we test whether managers round diluted EPS through working capital accruals. The
results indicate that CFOs do not sell their shares after rounding either diluted or basic EPS through
the adjustments of discretionary working capital accruals. We interpret this result as working
capital adjustments being an inefficient way to manage only diluted EPS, as those adjustments
affect both diluted and basic EPS numbers, the latter of which is less important to investors and
managers.
We make several contributions to the literature. First, our study adds to the literature that
documents rounding of reported EPS (Thomas 1989; Das and Zhang 2003), analysts’ EPS
forecasts (Herrmann and Thomas 2005; Dechow and You 2012; Zhou 2010), and managers’ EPS
forecasts (Bamber et al. 2010). A primary focus of this literature is to explore the unusual patterns
in actual (or forecasted) EPS numbers and identify firm (or analyst) specific characteristics that
can explain such patterns. We take a different approach by focusing on the potential benefits that
managers can enjoy following the rounding of reported EPS. By doing so, we provide evidence
5
that highlights managers’ incentives as an important factor behind the unusual patterns of reported
EPS.
Second, we contribute to the insider trading literature. While the bulk of this literature
focuses on whether insider sales are informative about future firm performance (e.g., Beneish and
Vargus 2002; Ke et al. 2003; Lakonishok and Lee 2001; Noe 1999; Piotroski and Roulstone 2005;
Seyhun 1998), several studies focus on earnings patterns prior to insider sales (e.g., Beneish 1999;
McVay et al. 2006; Summers and Sweeney 1998). In particular, closely related to our study is
McVay et al. (2006), which documents that the likelihood of just meeting versus just missing the
analyst forecast is associated with subsequent managerial stock sales. By showing that rounding
diluted EPS also exhibits a significant association with managerial stock sales after controlling for
the effect of just meeting analysts’ forecasts, our study provides evidence that extends, but is
distinct from, McVay et al.’s (2006). In addition, while they use firm-quarter observations where
the quarterly consensus analyst forecast error is between negative two cents and positive one cent,
we seek to provide evidence generalizable to a larger sample that covers virtually all ranges of
forecast errors.
Third, our study adds to the emerging literature on the relative importance of CFO and CEO
incentives for corporate outcomes (e.g., Chava and Purnanandam 2010; Feng et al. 2011; Jiang et
al. 2010; Kim et al. 2011). One consensus from this research is that the incentives of CFOs could
be more influential than those of CEOs in a decision setting where sophisticated financial expertise
is required. Our evidence suggesting that CFOs, but not CEOs, strategically use stock repurchases
to round diluted EPS prior to selling their shares is consistent with the broad theme emerging from
this research, while illustrating CFOs’ incentives in another area—insider stock sales.
6
Finally, our evidence contributes to the literature on limited attention in capital markets
(Hirshleifer and Teoh 2003, Hirshleifer et al. 2011, Huang et al. 2013; Song and Scharwz 2008).
This literature shows that investors rely strongly on subsets of publicly available information that
exhibit higher salience. Given that rounding is a salient and easy-to-observe attribute, our evidence
that equity investors react positively to rounded diluted EPS, but not basic EPS, enhances our
understanding of investor preference for salience in reported earnings.
The remainder of the paper is organized as follows: Section II develops the hypotheses.
Section III describes the data and sample. Section IV presents the research design. Section V
reports the empirical results. Section VI concludes.
II. HYPOTHESIS DEVELOPMENT
The primary objective of this paper is to explore whether managerial trading incentives can
help explain the rounding of reported EPS. We pursue this objective through several stages. First,
we identify the EPS measure that investors focus on and thus has a relatively high likelihood of
being rounded. Second, we establish a direct link between the rounding of that EPS measure and
stock prices. Third, using managerial stock sales as a proxy for managerial incentives, we test for
its association with the EPS rounding. Fourth, we explore the mechanism through which managers
round reported EPS.
Unusual Digit Patterns in Reported EPS: Hypothesis 1
As a first step, we attempt to confirm prior evidence of rounding using the EPS numbers
reported under the current standard, SFAS No. 128. While Thomas (1989) and Das and Zhang
(2003) document the unusual digit patterns using the primary EPS data prior to SFAS No. 128,
7
and Jorgensen et al. (2014) confirm these patterns using annual diluted EPS reported under the
standard, it remains an empirical question as to whether such unusual patterns will hold for basic
and diluted EPS numbers reported quarterly. More importantly, we seek to identify the EPS
measure on which investors tend to focus the most and rely on that measure in pursuing our
primary objective above.
While all firms are required to report basic and diluted EPS under the current rule, recent
evidence suggests that diluted EPS has become the focal measure. Marquardt and Wiedman (2005)
document that analysts forecast diluted EPS, not basic EPS, for 98 percent of their sample firms.
Further, in discussing the decision to require reporting of both diluted and basic EPS under SFAS
No. 128, paragraph 88 indicates that “some respondents noted that they did not find basic EPS to
be a useful statistic and thought that users would focus only on diluted EPS.” Based on these
discussions, Jorgensen et al. (2014) suggest that the focal EPS measure has shifted from primary
EPS under APB No. 15 to diluted EPS under SFAS No. 128, and confirm the unusual digit patterns
using only diluted EPS.
Collectively, prior evidence reflects the relative importance of diluted EPS over basic EPS.
It further indicates that diluted EPS attracts the most attention from investors recently and thus is
likely to be rounded. In contrast, the reduced focus on the basic EPS measure could lead managers
to doubt the potential benefits from rounding this measure. These arguments lead to the following
directional hypothesis:
H1: The unusual digit patterns in reported EPS manifest only for diluted EPS but not for
basic EPS.
8
Market Price Response to Rounded EPS: Hypothesis 2
Before turning to the examination of managerial stock sales, we test for a direct link between
rounding reported EPS and stock prices. A positive investor reaction to rounded EPS would create
a favorable environment for managers planning to sell their stock, leading them to make additional
effort to round EPS.
In this light, we build upon two streams of literature. First, the literature on limited attention
in capital markets generally suggests that information presented in a salient form is absorbed more
easily than information that is less salient and more difficult to process (Hirshleifer and Teoh 2003;
Hirshleifer et al. 2011; Huang et al. 2013; Song and Scharwz 2008). As a result, investors with
limited attention tend to base their decisions on the type of information that is salient and easy to
process, a feature that rounded EPS has. Second, the literature on the rounding of reported EPS
suggests that, if the rounding phenomenon describes managers’ perceptions of how stock is valued
as well as users’ decision making, small changes in reported earnings near user reference points
will have disproportionately large effects on perceived firm value (Carslaw 1988; Thomas 1989).
Taken together, prior evidence implies that equity investors are likely to react positively to
rounded earnings. However, if investors believe that rounded EPS reflects overstatement of firm
performance, then their reaction will not necessarily be positive. Therefore it is an open question
whether the market reaction to rounded EPS is positive. Further, given that the current focal
measure is diluted EPS, we expect such positive reaction to be more pronounced for diluted EPS
than for basic EPS. These arguments lead to the following directional hypothesis:
H2: Equity investors react positively to the unusual digit patterns in diluted EPS but not to
those in basic EPS.
9
Managerial Stock Sales Subsequent to Rounding of EPS: Hypothesis 3
The primary line of research we build upon focuses on earnings patterns prior to insider sales
(e.g., Beneish 1999; McVay et al. 2006; Summers and Sweeney 1998). This line of research
generally suggests that managers’ welfare depends on meeting some earnings thresholds, and
managers with greater net personal benefits to meeting the threshold are more likely to manage
earnings. In particular, McVay et al. (2006) argue that the effect of earnings management on stock
price is likely to have a finite horizon, and, as a result, managers undertaking earnings management
to heighten prices must reap the benefits in this horizon. We draw parallels from this argument to
assess whether managers reap the benefits through selling their shares subsequent to the rounding
of reported EPS.
Our main prediction is that managers anticipate a disproportionately large price reaction to
the reporting of rounded EPS and exert additional effort to round EPS when they plan to sell shares
following the earnings announcement. Evidence consistent with this prediction would help explain
unusual digit patterns in reported EPS in terms of managerial trading incentives. As discussed in
McVay et al. (2006) and Sehyun (1998), however, all insiders in their sales decisions could face
potential insider trading penalties. Most insider trading investigations are spurred by insider
trading that occurs before announcements of earnings, dividends, or takeovers. Since we examine
insider trading that occurs after the earnings announcement, our setting provides a convenient way
for insiders to strategically sell shares without triggering price-drop based penalties. Furthermore,
consistent with H1 and H2, we do not predict any association between managerial insider sales
and rounding of basic EPS. In this light, our main hypothesis, stated in the alternative form, is as
follows:
10
H3: Managers who round diluted EPS have higher managerial insider sales following the
earnings announcement relative to managers who do not round diluted EPS.
Rounding EPS via Stock Repurchases: Hypothesis 4
Our final hypothesis relates to how managers round reported EPS. We posit that insiders sell
shares to strategically profit from their trading (“active trading”). However, insiders could simply
sell after good firm performance (e.g., Heath et al. 1999; Seyhun 1998; McVay et al. 2006).
Examining the mechanism through which managers round reported EPS provides an ideal setting
to distinguish between active and passive trading alternatives.
While EPS can be managed either through the numerator or the denominator, we focus on
the latter, which could be closely related to the rounding of diluted EPS. In particular, Bens et al.
(2003) find that stock repurchases increase in years when options-related EPS dilution increases,
and conclude that executives’ stock repurchase decisions are driven by incentives to manage
diluted EPS, but not basic EPS. Thus, the rounding of diluted EPS is more likely indicative of EPS
management when the level of stock repurchases is abnormally high. Therefore, if we find
evidence that the positive association between rounding of diluted EPS and subsequent managerial
sales is stronger when the level of abnormal stock repurchases is higher, such evidence would be
consistent more with active trading than passive trading. Therefore, our directional hypothesis is
as follows:
H4: Managers who sell stock following the earnings announcement have a higher level of
unexpected stock repurchases to round diluted EPS.
The growing literature on the relative importance of CFO and CEO incentives for corporate
outcomes generally suggests that CFO equity incentives play a stronger role than those of the CEO
11
in earnings management and other decisions related to financial reporting. For example, Jiang et
al. (2010) find that the magnitude of accruals and the likelihood of beating analyst forecasts are
more sensitive to CFO equity incentives than to those of the CEO. Moreover, Chava and
Purnanandam (2010) document that CFOs’ risk-decreasing (-increasing) incentives are associated
with safer (riskier) debt-maturity choices and higher (lower) earnings-smoothing through accruals.
These prior findings highlight the important role of CFOs’ incentives in corporate financial
policies. We extend this literature by testing whether rounding EPS is associated with insider stock
sales undertaken by CFOs and CEOs (test of H3). Further, in order to understand the mechanism
through which reported EPS is rounded, we investigate whether, prior to selling their shares, CFOs
(and CEOs) strategically use stock repurchases (test of H4), a decision that requires specialized
knowledge in accounting and finance.
III. DATA AND SAMPLE SELECTION
The data for the main tests in this study are gathered from the following sources: (1) Thomson
Financial insider trading database, (2) Compustat for financial information, (3) Execucomp for
stock option data, (4) CRSP for stock returns, and (5) I/B/E/S for analyst forecasts. Sample size
varies with the data requirement for each test.
Table 1 summarizes the sample selection process. Our initial sample of 183,963 firm-quarter
observations starts with the intersection of Compustat Quarterly File and I/B/E/S Unadjusted
Quarterly Files for fiscal years between 1999 and 2012. We choose 1999 as our first sample year
because SFAS No. 128 was implemented for firms whose fiscal year ends after December 15,
1997. We next exclude financial firms (SIC codes 6000 – 6999) and utility firms (based on Fama
and French (1997) 48 industry classification). Following Jorgensen et al. (2014), we only keep
12
observations where both reported basic and diluted EPS are within the range of -$1.00 and $2.50.5
We also delete observations with price per share less than a dollar and market value of equity less
than $5 million.
Next, we drop data where the variables used in the regressions for H1 and H2 are missing.
Further, we eliminate observations which have the opposite signs between basic and diluted EPS
or the opposite signs between reported EPS and calculated EPS. The final sample for H1 and H2
consists of 118,513 firm-quarter observations and 6,561 unique firms. Finally, we restrict the firmquarters to have non-missing values of insider transactions by CEOs and CFOs and abnormal stock
repurchase. Our final sample for H3 and H4 contains 12,108 firm-quarter observations and 3,237
unique firms.
IV. RESEARCH DESIGN
Test of H1: Comparison of Digit Management between Diluted EPS and Basic EPS
H1 predicts that the unusual digit patterns in reported EPS are more pronounced for diluted
EPS than for basic EPS. In order to test this hypothesis, we replicate results from Thomas (1989)
and Das and Zhang (2003), respectively. First, we compare the distribution of the last EPS digits
(i.e., cents) reported in Compustat between diluted EPS (item: EPSFXQ) and basic EPS (item:
EPSPXQ). Following Thomas (1989), to assess the statistical significance of each EPS reporting
irregularity, we use local last-cent referents under the null that the distribution should be “smooth.”
For example, the expected proportion of $0.05 observations is the mean proportion of $0.04 and
$0.06 observations. We then use the percent deviations from expectations and compute the median
value of the deviations for each last digit and conduct a signed rank test on the distribution of
5
Note that this requirement increases the power of our test since EPS digits are less likely to be managed
when the absolute magnitude of the EPS is large (Thomas 1989; Das and Zhang 2003).
13
median values. We expect that zeros and fives are overrepresented whereas nines are
underrepresented, relative to expectation, for nonnegative diluted EPS but not for basic EPS.6
Essentially, we use the setting of basic EPS as a ‘control group’ since each pair of diluted and basic
EPS numbers is computed for the same firm and quarter observations where the underlying
transactions can be held constant.
Second, similar to Das and Zhang (2003), the third digits of diluted (basic) EPS are
calculated by dividing total earnings (item: IBQ) by the number of diluted (basic) shares (items:
CSHFDQ and CSHPRQ). Under the null hypothesis of no rounding EPS, one would expect 50%
of the sample firms to round-up purely by chance. Thus, observing a greater proportion of the third
digits between 5 and 9 for positive earnings and a greater proportion of the third digits between 0
and 4 for negative earnings would indicate EPS being rounded-up by management. We compare
the distribution of the third EPS digits (i.e., one tenth of a cent) between diluted EPS and basic
EPS and predict that the third digit management is prevalent for diluted EPS but not for basic EPS.
Test of H2: Market Reaction to EPS Digit Management
We test H2 with the following regression model, with industry, year, and quarter fixed
effects included and standard errors clustered by firms (Petersen 2009). All continuous variables
are winsorized at the top and bottom 1% levels. We suppress the subscripts for brevity.
BHAR (-1,+1) = 0 + 1 ESUR + 2 DIGITMGT + 3 ESUR × DIGITMGT + 4 BEAT
+ 5 PROFIT + 6 LNMV + 7 B/M + Σ β (ESUR × Controls)
+ Σ γ (Industry Effects) + Σ δ (Year Effects) + Σ η (Quarter Effects) + ε,
6
(1)
We do not offer prediction based upon negative EPS because the patterns in the second digit for negative
earnings are not, a priori, manifest (see Thomas (1989) and Jorgensen et al. (2014)).
14
where BHAR (-1,+1) is the three-day (-1, +1) market-adjusted buy-and-hold return around the
earnings announcement date, and ESUR is calculated as the difference between the current quarter
EPS and the previous fourth quarter EPS deflated by price at the end of prior fourth quarter. We
estimate regression model (1) separately for diluted EPS and basic EPS.
DIGITMGT, our proxy for management EPS rounding, is an indicator variable which
equals one if the second digit of the reported EPS is zero or five and if the third digit of the
calculated EPS falls in the interval of 5 and 9, and zero otherwise. In other words, we expect
stronger market reactions when the unusual digit patterns are observed both for Thomas (1989)
and Das and Zhang (2003), compared with when each pattern is observed alone. 7 If the digit
rounding is for diluted (basic) EPS, we denote D (B) for the last letter in the variable. The variable
of interest is the interaction term, ESUR × DIGITMGT. We expect 3 to be positive if the rounding
relates to diluted EPS, indicating that investors’ reaction to earnings news is greater when the
diluted EPS digit is rounded by management. On the contrary, we do not expect any incremental
market reaction to earnings news when the basic EPS digit is rounded by management.
Turing to the control variables, we first include BEAT, an indicator variable which equals
one if the firm exceeds analysts’ consensus earnings forecasts, and zero otherwise. BEAT is
positively associated with the abnormal return around earnings announcement date (Bartov et al.
2002; Lopez and Rees 2002), and the propensity to EPS digit rounding (Das and Zhang 2003). We
also include PROFIT, an indicator variable which equals one if firm’s earnings before
extraordinary items is nonnegative. We control for PROFIT since both Hayn (1995) and Basu
(1997) find that the magnitude of earnings response coefficient (ERC) is asymmetric between
Thus, in response to Burgstahler’s (2014) inquiry as to whether incentives to manage the third digit of
EPS depend on the second digit of EPS, we take the perspective that management of the third digit is driven
primarily by those cases where rounding up will bring the second digit to a multiple of $0.05.
7
15
quarters with losses and profits. Finally, LNMV and B/M are included to control for firm risk and
information environment. LNMV is the logarithm of the market capitalization, which equals the
number of shares outstanding times the end of quarter price. B/M is calculated as the ratio of book
value of equity to market value of equity.
Test of H3: Insider Stock Sale subsequent to EPS Digit Management
Our model specification for H3 is based on firm fixed effects regression with year and
quarter fixed effects included, and estimated separately for diluted EPS and basic EPS. All
continuous variables are winsorized at the top and bottom 1% levels.
NST = 1 DIGITMGT + 2 FESUR + 3 ESUR + 4 BEAT + 5 PROFIT + 6 LNMV
+ 7 B/M + 8 PRIORRET + 9 POSTRET + 10 EVENTRET + 11 GRANTS_INSIDER
+ 12 OPTEXER_INSIDER + 13 EXCDUM_INSIDER + Σ β (Year Effects)
+ Σ γ (Quarter Effects) + ε,
(2)
where NST is the net number of shares sold by insiders (Beneish and Vargus 2002). More
specifically, for each day, we first compute the difference between the number of shares of insider
sales and insider purchases each deflated by the number of shares outstanding on the same day.
We focus only on open market transactions (Beneish and Vargus 2002; Ke et al. 2003; McVay et
al. 2006). Then, the net proportion of shares sold is summed over each firm-quarter. The trading
window is between two days after the earnings announcement date and the end of the fiscal quarter
following Ke et al. (2003). To facilitate interpretation of the coefficient, we multiply NST by 100.
We consider only the CFO and CEO insiders, and define insiders in two different ways: (1) CFOs
only, and (2) CEOs only. Thus, we estimate model (2) separately by replacing NST with CFONST,
and CEONST depending on insider definitions.8
8
Later, we include other top executives, such as COOs, presidents, and board chairs, as a robustness check.
16
Our main interest variable is DIGITMGT. Similar to model (1), we estimate regression
model (2) separately for diluted EPS (“DIGITMGTD”) and basic EPS (“DIGITMGTB”). If
managers (i.e., CEOs and/or CFOs) who rounded diluted EPS profit from their sales, the
coefficient on DIGITMGTD will be positive. Since there is less managerial incentives to round
basic EPS, we offer no prediction on the coefficient on DIGITMGTB.
We control for various firm-specific factors affecting managers’ decision to trade shares.
Future earnings surprise (FESUR), current earnings surprise (ESUR), and future sock return
(POSTRET) are included in the model to control managers’ superior knowledge of firms’ future
earnings news and are expected to be negatively correlated with net insider sales (Seyhun 1998;
Ke et al. 2003; Piotroski and Roulstone 2005). FESUR is the difference between the future fourth
quarter EPS and the current quarter EPS deflated by price at the end of current quarter. POSTRET
is the stock return over the 12 months following the earnings announcement month. We also
include BEAT since McVay et al. (2006) find that insiders are more likely to sell shares after the
earnings announcement when the firm exceeds analysts’ earnings forecasts, thus 4 is expected to
be positive. LNMV and B/M control for the effect of firm size and book-to-market ratio on insider
sales. Following Lakonishok and Lee (2001) and Rozeff and Zaman (1998), we predict that the
coefficient on LNMV (B/M) to be positive (negative). Since insiders are contrarian traders, both
PRIORRET and EVENTRET are expected to be positively associated with insider sales (Ke at al.
2003). PRIORRET is the stock return for the 12-month period ending on the last day of the month
prior to the month of the earnings announcement date whereas EVENTRET is the return over the
period from one day before to one day after the earnings announcement date.
Prior research documents that insiders’ trading behavior is influenced by changes in their
holdings due to the receipt of stock and option grants and the exercising of stock options (Ofek
17
and Yermack 2000; Piotroski and Roulstone 2005). Accordingly, we control for the effect on
subsequent insider sales of the following compensation-related changes in insider holdings: the
number of shares of restricted stock and stock options granted, and the number of stock options
exercised. Specifically, we define GRANTS_CFO (GRANTS_CEO) as the log of one plus the
percentage ratio of the sum of the number of options and shares of restricted stock granted to the
CFOs (CEOs) during the fiscal year to total outstanding shares at the end of the year. Similarly,
we define OPTEXER_CFO (OPTEXER_CEO) as the log of one plus the percentage ratio of the
sum of the number of options exercised by the CFOs (CEOs) during the fiscal year to total
outstanding shares at the end of the year. Since these option-related variables are measured on an
annual basis, we use the annual value for all quarters during the year. Also, in order to avoid losing
lots of observations, we add EXCDUM_CFO (EXCDUM_CEO), which is an indicator variable set
to one if the option-related variables for CFOs (CEOs) are not provided by Execucomp and zero
otherwise.9
Test of H4: Insider Stock Sale subsequent to EPS Digit Management via Abnormal Stock
Repurchase
Our firm fixed effects regression specification for H4 is similar to model (2) except that
we additionally include ABREPUR and the interaction term of DIGITMGT and ABREPUR. All
continuous variables are winsorized at the top and bottom 1% levels.
NST = 1 DIGITMGT + 2 ABREPUR + 3 DIGITMGT × ABREPUR + Σ β (Controls)
+ Σ γ (Year Effects) + Σ δ (Quarter Effects) + ε,
9
See, e.g., Rauh (2009, p.2507) for the use of an indicator variable defined for missing values.
18
(3)
where ABREPUR is the number of shares of abnormal stock repurchases during the fiscal quarter.
We follow the procedure described in Hribar et al. (2006) to measure ABREPUR.10 H4 posits that
insiders who sell shares after rounding the diluted EPS digit are more likely to do so when the
level of stock repurchases are abnormally high. Therefore, we expect 3 to be positive for
DIGITMGTD, implying that stock repurchases are effective tools to round diluted EPS and that
insiders opportunistically benefit by selling their shares after the earnings announcement date. We
do not offer any prediction on the model using basic EPS. The rest of the control variables are
defined as previously.
V. EMPIRICAL RESULTS
Descriptive Statistics
In Table 2, we report the descriptive statistics for our sample. Panel A tabulates the firm
characteristics of the sample for H1 and H2. The mean (median) of BHAR (-1,+1) is 0.3% (0.2%).
On average, 8.3% of the firms rounded diluted EPS and 7.4% of the firms rounded basic EPS. The
average market value is $0.87 billion (= e6.770) which is somewhat smaller than that reported in Ke
et al. (2003). About 60.4% of our firms exceeded analysts’ earnings forecasts similar to McVay et
al. (2006).
Panel B presents firm characteristics of the sample for H3 and H4. In this subsample, we
require that both CEOs and CFOs trade their shares during the quarter, and there are non-missing
values for abnormal stock repurchases (ABREPUR). CEO net quarterly sales after the earnings
announcement date is five times as large as CFO net quarterly sales. CEO net sales are, on average,
0.238% of the total outstanding shares. Similar to the sample in Panel A, firms are more likely to
10
For more discussions, refer to Appendix A.
19
round diluted EPS (8.2%) than basic EPS (7.1%). The average level of abnormal stock repurchase
during the fiscal quarter is close to zero.
Test of H1: Comparison of Digit Management between Diluted EPS and Basic EPS
Table 3 reports the distribution of the last digit of EPS reported in Compustat. We focus
primarily on nonnegative EPS since the patterns in the second digit rounding are not manifest for
negative EPS (Thomas 1989; Jorgensen et al. 2014). Similar to Thomas (1989), Panel A shows
that there are significantly more zero cents and less nine cents than expectation using the Spearman
signed-rank test for the diluted EPS. For example, the actual proportion of the zero cents is 10.5%
while the actual proportion of the nine cents is 8.5%. However, the results are quite different for
basic EPS. In Panel B of Table 3, we do not observe unusual patterns in the last digit, particularly
for the zero (10.0%) and nine cents (8.9%). We emphasize again that the firms in Panels A and B
are held constant except that only the per share earnings numbers differ. Therefore, the results
indicate that managers are likely to round only the second digit of diluted EPS, which is the primary
performance measure for investors.
In Table 4, we replicate Das and Zhang (2003) and compare the results between diluted
EPS and basic EPS. X refers to the third digit (i.e., one tenth of a cent) of the calculated EPS. In
Panel A, we find that the first digit immediately right of the decimal EPS is more likely to be equal
to or greater than 5 cents when firms report nonnegative EPS. On the other hand, the proportion
of the third digit is abnormally high for firms with X between 0 and 4 and abnormally low for firms
with X between 5 and 9 when firms report negative EPS. Thus, our results confirm prior evidence
that firms round up the third digit of EPS, using quarterly diluted EPS (as opposed to primary EPS
as in Das and Zhang (2003) and annual diluted EPS as in Jorgensen et al. (2014)). Next we turn to
20
Panel B. Although the third digit patterns of basic EPS are similar to those of diluted EPS when
firms report negative earnings, the proportion of firms reporting X at least five cents are not
significantly different from that of firms reporting X smaller than five cents (p-value = 0.12).
Results in Panels A and B show that firms manage the diluted EPS digit but not the basic EPS
digit. In sum, we provide evidence consistent with our hypothesis that the unusual digit patterns
are observed only for diluted EPS but not for basic EPS.
Test of H2: Market Reaction to EPS Digit Management
Table 5 presents the regression results of the stock market reactions to rounded EPS. In
columns (1) and (2), the results are presented based on the sample described in Table 1. We also
repeat the analysis requiring firms to report profit in columns (3) and (4) because EPS digit
management is more prevalent when firms report positive earnings (see Tables 3 and 4). The
results are similar across the two samples. In addition, for each sample, we separately report the
incremental market reactions to diluted EPS and basic EPS. Therefore, ESUR is calculated using
the seasonal difference of diluted (basic) EPS in columns (1) and (3) (columns (2) and (4)).
We find that investors positively react to earnings news regardless of the EPS types. More
importantly, we find differential investor reaction to EPS rounding between diluted EPS and basic
EPS. The interaction term, ESUR × DIGITMGTD, is positive (coefficient = 0.087) and significant
(t-statistic = 2.53), implying that stock investors more strongly react to earnings news when the
diluted EPS is rounded. On the other hand, there is no incremental market reaction to earnings
news when the basic EPS is rounded (coefficient = 0.000, t-statistic = 0.01), consistent with our
hypothesis. In essence, we document a possible mechanism through which insiders
opportunistically profit from the favorite market reaction to diluted EPS rounding.
21
Test of H3: Insider Stock Sale subsequent to EPS Digit Management
In Panel A of Table 6, we report the univariate results on insider stock sales subsequent to
rounding of EPS. Note that we define insiders in two different ways: (1) CFOs only, and (2) CEOs
only. The results confirm our conjecture that both CFOs and CEOs who round the diluted EPS
have higher insider sales following the earnings announcement date than those who do not round
the diluted EPS. The mean differences are all significant at the 1% levels. However, the same
applies to basic EPS, that is, insider sales are greater for firm with rounded basic EPS, contrary to
our expectation. Since controlling for factors (e.g., BEAT and EVENTRET) associated with both
managers’ decision to round EPS and trade insider shares (Das and Zhang 2003; McVay et al.
2006) is important, we instead rely on the firm fixed effects regressions to interpret the results.
Panel B shows that the rounding of diluted EPS digit is positively related to managerial
insider net sales. The coefficient on DIGITMGTD is positive and statistically significant at the 5%
level or lower in columns (1) and (3). For example, the insider stock sales (as a percentage of the
number of shares outstanding) undertaken by CFOs (CEOs) during the subsequent quarter are
higher by 0.7 (3.2) basis points when the firm rounds diluted EPS, compared with when the firm
does not. More importantly, contrary to the univariate analysis, we do not observe any association
between DIGITMGTB and insider sales. The coefficients on DIGITMGTB are all close to zero,
indicating that increases in managers’ net sales occur only after rounding diluted EPS not basic
EPS. Taken together, these results are consistent with our main prediction that managers who
round EPS have higher insider stock sales following the earnings announcement, relative to
managers who do not round EPS.
We also report that insiders are more likely to sell shares after firms exceeded the analysts’
forecast benchmark, consistent with McVay et al. (2006). For example, in column (3), the
22
coefficient on BEAT is 0.043 (t-statistic = 4.48), a similar magnitude to the coefficient on
DIGITMGTD (coefficient = 0.032, t-statistic = 2.14). We confirm prior literature that insiders are
generally contrarian traders because insider sales are positively associated with PRIORET and
EVENTRET, and negatively associated with B/M. Furthermore, insiders are likely to possess
superior knowledge of firm future performance. The coefficients on future 12 month stock return
(POSTRET) are negatively related to insider sales for all specifications. Considering the evidence
shown in Tables 5 and 6, insiders who rounded diluted EPS are likely to be successful in
opportunistically benefiting from their sales.
Test of H4: Insider Stock Sale subsequent to EPS Digit Management via Abnormal Stock
Repurchase
Table 7 reports the regression results of how insiders round EPS. We summarize the results
as follows. First, insiders are likely to achieve rounding EPS via abnormal stock repurchase. Both
DIGITMGTD and DIGITMGTD × ABREPUR are positive in columns (1) and (3), implying that
managers sell more stocks if the digit in diluted EPS is rounded up by repurchasing more optionrelated stocks (i.e., lowering the denominator of diluted EPS). However, the association between
insider sales and stock repurchase is mainly driven by CFOs. While the coefficient on
DIGITMGTD × ABREPUR is positively significant for CFOs (coefficient = 1.394, t-statistic =
3.89), the same coefficient is not statistically significant for CEOs (coefficient = 1.885, t-statistic
= 1.19). The F-test also indicates that the sum of the coefficients on DIGITMGTD and
DIGITMGTD × ABREPUR is significant only for CFOs (F-statistic = 15.30) but not for CEOs (Fstatistic = 1.47). We interpret these results as CFOs’ incentives being more important than CEOs’
incentives in making decisions on corporate financial policies, such as stock repurchases,
23
particularly because CFOs have more specialized knowledge in accounting and finance. Second,
all the results based on basic EPS are not significant, consistent with our conjecture and previous
evidence documented above.
Overall, the results from Table 7 suggest that the positive association between rounding of
diluted EPS and CFOs’ subsequent stock sales is stronger when the level of abnormal stock
repurchases is higher, consistent with the active trading story. The results further imply that
insiders, especially CFOs, opportunistically profit from selling their shares after rounding EPS via
stock repurchases.11
Additional Analyses
In this section, we conduct several alterative analyses and report the sensitivity results in
Table 8. First, we replace CFONST, the ratio of the number of net sales to the number of shares
outstanding, with CFONST_VALUE. Similar to Noe (1999) and Jenter (2005), CFONST_VALUE
is measured as the difference in square root of the dollar value of insider sales and insider purchases
deflated by the square root of market value of the firm. We obtain similar results in columns (1)
and (2). For example, both DIGITMGTD and the interaction term with ABREPUR are positive and
significant at the 5% levels.
Second, we examine whether other insiders, such as COOs, presidents, and chairmen,
exhibit insider trading behavior, similar to CFOs and CEOs. Specifically, we repeat the analyses
by replacing CFONST with OTHERSNST, which is calculated as the net number of shares sold by
the other three executives: COOs, presidents, and chairmen. These insiders, compared with CFOs
11
The sample in Tables 6 and 7 include both profit and loss firms. We obtain similar results when we repeat
the analyses only for profit firms (n=9,153). For example, the coefficients on DIGITMGTD and
DIGITMGTD × ABREPUR are 0.008 (t-statistic = 2.26) and 1.440 (t-statistic = 3.51), respectively.
24
(or CEOs), are less likely to have the ability to round EPS when they want to sell their shares.
These insiders are also unlikely to strategically use a stock repurchase, which requires specialized
knowledge in accounting and finance. Hence, we expect to find neither an increase in their stock
sales following the rounding of diluted EPS nor an incremental increase in their subsequent sales
following abnormal stock repurchases. Columns (3) and (4) report the results. As shown,
DIGITMGTD as well as DIGITMGTD × ABREPUR enters the regressions insignificantly,
consistent with our conjecture. This result provides further assurance that our baseline results are
driven by managers’ strategic behavior, rather than the passive performance alternative.
Finally, we test whether CFOs round up the digit of diluted EPS through working capital
accruals. Das and Zhang (2003) find that firms use working capital accruals to boost earnings for
rounding purposes. Consequently, CFOs’ net sales could increase after EPS digit management via
discretionary working capital accruals.12 We tabulate the results in columns (5) and (6). The results
show that CFOs do not sell shares after rounding either diluted EPS or basic EPS through
discretionary working capital accruals. This is in fact consistent with our previous findings because
working capital adjustments before the end of quarter affect both the diluted and basic EPS (i.e.,
the numerator effect), and thus could be a less efficient way to round only diluted EPS, compared
with stock repurchases. This result therefore confirms our previous finding that CFOs, prior to
selling their shares, use stock repurchases to round diluted EPS, which matters to investors and
managers more than basic EPS.
12
Following Das and Zhang (2003) and McVay et al. (2006), we measure discretionary working capital
accruals by estimating the residuals from the following cross-sectional regression for each industry and
quarter: WC/Assets = (1/Assets) + β(∆Cash Sales/Assets) + ε, where WC = (∆Current Assets - ∆Cash) –
(∆Current Liabilities - ∆Current Portion of Debt). We require each industry-year to have at least ten firms
included.
25
VI. CONCLUSIONS
This study examines whether insiders strategically profit from selling shares after
rounding the reported EPS. Following previous literature (e.g., Thomas 1989; Das and Zhang,
2003), we define rounding EPS when the last digit of reported EPS is either zero or five and when
the one tenth of a cent of calculated EPS lies between 5 and 9 cents for profit firms.
The results are summarized as follows: First, we find that the unusual digit patterns in
reported EPS are observed only for the diluted EPS but not for the basic EPS after the mandatory
adoption of SFAS No. 128, implying managers’ incentive to round only the EPS number which
investors focus on. Second, we provide direct evidence that investors’ reaction to earnings news
is more pronounced when the diluted EPS is rounded whereas the incremental reaction is muted
to the rounding of basic EPS, which is corroborating evidence on why managers opportunistically
round the diluted EPS. Third, our firm fixed effects regressions results show that insiders who
round the diluted EPS are more likely to sell shares after the earnings announcement than those
who do not. Finally, we find that insiders, particularly CFOs who have greater incentives and
opportunities to make financial decisions, are able to achieve the rounding of diluted EPS via
abnormal stock repurchase prior to selling their shares. Collectively, our evidence is suggestive of
managerial trading incentives explaining the behavior of rounding patters of EPS.
This paper contributes primarily to the literature on both rounding of reported EPS and
insider trading. We identify a more generalized factor, i.e., insider trading profits, to explain the
rounding behavior of EPS even after controlling for managers’ incentive to exceed analysts’
earnings forecasts (Das and Zhang 2003; McVay et al. 2006). We also add to the literature by
documenting the importance of CFOs’ incentives, relative to CEOs’ incentives, in explaining firms’
decision to repurchase stock. Lastly, this study relates to the literature on limited attention in the
26
capital markets (e.g., Hirshleifer and Teoh 2003; Hirshleifer et al. 2013). Our evidence that
investors react more positively to rounded EPS, which is in a salient form, is consistent with
investors’ fixation on information easier to process.
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Appendix A. Estimation of Abnormal Stock Repurchase
We follow the procedures described in Dittmar (2000) and Hribar et al. (2006) to measure
the level of abnormal stock repurchase at the firm-quarter level. First, we impose several sample
restrictions that: (1) exclude financials and utilities, (2) exclude firms if the ratio of the number of
stock repurchase to the number of shares outstanding is larger than 20%, and (3) require nonmissing values for variables used in H3 and H4. Next, we adopt the Heckman (1976) two-stage
regression approach to compute the level of abnormal stock repurchase. In the first stage, we
estimate the following probit model:
Prob. (DREPUR= 1)i,t = 0 + 1 DREPUR1i,t-1 + 2 DREPUR2i,t-2 + 3 CASHi,t-1 + 4 CAPEXi,t-1
+ 5 DIVYIELDi,t-1 + 6 DEBTi,t-1 + 7 SIZEi,t-1 + Σ β (Industry Effects)
+ Σ γ (Year Effects) + Σ δ (Quarter Effects) + ε
(A.1)
DREPUR is an indicator variable which equals one if the firm repurchased stock during the quarter,
zero otherwise. DREPUR1 (DREPUR2) is the one-quarter (two-quarter) lagged value of DREPUR.
CASH is cash and equivalents divided by lagged total assets. CAPEX is the average of capital
expenditure during the previous four quarters. DEBT is calculated as the ratio of short-term plus
long-term debt to lagged total assets. SIZE is logarithm of the lagged total assets.
Panel A of Table A.1 presents the results on estimating the first-stage model. There are
12,108 firm-quarter observations, including 2,591 (about 21.40%) firm-quarters with stock
repurchase and 9,517 (about 78.60%) firm-quarters without stock repurchase. Except for CASH
and DIVYIELD, all explanatory variables are significant with the signs consistent with predictions.
The Pseudo R2 is 46.1%, even higher than that reported in Hribar et al. (2006).
In the second stage, we replace DREPUR with REPUR, the dollar value of the stock
repurchase. Furthermore, we calculate the probability density function (PDF) and the cumulative
density function (CDF) and include PDF as a regressor and multiply CDF by each independent
31
variable used in the first stage to order to calculate the expected level of stock repurchase (Maddala
1983). We present the estimated results in Panel B. All variables, except for DIVYIELD, are
consistent with prior expectations, and the adjusted R2 is about 39%. Finally, we divide the residual
from the second-stage regression by the beginning market value of the firm to obtain the number
of shares of abnormal stock repurchase (ABREPUR).
TABLE A.1
Estimation of Abnormal Stock Repurchase
Panel A: First Stage Probit Regression
Variables
DREPUR1
DREPUR2
CASH
CAPEX
DIVYIELD
DEBT
SIZE
Industry / Year / Quarter Fixed Effects
n
Pseudo R2
Dependent Variable: DREPUR
Predicted Sign
Coefficient
Wald χ2
(+)
1.310***
1270.24
(+)
0.741***
397.49
(+)
-0.195**
5.58
(-)
-2.179*
2.84
(+)
-0.528
0.01
(-)
-0.545***
32.22
(+)
0.053***
24.81
Yes
12,108
0.461
Panel B: Second Stage Regression
Variables
PDF
CDF × REPUR1
CDF × REPUR2
CDF × CASH
CDF × CAPEX
CDF × DIVYIELD
CDF × DEBT
CDF × SIZE
Industry / Year / Quarter Fixed Effects
n
Adjusted R2
Dependent Variable: REPUR
Predicted Sign
Coefficient
t-statistic
(+) / (-)
-5.385***
-6.54
(+)
0.155***
33.46
(+)
0.082***
18.32
(+)
1.694*
1.86
(-)
-52.419***
-3.21
(+)
-4.985
-0.08
(-)
-5.068***
-4.42
(+)
0.989***
13.40
Yes
12,108
0.390
32
TABLE 1
Sample Construction
Firm-quarters between fiscal years 1999 and 2012:
Intersection of Compustat and I/B/E/S
Less:
Financials and utilities
Basic and diluted EPS outside the range of -$1.00 and
$2.50
Penny stocks
Missing data for variables used in the regressions
Opposite sign between diluted and basic EPS, or
opposite sign between reported and calculated EPS
Sample for H1 and H2
Less:
Missing data for variables used in the regressions
Sample for H3 and H4
Number of
Firm-quarters
Number of
Firms
183,963
9,123
(41,848)
(1,999)
(5,461)
(50)
(3,723)
(8,092)
(90)
(359)
(6,326)
(64)
118,513
6,561
(106,405)
(3,324)
12,108
3,237
Table 1 presents the sample selection process. We start with the intersection of Compustat Quarterly File
and I/B/E/S Unadjusted Quarterly File for fiscal years between 1999 and 2012. We exclude financial firms
(SIC codes 6000 – 6999) and utility firms (based on Fama and French (1997) 48 industry classification).
We also drop firms whose Basic and diluted EPS are outside the range of -$1.00 and $2.50. Next we delete
penny stocks whose price per share is smaller than a dollar and the market value of the firm is less than $5
million. After restricting the sample to have non-missing data for variables used in the regression for H1
and H2, and after excluding observations where diluted and basic EPS have the opposite sign or where
reported and calculated EPS have the opposite sign, the sample for H1 and H2 contains 118,513 firmquarter observations. Finally, we require firms to have non-missing values of insider transactions by CEO
and CFO, and delete missing observations for abnormal stock repurchase. Our sample for H3 and H4
consists of 12,108 firm-quarter observations.
33
TABLE 2
Descriptive Statistics
Panel A: Sample for H1 and H2 (n=118,513)
Variables
Mean
BHAR (-1,+1)
0.003
DIGITMGTD
0.083
DIGITMGTB
0.074
ESURD
0.007
ESURB
0.007
BEAT
0.604
PROFIT
0.769
LNMV
6.770
B/M
0.517
SD
0.088
0.276
0.262
0.043
0.044
0.489
0.421
1.740
0.420
P25
-0.042
0.000
0.000
-0.005
-0.005
0.000
1.000
5.531
0.246
Median
0.002
0.000
0.000
0.001
0.001
1.000
1.000
6.628
0.422
P75
0.048
0.000
0.000
0.008
0.008
1.000
1.000
7.861
0.676
Panel B: Sample for H3 and H4 (n=12,108)
Variables
Mean
CFONST
0.050
CEONST
0.238
DIGITMGTD
0.082
DIGITMGTB
0.071
ABREPUR
0.000
PROFIT
0.756
BEAT
0.536
FESURD
0.000
FESURB
0.000
ESURD
0.010
ESURB
0.011
LNMV
6.401
B/M
0.482
PRIORRET
0.381
EVENTRET
0.015
POSTRET
0.136
GRANTS_CFO
0.000
OPTEXER_CFO
0.000
EXCDUM_CFO
0.778
GRANTS_CEO
0.001
OPTEXER_CEO
0.001
EXCDUM_CEO
0.507
SD
0.107
0.474
0.274
0.256
0.013
0.430
0.499
0.041
0.041
0.052
0.054
1.763
0.433
0.945
0.105
0.623
0.001
0.001
0.415
0.003
0.003
0.500
P25
0.000
0.002
0.000
0.000
-0.002
1.000
0.000
-0.006
-0.006
-0.004
-0.004
5.254
0.218
-0.139
-0.040
-0.246
0.000
0.000
1.000
0.000
0.000
0.000
Median
0.019
0.085
0.000
0.000
0.000
1.000
1.000
0.001
0.001
0.002
0.002
6.462
0.382
0.183
0.011
0.048
0.000
0.000
1.000
0.000
0.000
1.000
P75
0.065
0.301
0.000
0.000
0.001
1.000
1.000
0.007
0.007
0.011
0.011
7.519
0.610
0.589
0.068
0.372
0.000
0.000
1.000
0.001
0.000
1.000
34
TABLE 2 (continued)
Table 2 reports the firm characteristics of our sample. Panel A presents the sample for H1 and H2 whereas
Panel B shows the sample for H3 and H4. All continuous variables are winsorized at the top and bottom 1%
levels. BHAR (-1,+1) is the three-day (-1, +1) market-adjusted buy-and-hold return around the earnings
announcement date. DIGITMGTD (DIGITMGTB) is an indicator variable which equals one if the second
digit of the reported diluted (basic) EPS is zero or five and if the third digit of the calculated diluted (basic)
EPS falls in the interval of 5 and 9, and zero otherwise. ESURD (ESURB) is calculated as the difference
between the current quarter diluted (basic) EPS and the previous fourth quarter diluted (basic) EPS deflated
by price at the end of prior fourth quarter. BEAT, an indicator variable which is one if the firm exceeds
analysts’ consensus earnings forecasts, and zero otherwise. PROFIT is an indicator variable which equals
one if firm’s earnings before extraordinary items is nonnegative. LNMV is the logarithm of the market
capitalization, which equals the number of shares outstanding times the end of quarter price. B/M is
calculated as the ratio of book value of equity to market value of equity.
CFONST (CEONST) is the net number of shares sold by CFOs (CEOs). More specifically, for each day,
we first compute the difference between the number of shares of insider sales and insider purchases each
deflated by the number of shares outstanding on the same day. Then, the net proportion of shares sold is
summed over each firm-quarter. The trading window is between two days after the earnings announcement
date and the end of the fiscal quarter. To facilitate interpretation of the coefficient, we multiply NST by 100.
ABREPUR is the level of abnormal stock repurchases, as defined in Appendix A. FESURD (FESURB) is
the difference between the future fourth quarter diluted (basic) EPS and the current fourth quarter diluted
(basic) EPS deflated by the price at the end of current quarter. PRIORRET is the stock return for the 12month period ending on the last day of the month prior to the month of the earnings announcement date
whereas EVENTRET is the return over the period from one day before to one day after the earnings
announcement date. POSTRET is the stock return over the 12 months following the earnings announcement
month.
GRANTS_CFO (GRANTS_CEO) is the log of one plus the percentage ratio of the sum of the number of
options and shares of restricted stock granted to the CFO (CEO) during the fiscal year to total outstanding
shares at the end of the year. OPTEXER_CFO (OPTEXER_CEO) is the log of one plus the percentage ratio
of the sum of the number of options exercised by the CFO (CEO) during the fiscal year to total outstanding
shares at the end of the year. Since these option-related variables are measured on an annual basis, we use
the annual value for all quarters during the year. EXCDUM_CFO (EXCDUM_CEO) is an indicator variable
which equals one if the option-related variables for CFOs (CEOs) are not provided by Execucomp and zero
otherwise.
35
TABLE 3
Distribution of the Second Digits for Reported Diluted EPS and Basic EPS
Panel A: Diluted EPS
Second Digit
Nonnegative Median Diff. (%)
EPS
p-value
(n=91,132)
Actual Proportion
0
14.872
0.039
0.105
1
-6.326
0.082
0.108
2
4.348
0.088
0.108
3
-0.674
0.407
0.103
4
-1.167
0.948
0.100
5
-2.564
0.530
0.101
6
2.795
0.150
0.099
7
-5.913
0.001
0.094
8
5.886
0.004
0.096
9
-14.546
0.002
0.085
Median Diff. (%) -87.349
Negative EPS
p-value
0.004
(n=27,381)
Actual Proportion 0.011
76.927
0.002
0.119
-2.257
0.432
0.120
2.854
0.432
0.122
-2.300
0.625
0.115
-0.519
0.432
0.112
3.248
0.375
0.108
0.708
0.695
0.103
-1.051
0.625
0.097
74.454
0.002
0.093
Panel B: Basic EPS
Second Digit
Nonnegative Median Diff. (%)
EPS
p-value
(n=91,132)
Actual Proportion
0
-0.452
0.948
0.100
1
3.922
0.378
0.110
2
2.857
0.117
0.107
3
-2.768
0.064
0.103
4
4.135
0.030
0.102
5
-2.436
0.208
0.100
6
-1.942
0.907
0.099
7
-3.793
0.393
0.094
8
6.346
0.154
0.097
9
-4.918
0.205
0.089
Median Diff. (%) -87.452
Negative EPS
p-value
0.004
(n=27,381)
Actual Proportion 0.011
75.724
0.002
0.119
-2.418
0.432
0.120
2.629
0.432
0.122
-2.251
0.492
0.115
0.305
0.695
0.112
3.560
0.375
0.108
1.098
0.695
0.103
-0.842
0.625
0.097
75.035
0.002
0.094
Table 3 reports the distribution of the last digit of EPS reported in Compustat. The sample contains 118,513 firm-quarter observations for the period
between 1999 and 2012. Panel A tabulates the distribution of diluted EPS (EPSFXQ) whereas Panel B presents the distribution of basic EPS
(EPSPXQ). The observed proportion (p) for each EPS value is compared with an expected proportion (p0) to obtain the percent difference (= 100 ×
(p – p0)/p0). Expected proportions equal the mean of observed proportion for adjacent EPS values. The median difference is computed for all EPS
values with the same last digits. The p-value refers to a signed-rank test of the null hypothesis that the median difference is 0. The actual proportion
is the percentage of the sample for each last digit.
36
TABLE 4
Distribution of the Third Digits for Calculated Diluted EPS and Basic EPS
Panel A: Diluted EPS
Frequency
Actual Proportion (%)
p-value
n
Nonnegative EPS
0≤X<5
5≤X
42,172
48,960
46.28
53.72
0.000
91,132
Negative EPS
0≤X<5
5≤X
14,513
12,868
53.00
47.00
0.000
27,381
Nonnegative EPS
0≤X<5
5≤X
45,331
45,801
49.74
50.26
0.120
91,132
Negative EPS
0≤X<5
5≤X
14,526
12,855
53.05
46.95
0.000
27,381
Panel B: Basic EPS
Frequency
Actual Proportion (%)
p-value
n
Table 4 provides the results comparing the distribution of the third digits of calculated diluted (basic) EPS,
which are calculated by dividing total earnings (item: IBQ) by the number of diluted (basic) shares (items:
CSHFDQ and CSHPRQ). The sample contains 118,513 firm-quarter observations for the period between
1999 and 2012. Panel A presents results based on diluted EPS, whereas Panel B tabulates results based on
basic EPS. X refers to the third digit of EPS-i.e., the first digit immediately right of the decimal of the
calculated EPS expressed in cents. The p-value refers to Chi-square test with the test proportion equal to
the expected proportion, which is 50%. We compare the distribution of the third EPS digits (i.e., one tenth
of a cent) between diluted EPS and basic EPS.
37
TABLE 5
Market Reaction to Rounded EPS
Variables
ESUR
DIGITMGTD
ESUR × DIGITMGTD
DIGITMGTB
ESUR × DIGITMGTB
BEAT
ESUR × BEAT
PROFIT
ESUR × PROFIT
LNMV
ESUR × LNMV
B/M
ESUR × B/M
Industry Fixed Effects
Year Fixed Effects
Quarter Fixed Effects
n
Adjusted R2
Dependent Variable: BHAR (-1, +1)
Full Sample
Profit Sample
Diluted EPS Basic EPS Diluted EPS Basic EPS
(1)
(2)
(3)
(4)
0.237***
0.231***
0.349***
0.340***
(7.74)
(7.65)
(7.54)
(7.58)
0.000
0.000
(0.55)
(0.45)
0.087**
0.098***
(2.53)
(2.64)
0.001
0.001
(1.47)
(1.44)
0.000
0.001
(0.01)
(0.04)
0.046***
0.046***
0.047***
0.047***
(72.36)
(72.36)
(67.81)
(67.82)
0.006
0.006
0.034
0.032
(0.43)
(0.41)
(1.57)
(1.55)
0.013***
0.013***
(16.90)
(16.80)
0.063***
0.068***
(4.19)
(4.59)
-0.001***
-0.001***
-0.002***
-0.002***
(-8.51)
(-8.53)
(-8.68)
(-8.74)
-0.039***
-0.038***
-0.049***
-0.047***
(-8.60)
(-8.49)
(-8.22)
(-8.04)
0.008***
0.008***
0.010***
0.010***
(10.06)
(10.07)
(9.66)
(9.68)
0.041***
0.040***
0.049**
0.048**
(2.92)
(2.93)
(2.03)
(2.03)
Yes
Yes
Yes
118,513
0.079
Yes
Yes
Yes
118,513
0.079
Yes
Yes
Yes
91,132
0.084
Yes
Yes
Yes
91,132
0.084
***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively, from two-tailed tests.
38
TABLE 5 (continued)
Table 5 presents the results of market response to EPS digit management. The following OLS regression is
estimated with industry, year, and quarter fixed effects included. Standard errors are clustered by firm:
BHAR (-1,+1) = 0 + 1 ESUR + 2 DIGITMGT + 3 ESUR × DIGITMGT + 4 BEAT
+ 5 PROFIT + 6 LNMV + 7 B/M + Σ β (ESUR × Controls)
+ Σ γ (Industry Effects) + Σ δ (Year Effects) + Σ η (Quarter Effects) + ε
Columns (1) and (2) contain the results based on 118,513 firm-quarter observations and columns (3) and
(4) contain the results restricting firms to report profit during the quarter. Results using diluted EPS are
reported in columns (1) and (3) whereas results using basic EPS are reported in columns (2) and (4). BHAR
(-1,+1) is the three-day (-1, +1) market-adjusted buy-and-hold return around the earnings announcement
date. DIGITMGTD (DIGITMGTB) is an indicator variable which equals to one if the second digit of the
reported diluted (basic) EPS is zero or five and if the third digit of the calculated diluted (basic) EPS falls
in the interval of 5 and 9, and zero otherwise. In other words, we assume EPS rounding are more likely to
occur when the unusual digit patterns are observed both for Thomas (1989) and Das and Zhang (2003).
ESURD (ESURB) is calculated as the difference between the current quarter diluted (basic) EPS and the
previous fourth quarter diluted (basic) EPS deflated by price at the end of prior fourth quarter. BEAT, an
indicator variable which is one if the firm exceeds analysts’ consensus earnings forecasts, and zero
otherwise. PROFIT is an indicator variable which equals one if firm’s earnings before extraordinary items
is nonnegative. LNMV is the logarithm of the market capitalization, which equals the number of shares
outstanding times the end of quarter price. B/M is calculated as the ratio of book value of equity to market
value of equity. All continuous variables are winsorized at the top and bottom 1% levels. Refer to Table 2
for the definitions of variables.
39
TABLE 6
Insider Stock Sales Subsequent to EPS Rounding
Panel A: Univariate Analysis
Diluted EPS
Basic EPS
n
CFONST
CEONST
n
CFONST
CEONST
Rounding
987
0.065
0.306
855
0.062
0.293
No Rounding
11,121
0.048
0.232
11,253
0.049
0.234
Mean Diff.
p-value
0.017***
0.073***
0.000
0.000
0.013***
0.059***
0.000
0.000
Panel B: Multivariate Analysis
Variables
DIGITMGTD
FESURD
ESURD
DIGITMGTB
FESURB
ESURB
BEAT
PROFIT
LNMV
B/M
PRIORRET
POSTRET
EVENTRET
Dependent Variable:
Dependent Variable:
CFONST
CEONST
Diluted EPS Basic EPS Diluted EPS Basic EPS
(1)
(2)
(3)
(4)
0.007**
0.032**
(2.17)
(2.14)
-0.061**
-0.148
(-2.25)
(-1.23)
-0.046**
-0.058
(-2.18)
(-0.62)
-0.000
0.001
(-0.01)
(0.07)
-0.063**
-0.158
(-2.36)
(-1.34)
-0.045**
-0.044
(-2.16)
(-0.49)
0.004
0.004
0.043***
0.043***
(1.60)
(1.62)
(4.48)
(4.49)
0.015***
0.016***
0.037***
0.040***
(4.62)
(4.82)
(2.63)
(2.79)
-0.005**
-0.005**
0.010
0.010
(-2.21)
(-2.24)
(1.01)
(1.01)
-0.039***
-0.039***
-0.180***
-0.180***
(-9.22)
(-9.22)
(-9.61)
(-9.61)
0.012***
0.012***
0.065***
0.065***
(9.64)
(9.64)
(11.52)
(11.47)
-0.006***
-0.006***
-0.027***
-0.027***
(-2.91)
(-2.91)
(-3.17)
(-3.17)
0.119***
0.119***
0.714***
0.712***
(12.56)
(12.52)
(17.11)
(17.06)
40
TABLE 6 (continued)
GRANTS_CFO
OPTEXER_CFO
EXCDUM_CFO
-2.336
(-1.14)
-1.274
(-0.75)
-0.004
(-0.84)
-2.346
(-1.15)
-1.207
(-0.71)
-0.004
(-0.81)
GRANTS_CEO
OPTEXER_CEO
EXCDUM_CEO
Firm Fixed Effects
Year Fixed Effects
Quarter Fixed Effects
n
Adjusted R2
Yes
Yes
Yes
12,108
0.340
Yes
Yes
Yes
12,108
0.340
1.351
(0.92)
-2.671
(-1.44)
0.099***
(4.56)
1.392
(0.94)
-2.648
(-1.42)
0.100***
(4.59)
Yes
Yes
Yes
12,108
0.342
Yes
Yes
Yes
12,108
0.342
***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively, from two-tailed tests.
Table 6 presents the results of insider stock sales subsequent to EPS digit management. Panel A tabulates
the mean difference of insider sales between firms which round EPS and firms which do not round EPS. In
Panel B, the following firm fixed effects regression is estimated with year and quarter fixed effects included:
NST = 0 + 1 DIGITMGT + 2 FESUR + 3 ESUR + 4 BEAT + 5 PROFIT + 6 LNMV
+ 7 B/M + 8 PRIORRET + 9 POSTRET + 10 EVENTRET + 11 GRANTS_INSIDER
+ 12 OPTEXER_INSIDER + 13 EXCDUM_INSIDER + Σ β (Year Effects)
+ Σ γ (Quarter Effects) + ε
Columns (1) and (2) contain the results when the dependent variable is CFONST. Columns (3) and (4)
contain the results when the dependent variable is CEONST. Results using diluted EPS are reported in
columns (1) and (3), whereas results using basic EPS are reported in columns (2) and (4). Refer to Table 2
for the definitions of variables. All continuous variables are winsorized at the top and bottom 1% levels.
41
TABLE 7
Insider Stock Sales Subsequent to EPS Rounding via Abnormal Stock Repurchase
Variables
DIGITMGTD
DIGITMGTD × ABREPUR
FESURD
ESURD
DIGITMGTB
DIGITMGTB × ABREPUR
FESURB
ESURB
ABREPUR
BEAT
PROFIT
LNMV
B/M
PRIORRET
POSTRET
EVENTRET
Dependent Variable:
Dependent Variable:
CFONST
CEONST
Diluted EPS Basic EPS Diluted EPS Basic EPS
(1)
(2)
(3)
(4)
0.008**
0.033**
(2.44)
(2.20)
1.394***
1.885
(3.89)
(1.19)
-0.060**
-0.143
(-2.22)
(-1.20)
-0.046**
-0.052
(-2.15)
(-0.55)
0.000
0.001
(0.09)
(0.05)
0.428
0.198
(1.24)
(0.13)
-0.062**
-0.154
(-2.33)
(-1.31)
-0.044**
-0.039
(-2.14)
(-0.42)
-0.168*
-0.127
-1.029**
-0.956**
(-1.70)
(-1.27)
(-2.37)
(-2.19)
0.004
0.004
0.043***
0.043***
(1.60)
(1.62)
(4.47)
(4.48)
0.015***
0.016***
0.038***
0.040***
(4.71)
(4.86)
(2.70)
(2.85)
-0.005**
-0.005**
0.009
0.009
(-2.30)
(-2.31)
(0.87)
(0.88)
-0.039***
-0.039***
-0.181***
-0.181***
(-9.26)
(-9.26)
(-9.66)
(-9.66)
0.012***
0.012***
0.065***
0.065***
(9.57)
(9.61)
(11.46)
(11.42)
-0.006***
-0.006***
-0.027***
-0.027***
(-2.95)
(-2.94)
(-3.22)
(-3.22)
0.119***
0.119***
0.715***
0.714***
(12.53)
(12.55)
(17.14)
(17.11)
42
TABLE 7 (continued)
GRANTS_CFO
OPTEXER_CFO
EXCDUM_CFO
-2.331
(-1.14)
-1.277
(-0.75)
-0.004
(-0.73)
-2.328
(-1.14)
-1.218
(-0.72)
-0.004
(-0.72)
GRANTS_CEO
OPTEXER_CEO
EXCDUM_CEO
F-test:
DIGITMGTD + DIGITMGTD ×
ABREPUR) = 0
DIGITMGTB + DIGITMGTB ×
ABREPUR) = 0
Firm Fixed Effects
Year Fixed Effects
Quarter Fixed Effects
n
Adjusted R2
15.30***
Yes
Yes
Yes
12,108
0.341
1.343
(0.91)
-2.628
(-1.41)
0.100***
(4.60)
1.387
(0.94)
-2.604
(-1.40)
0.101***
(4.62)
1.47
0.02
Yes
Yes
Yes
12,108
0.343
Yes
Yes
Yes
12,108
0.342
1.53
Yes
Yes
Yes
12,108
0.340
***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively, from two-tailed tests.
Table 7 presents the results of insider stock sales subsequent to EPS digit management via abnormal stock
repurchase. The following firm fixed effects regression is estimated with year and quarter fixed effects
included:
NST = 0 + 1 DIGITMGT + 2 ABREPUR + 3 DIGITMGT × ABREPUR + Σ β (Controls)
+ Σ γ (Year Effects) + Σ δ (Quarter Effects) + ε
Columns (1) and (2) contain the results when the dependent variable is CFONST. Columns (3) and (4)
contain the results when the dependent variable is CEONST. Results using diluted EPS are reported in
columns (1) and (3) whereas results using basic EPS are reported in columns (2) and (4). Refer to Table 2
for the definitions of variables. Refer to Appendix A for the definition of ABREPUR. All continuous
variables are winsorized at the top and bottom 1% levels.
43
TABLE 8
Robustness Checks on Insider Sales Subsequent to EPS Rounding
Variables
DIGITMGTD
DIGITMGTD × ABREPUR
Dependent Variable:
CFONST_VALUE
Diluted
Diluted
EPS
EPS
(1)
(2)
0.041**
0.046**
(2.02)
(2.24)
7.608***
(3.57)
DIGITMGTD × DWC
DIGITMGTB
DIGITMGTB × DWC
F-test:
DIGITMGTD + (DIGITMGTD
× ABREPUR) = 0
DIGITMGTD + (DIGITMGTD
× DWC) = 0
Controls
Firm Fixed Effects
Year Fixed Effects
Quarter Fixed Effects
n
Adjusted R2
Dependent Variable: Dependent Variable:
OTHERSNST
CFONST
Diluted Diluted
Diluted
Basic
EPS
EPS
EPS
EPS
(3)
(4)
(5)
(6)
0.006*
0.032
0.029
(1.71)
(1.25)
(1.10)
-3.757
(-1.28)
0.008
(0.16)
-0.001
(-0.16)
0.043
(0.81)
12.90***
1.61
0.09
Yes
Yes
Yes
Yes
12,108
0.471
Yes
Yes
Yes
Yes
12,108
0.472
Yes
Yes
Yes
Yes
2,752
0.417
Yes
Yes
Yes
Yes
2,752
0.417
Yes
Yes
Yes
Yes
11,387
0.338
Yes
Yes
Yes
Yes
11,387
0.338
***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively, from two-tailed tests.
Table 8 presents the firm fixed regression results of sensitivity analyses. We repeat the analyses in Tables
6 and 7. Columns (1) and (2) contain the results when we replace CFONST, the ratio of the number of net
sales to the number of shares outstanding, with CFONST_VALUE. CFONST_VALUE is measured as the
difference in square root of the dollar value of insider sales and insider purchases deflated by the square
root of market value of the firm. Columns (3) and (4) report the results when we replace the dependent
variable CFONST with OTHERSNST. OTHERSNST is calculated as the net number of shares sold by the
other three executives: COOs, presidents, and chairmen. In Columns (5) and (6), we replace ABREPUR
with discretionary working capital accruals (DWC). We measure DWC by estimating the residuals from the
following cross-sectional regression for each industry and quarter: WC/Assets = (1/Assets) + β(∆Cash
Sales/Assets) + ε, where WC = (∆Current Assets - ∆Cash) – (∆Current Liabilities - ∆Current Portion of
Debt). We require each industry-quarter to have at least ten observations included. For each regression
model, control variables are included (but not reported) for brevity. Refer to Table 2 for the definitions of
variables. Refer to Appendix A for the definition of ABREPUR. All continuous variables are winsorized at
the top and bottom 1% levels.
44