Gaming the Float: How Managers Respond to EPS-based Incentives

Gaming the Float:
How Managers Respond to EPS-based Incentives ∗
Alan D. Crane †
Jones Graduate School of Business
Rice University
Chishen Wei §
Nanyang Business School
Nanyang Technological University
July 11, 2013
Andrew Koch ‡
Katz Graduate School of Business
University of Pittsburgh
Abstract
We show that the likelihood of meeting earnings per share (EPS) forecasts is mechanically positively
related to the number of shares outstanding. As a result, by changing shares outstanding, managers can
affect the long run probability of meeting future EPS forecasts without affecting earnings or analysts’
forecasts. We find that firms with unpredictable earnings and firms with managers that have compensation
more sensitive to EPS outcomes have more shares outstanding. To address causality, we find that an
exogenous drop in the likelihood of meeting a forecast causes managers to increase shares outstanding,
primarily through stock splits. Following an increase in shares, accounting and real earnings management
drop and the firm meets EPS forecasts more frequently going forward. Our results suggest that managers
use stock splits as a long term substitute for traditional earnings management tools. This provides an
important link between EPS reporting and capital market activities.
Keywords. Earnings per share; Earnings management; Stock splits
∗ We thank Brian Akins, Leonce Bargeron, Alex Butler, Mike Crawley, Dave Denis, Diane Denis, Steve Dimmock, Mei Feng,
Nishad Kapadia, Bin Ke, Paul Malatesta, Sebastien Michenaud, K. Ramesh, Shawn Thomas, K.C. John Wei, James Weston
and seminar participants at Rice University and University of Pittsburgh for their helpful comments.
† acrane@rice.edu
‡ awkoch@pitt.edu. Corresponding author. 326 Mervis Hall, Roberto Clemente Drive, Pittsburgh, PA, 15260. 412-648-1187.
§ cswei@ntu.edu.sg

1 Introduction
Earnings per share (EPS) is a widely followed and heavily scrutinized financial indicator in the US. Evidence
suggests that managers care about EPS targets (Graham et al. (2005)). A large literature documents a
variety of actions that managers take to affect the gap between earnings realizations and EPS forecasts by
changing earnings, forecasts, or both. 1 This literature generally takes the concept of “meeting”, “beating”,
or “missing” forecasts as given. We show that, even if two managers have identical earnings and forecasts,
one can “miss” while the other “meets”. The rules of the game are actually the manager’s choice. In this
paper, we show that managers can affect the likelihood that their firm meets future EPS forecasts without
affecting their firm’s reported earnings or guiding forecasts. They do so by choosing the number of shares
outstanding.
For any given EPS forecast, there exists a range of total earnings that will meet that EPS forecast.
For example, a firm with 1000 shares outstanding and EPS forecast of $0.20 will meet the forecast with any
earnings ∈ [$195, $205). This range exists because per-share earnings are rounded to the penny. Importantly,
the amount of rounding is a choice variable; it is an increasing function of the number of shares outstanding.
If the same firm has twice as many shares outstanding, the firm meets the forecast for any earnings ∈ [$190,
$210). The wider this range, the higher the probability of meeting EPS forecasts, more specifically:
P r(meet) = P r(µ − s ∗ 0.5¢ ≤ x < µ + s ∗ 0.5¢)
where x represents the realization of total earnings, s is the number of shares outstanding, and µ is the
forecasted total earnings implied by the EPS forecast. Increasing the number of shares increases the size of
this range (the “target size”). To put it simply, the practice of rounding EPS outcomes has a bigger effect
the more shares a firm has. Managers can exploit this fact to influence the probability of meeting all EPS
forecasts going forward. However, this is not costless; as managers increase the number of shares, the share
price drops mechanically. This can have liquidity costs and, in the limit, result in delisting.
We develop and test several implications of the hypothesis that managers engage in target size management
(TSM) - adjusting shares outstanding to affect the size of the range of total earnings that meets
EPS forecasts. 2 Our primary hypothesis is that managers of firms that are likely to miss EPS targets due to
chance in the future will choose a larger target size. This is equivalent to saying that firms with unpredictable
1 For comprehensive reviews of the earnings management literature, see Healy and Wahlen (1999), Dechow and Skinner
(2000) and Dechow et al. (2010).
2 We focus on EPS forecasts as the relevant threshold, however target size management could apply to any threshold, as long
as the threshold is measured and rounded at the share level.
2

earnings will choose more shares outstanding, all else equal. By choosing this larger target, a larger range
of earnings outcomes will round to any given EPS forecast. If firms with unpredictable earnings did not
choose larger targets, they would miss EPS forecasts more often than similar firms with earnings that are
easy to forecast. We proxy for unpredictable earnings in several ways, one of which is net income volatility. 3
We find that firms in the highest decile of net income volatility have over three times the number of shares
outstanding compared to firms with the lowest volatility.
We also expect target size to be related to the manager’s incentives to meet or beat EPS forecasts. A
large target makes a firm less likely to miss the EPS forecast. However, it also makes it more difficult for the
firm to beat that forecast. Therefore, we expect to find larger targets among managers with a high cost to
missing forecasts relative to the benefits of beating those same EPS forecasts. Using data on executive bonus
and option ownership, we proxy for the sensitivity of the manager’s compensation in EPS outcomes. 4
We
find that firms with managers in the top decile of incentive compensation have 40% more shares outstanding
relative to firms with managers in the bottom decile.
Next, we examine the implications of target size management for time series variation in shares outstanding
and how this impacts firms’ usage of earnings management. Over time, the fundamentals of a firm
may change, and therefore the optimal target size may also change. For example, if the firm’s net income
grows, the size of the target relative to the firm will shrink simply as a result of this growth. As the target
size shrinks, the probability of rounding to the EPS forecast will decrease and the manager may need to use
more accounting and real earnings management tools in order to meet this shrinking target. Managers can
increase the firm’s number of shares in order to change the target to a size appropriate for that of the larger
firm. 5
We expect an increase in shares to have one or both of the following effects: the firm should meet
EPS forecasts more frequently, and/or the usage of other earnings management tools should drop. We find
evidence of both. The magnitudes of accruals and discretionary investment drop significantly following an
increase in shares outstanding, and simultaneously the firm is 18% less likely to miss EPS forecasts.
Managers have numerous mechanisms to adjust share float.
We find that target size management is
primarily achieved through stock splits. There is little evidence that the target size is adjusted through the
issuance (or repurchase) of new shares. This is not surprising given that splits are simply an accounting
change in the number of tradeable securities, whereas issuances have direct economic effects unrelated to
3 We often use the term net income interchangeably with total earnings. We recognize that EPS may reflect adjustments to
net income. Our results are robust to using various definitions of total earnings.
4 Cheng and Warfield (2005) and Bergstresser and Philippon (2006) find that higher option and stock compensation is
associated with EPS incentives.
5 This is consistent with the prior evidence that stock splits follow net income growth. We discuss how our results relate to
the literature on stock splits in later sections.
3

target size. 6
Importantly, changes to target size as a result of stock splits are quite common. In a typical
year, roughly 5% of firms split. Over the full sample, almost all firms adjust the target size to keep up with
firm growth. 7
This suggests that TSM is economically important and widely used. Some firms, however,
may find it too costly to manage the target size. We find that TSM is limited by costs associated with
having a large quantity of shares. A firm with a large target size will have a low stock price. A low stock
price may lower stock liquidity, potentially to the point of delisting. For firms with low liquidity, we find a
minimal response to exogenous changes in net income volatility.
Our analysis is complicated by the fact that the predictability of earnings is itself a managerial choice
variable. Managers can explicitly manage the volatility of net income using accruals or real investments
(e.g. Beidleman (1973), Subramanyam (1996), Healy and Wahlen (1999)), and they can use guidance to
manage the forecast. In order to demonstrate that our effects are evidence of TSM and not due to some other
factor related to the use of accruals or guidance, we employ an instrumental variable approach that uses an
exogenous change in analyst coverage (Hong and Kacperczyk (2010), Degeorge et al. (2012), Derrien and
Kecskés (2012), Kelly and Ljungqvist (2012)) to instrument for changes in the predictability of the firm’s
net income. This instrument captures the fact that fewer analysts will result in noisier estimates on average.
Therefore, the firm experiences an increase in the probability of missing earnings forecasts that is unlikely
to be related to the fundamentals of the firm. The causal effect is large. A one standard deviation increase
in instrumented volatility results in an increase in shares of one-half of one standard deviation.
Managerial payoffs are also endogenous. Compensation contracts and the market reaction to EPS surprises
(and therefore the change in value of the manager’s stock and option holdings) are likely to be
determined based on the underlying fundamentals of the firm, including the predictability of the earnings. 8
Using the same instrumental variable approach, we examine if an exogenous shock to this predictability has
a greater effect on shares among firms whose managers have pay that is ex-ante highly sensitive to EPS outcomes.
We find that the relation between shares and instrumented volatility is primarily driven by managers
with high incentive compensation.
To summarize, on balance our evidence is consistent with TSM. In the cross section, firms with more
unpredictable earnings and firms with managers more sensitive to negative EPS outcomes choose larger
6 Passive changes to float occur as a result of certain policies, such as ESOP plans. We find that these changes do not drive
our results.
7 Berkshire Hathaway is a notable example of a firm that does not appear to engage in TSM. The size of Berkshire Hathaway’s
earnings target is small relative to the size of the firm’s earnings. They must realize earnings within ±0.00005% of the consensus
forecasts to meet expectations.
8 Evidence of this endogeneity can be seen in Dechow and You (2012). They document that the market reaction to EPS
surprises is weaker for firms with higher EPS levels which, holding earnings fixed, is equivalent to firms with lower shares
outstanding.
4

targets.
Managers change the target size in response to changes in the predictability of those earnings.
Importantly, these effects are stronger for firms with higher incentive compensation, weaker for firms with
low liquidity.
Finally, following an increase in the target size, firms meet forecasts more frequently and
earnings management drops.
Our paper is related to, but distinct from, the broad literature on earnings management. Prior evidence
suggests that earnings management occurs when managers face short term incentives to meet or beat a
threshold.
The manager privately observes the firm’s earnings, and chooses accruals, investment, stock
repurchases, or some other corporate action such that the firm’s reported earnings meet the threshold. In
contrast, our evidence suggests that managers manage the target size not to affect the current period EPS,
but to affect the ease with which the firm will meet future EPS thresholds in the long run.
No private
information is required by the manager for TSM to be effective, and markets need not be fooled. TSM
and earnings management are related, however, in the sense that TSM is a long-term substitute for earnings
management. By setting the target size today, the manager is effectively determining the amount of earnings
that will need to be managed in expectation over multiple periods in the future. 9
Our findings contribute most directly to the literature on the choice of earnings management tools. For
example, recent literature focuses on the tradeoffs between earnings management tools (e.g.
Cohen and
Zarowin (2010) and Zang (2011)). As noted by Fields et al. (2001), it is important to examine the combined,
net effect of all earnings management tools used together to meet EPS thresholds. Our results are important
because they suggest that, prior to trading off these earnings management tools, managers decide the extent
to which they will need to manage earnings in the first place.
Our study highlights an important link between EPS reporting and capital market activities through
the real effects of stock splits. Our evidence offers a new explanation for stocks splits based on the need
for target size management. While previous explanations typically involve signaling motives or stock price
levels, we show that stock splits could be a result of managerial concerns regarding EPS outcomes. Thus,
we extend the prior literature that examines patterns in accounting metrics and their relationship to stock
splits (e.g. Louis and Robinson (2005)). Furthermore, a TSM-based explanation of stock splits is consistent
with prior literature that finds that splits follow earnings growth (Lakonishok and Lev (1987), Asquith et al.
(1989)), as well as the literature that documents a “nominal price puzzle”(Weld et al. (2009)). We discuss
this in more detail in Section 3.3.
9 Prior literature finds that firms use repurchases (which result in a change to the quantity of shares) to have an accretive
effect on current period EPS (e.g. Hribar et al. (2006) and Bens et al. (2003)). Our results do not dispute these findings, but
rather show that share changes can have long term effects on EPS outcomes. TSM is driven primarily through stock splits and
not through repurchases. We find little evidence that stock splits have an accretive effect on EPS in the short run.
5

Finally, TSM has implications for a variety of per-share metrics such as analyst dispersion and forecast
error.
In this sense, our findings compliment Dechow and You (2012), in which the authors make the
observation that the precision of an EPS number is greater for higher levels of EPS. 10 We show in Section
3.3 that the scale invariance of analysts’ forecast errors (Degeorge et al. (1999), Cheong and Thomas (2011),
and Ball (2011)) is the expected endogenous outcome of target size management.
Our paper proceeds as follows: Section 2 motivates our hypothesis and describes the mechanism we test.
Section 3 describes the data and empirical results. Section 3.3 discusses the implications of our findings, and
Section 4 concludes.
2 Discussion and Hypothesis Development
The convention of rounding EPS to the nearest penny creates a range of net income that will generate a
given EPS number. The size of this range is determined by the number of shares outstanding. Specifically,
the range of net income that meets expectations is: (E[EP S] ∗ s −
s
s
200
, E[EP S] ∗ s +
200
), where E[EP S]
is the analysts’ EPS expectation and s is the number of shares outstanding. The expected Net Income,
E[EP S] ∗ s, is the total earnings implied by the per share forecast and is the midpoint of this range. The
highest and lowest earnings that will round to the forecast are determined by s. At a maximum, each share’s
1
worth of earnings will be rounded by half a penny (or in dollar terms,
200
). For example, Microsoft Corp.
has roughly 8 billion shares outstanding. So, in any given quarter the total size of their earnings target is 80
million dollars, ± 40 million centered around the amount of total earnings implied by the forecast. In dollar
terms this amount might seem large, but relative to the magnitude of the firm’s earnings, perhaps less so.
The size of the earnings target relative to the size of the firm’s total earnings is ± 0.5
E[|EP S|]
%. The average
firm in our sample has EPS of $0.20.
So, the typical firm will meet the earnings forecast by producing
earnings within ±2.50% of expected earnings. This amount of flexibility might be considered large by some
managers and small by others. For example, 2.50% may be relatively large for a firm with stable business
fundamentals and predictable net income. However, a manager whose compensation is highly concave in
earnings surprises may consider this range to be small.
Managers have flexibility over the size of this earnings target. In dollar terms, the size of the target is
fixed solely by the number of shares. If the manager prefers an earnings target twice as large, she can simply
double the number of shares outstanding. Because the size of the earnings target measured in dollars is fixed,
10 In the next section, we show that the target size as a percentage of the firm’s expected net income equals one-half of the
inverse of EPS.
6

it does not increase as the firm’s earnings increase. Equivalently, the size of the earnings target measured
as a percent of the firm’s earnings shrinks as the firm’s earnings grow. The manager can counteract this by
adjusting shares outstanding. An example that highlights these effects is shown in Figure 1.
[Insert Figure 1 Here]
Our testable predictions focus on the manager’s choice for shares outstanding. First, we discuss predictions
on the firm and manager characteristics that are related to the cross sectional distribution of shares
outstanding. We discuss an identification strategy to address causality - that managers’ EPS-based incentives
cause them to choose shares outstanding. Last, we explore the conditions under which managers change
shares outstanding, how these changes relate to EPS outcomes, and how they relate to the usage of other
earnings management tools.
2.1 Determinants of the cross sectional distribution of shares outstanding
We expect the manager’s choice of target size to be a function of the incentives she faces to generate certain
EPS outcomes. Conceptually, these incentives can be summarized by the set of payoffs the manager receives
for generating certain EPS outcomes, and the probabilities that these outcomes occur. Neither payoffs nor
probabilities associated with a specific earnings realization can be directly measured.
Further, both are
likely endogenously determined along with the manager’s choice for shares outstanding. This makes both
hypothesis development and empirical design challenging. We begin by assuming probabilities and payoffs
are exogenous and measurable.
First, we hold payoffs fixed (e.g., managers receive the same bonus for beating EPS forecasts, the market
response to a negative earnings surprise is the same across firms, managerial ownership is constant, etc.)
and examine how variation in probabilities should relate to variation in the number of shares. For any firm,
the probability of meeting EPS forecasts is:
P r(meet) = P r(µ −
∫ s µ+ s
200 ≤ x < µ + s
200 ) = 200
µ− s
200
f(x) dx,
where f(x) is the pdf of the firm’s earnings, µ is analysts’ forecasted earnings (which equals s ∗ E[EP S]),
and s is the number of shares.
If we assume the firm has earnings distributed uniformly over [-e, e] and the consensus forecast is neither
noisy nor biased (and therefore equals $0.00), then the probability of meeting earnings is: P r(meet) =
∫ s
200
−
s
200
( 1
e+e ) dx =
s
200e
. From here it is easy to see that the probability of meeting forecasts is negatively
7

elated to the variance (variance is e2
12
) of the earnings and positively related to s. If payoffs are fixed and
homogenous across managers, then all managers will prefer the same probabilities of meeting, beating, and
missing EPS forecasts. Holding these payoffs constant, it follows directly that managers of firms with volatile
earnings will need to choose higher shares in order to obtain the same EPS outcome likelihoods. This positive
relation between net income volatility and shares outstanding is our main prediction:
H1: Managers of firms with highly volatile and unpredictable earnings will choose more shares outstanding
compared to firms with stable, predictable earnings, all else equal.
This prediction is difficult to test empirically for a variety of reasons. First, forward-looking volatility
is not observable.
Second, the volatility of earnings that is important for our purposes is the part that
is unpredictable. More precisely, the variance that is important is the variance in the difference between
realized earnings and expected earnings.
For example, if a firm has volatile earnings due to predictable
seasonal variation, then this volatility would not reflect the likelihood that the firm will generate earnings
different from forecasts. Third, as pointed out in the large literature on earnings smoothing (e.g. Beidleman
(1973), Subramanyam (1996), Healy and Wahlen (1999)), the variance in earnings is itself a choice variable.
To address the first two concerns, we use three proxies for net income volatility; i) variance around the
mean over the last twelve quarters, ii) variance around a seasonally adjusted expected mean over the last
twelve quarters, and iii) variance around the expectation implied by analysts’ forecasts over the last twelve
quarters.
We expect to find a positive relationship between these measures of net income volatility and
shares outstanding.
The last concern, that net income volatility is jointly determined with the number of shares, makes identification
difficult. To address causality, we use a source of plausibly exogenous variation in the probability
that the firm meets EPS forecasts and relate this to changes in shares outstanding. Specifically, we use an
exogenous drop in analyst coverage as a shock to the probability that the firm meets earnings forecasts. Our
reasoning is simple, if the consensus forecast is thought of as the sample mean (or median) of individual
analysts’ noisy forecasts, then the variance of this estimate is decreasing in the number of analysts, i.e.
the noise in the forecast is a decreasing function of the sample size. Therefore, a drop in analyst coverage
increases the variance in the EPS forecast simply because fewer analysts are sampled.
Increasing the volatility of the forecast is equivalent to increasing the volatility of earnings around the
forecast. In the Appendix, we show explicitly that an increase in forecast noise decreases the probability of
8

meeting that forecast. This leads to a variant of our main hypothesis:
H1a: Managers increase shares in response to an exogenous decrease in analyst coverage.
Next, we discuss how manager payoffs might relate to variation in shares outstanding. All else equal,
we expect a positive relationship between the sensitivity of payoffs to negative earnings surprises relative
to positive surprises (concavity) and shares outstanding. The more shares are outstanding, the lower is the
probability of missing earnings. However, because this rounding effect is symmetric, it also decreases the
probability of beating earnings. A manager with convex payoffs (higher sensitivity to meeting than missing)
should prefer a small range. In this case, the probability of missing is high, but the probability of beating
is high as well. A manager who incurs large costs when missing relative to beating (concave payoffs) will
prefer a larger range to minimize the chances of incurring those costs.
H2: Managers with payoffs that are concave (convex) in earnings surprises will choose higher (lower) level
of shares outstanding.
Similar to net income volatility, payoffs are neither observable nor exogenous. However, there is considerable
evidence that CEO’s receive compensation that is concave in earnings surprises. Bonuses in CEO
compensation contracts are often tied to EPS thresholds based on analyst forecasts (Murphy (1999), De Angelis
and Grinstein (2011) and Kim and Yang (2012)). Also, the negative stock price reactions to negative
earnings surprises are significantly larger than the positive reactions associated with beating forecasts. 11
Given that most CEOs have substantial ownership stakes in the company, this creates a stronger incentive
to avoid missing earnings expectations compared to the incentive to beat those targets. Burgstahler and
Dichev (1997) and Degeorge et al. (1999) show empirically that the distribution of EPS outcomes is consistent
with the view that managers respond to incentives to meet or beat EPS targets. Furthermore, prior
literature has documented a connection between EPS outcomes and managerial compensation. For example,
Cheng and Warfield (2005) find that managers with high equity ownership are less likely to miss EPS targets.
We expect managers with larger bonuses tied to accounting targets to have more shares outstanding, and
hence wider rounding ranges. We would also expect managers who have more ownership and more equity
11 Payne and Thomas (2003) and Skinner and Sloan (2002) show differences in the source of this effect, but both generally
find stronger negative reactions.
9

ased compensation to have similar incentives. The amount of incentive compensation as a percent of total
compensation captures both of these effects. Consequently, the percentage of incentive compensation will be
positively related to the number of shares outstanding.
Because compensation contracts are endogenous, we again utilize the exogenous drop in analyst coverage
to empirically test a variant of H2:
H2a: The effect of an exogenous drop in analyst coverage should be stronger (weaker) among firms whose
managers have high (low) incentive compensation.
2.1.1 Additional costs and benefits relating to shares outstanding
Discussion so far has focused on benefits and costs of shares outstanding as they relate to the rounding
effects and EPS-based incentives. If these were the only trade-offs faced by managers, then any manager
with concave payoffs should choose infinite shares outstanding. We do not observe this because there are
other costs and benefits related to shares outstanding. Prior literature has shown that stock liquidity is a
function of per-share price levels. In the extreme, if the price is too low the stock is de-listed, which severely
inhibits liquidity. Therefore, we expect that the relationships described in H1 and H2 to be weaker for illiquid
firms or those close to delisting. In this case, market microstructure considerations are likely to outweigh
EPS-based incentives when the manager is choosing shares outstanding.
H3: Managers will increase shares as a response to an exogenous decrease in analyst coverage, but only for
liquid firms.
Similarly, some corporate decisions are made for reasons not primarily related to shares outstanding, yet
these decisions result in a change in shares. For example, firms often repurchase or issue stock. While these
actions change the number of shares, this change is a byproduct, not the goal of the decision. We do not
expect our hypotheses to hold for changes in shares that result from repurchases or issuances. We expect our
results to be driven primarily by stock splits, which do not result in changes to the firms capital structure.
H4: Changes to shares outstanding as a response to an exogenous decrease in analyst coverage are driven
by stock splits.
10

2.2 Time series determinants of shares outstanding
In this section, we examine the conditions under which managers might choose to change shares outstanding.
In the previous section, we discuss how the level of shares should be related to earnings volatility and the
concavity of payoffs. If one of these cross sectional determinants were to change, then we would expect the
manager to correspondingly change shares outstanding and, in fact, we use a shock to net income volatility
(relative to forecasts) to address causality. However, we expect that much of the within-firm variation in
shares is driven not by changes in compensation contracts or analyst coverage, but simply by firm growth.
Dechow and You (2012) make the observation that the precision of an EPS number is increasing in the
level of EPS. We offer one way to quantify this effect; - the firm needs to produce net income within ± 0.5
E[|EP S|]
% of expected net income to meet expectations. Therefore as the firm’s net income grows, the target size as
a fraction of the firm’s expected net income shrinks. 12
It is well known that managers increase shares following earnings growth (see e.g.
Lakonishok and
Lev (1987) and Asquith et al. (1989)). We examine a conditional hypothesis that is unique to target size
management. This helps distinguish TSM from other explanations that also predict an increase in shares
following earnings growth.
The relationship between earnings growth and target size is non-monotonic, with a kink at EPS=0.
Earnings growth shrinks the target size, but only for firms with positive earnings. If the firm has negative
earnings and experiences earnings growth (a positive change in earnings), then this growth actually widens
the range making it easier to meet expectations, not harder. Therefore, we expect increases in shares to
follow earnings growth, but only among positive EPS firms.
H5: Managers increase shares following earnings growth, but only for firms with positive earnings.
A manager can compensate for a shrinking target by using more accruals, guidance, and other earnings
management tools. However, usage of these earnings management tools is costly. As the costs of the usage
of these alternatives increase, the manager can choose to “reset” the size of the earnings target, restoring
it to a size appropriate for the now-larger firm. Therefore, we expect that the manager will either meet
12 To be clear, if the firm’s mean earnings grows but there is no growth in variance, then this growth has no effect on the
probability of meeting forecasts, despite the fact that the target size relative to firm size has shrunk. Therefore, thinking of
target size relative to firm size is useful only if the size of the firm in terms of expected net income is related to the volatility
of the firm’s net income. Not surprisingly, we find empirically that earnings growth is associated with higher levels of earnings
volatility going forward.
11

EPS forecasts more frequently or will use less earnings management (or both) following an increase in shares
outstanding.
H6: The likelihood of meeting (missing or beating) EPS forecasts increases (decreases) following increases
in shares.
H7: The usage of accounting and real earnings management tools decreases following increases in shares.
2.3 Short-term rounding effects
Discussion up to this point has focused on the long-run effects of shares on the size of the earnings target.
Given that the number of shares persists from quarter-to-quarter, we expect managers to choose shares in
response to long horizon trade-offs and expectations. However, it is possible that managers ignore long term
effects and adjust shares outstanding in light of private information regarding current period earnings. To
the best of our knowledge, reported earnings must reflect splits that occur during the period between the
fiscal quarter end and actual earnings report date. Therefore, it is possible that managers adjust shares in
order to affect current period EPS outcomes. Prior evidence suggests that managers use stock repurchases
to affect current period EPS outcomes (Bens et al. (2003) and Hribar et al. (2006)).
If managers observe that current period earnings are lower than expectations, they may choose to increase
the target size such that they meet (the split adjusted) EPS expectation. This seems unlikely for a few
reasons. First, we do not observe managers rebalancing shares each quarter - if a firm splits in one quarter
for short-term reasons, the firm would prefer to reverse split in the next quarter to return to the optimal
target size. More importantly, there is a well established positive market reaction to stock splits. This
evidence is not consistent with managers splitting because of negative temporary earnings shocks.
However, there may be scope for short term considerations to affect not whether the firm should split, but
by how much. For example, perhaps the manager has determined that the firm needs to roughly double the
number of shares. The manager might choose a 7-for-3 split instead of a 2-for-1 split, so that the change has
an accretive effect on current period EPS. 13 We hypothesize that if managers choose split ratios out of short
term considerations, then we should observe atypical ratios more frequently in the period after earnings are
13 An example of an accretive split is the following: The manager observes current period net income to be $15.4. The firm
has 100 shares outstanding, and analysts’ forecasted EPS is 0.15. If the manager issues a 7-for-3 split, split-adjusted expectation
is 0.06. However, the manager will report split-adjusted EPS as 0.07.
12

ealized but before they are reported. We also expect that these splits should more frequently be accretive
than dilutive.
3 Data and Results
3.1 Data
The sample analyzed in this study is compiled from four major databases.
The primary data sample is
gathered from the quarterly CRSP/COMPUSTAT Merged database and combined with analyst forecast
data obtained from I/B/E/S. Our sample starts in 1984 since we require 12 previous quarters of analyst
forecasts in our main tests. Our sample ends in 2011. We include stock return data from CRSP. Only common
stock with CRSP share code 10 or 11 are included. We merge in institutional ownership obtained from the
Thomson Reuters 13(f) institutional holdings database. For a subset of tests, we include compensation data
from ExecuComp.
To distinguish between changes in shares outstanding due to stock splits, repurchases, or equity issuances,
we use distribution codes from CRSP. Stock splits have a distribution code equal to 5523. In our sample,
we assign a split to a fiscal quarter if the CRSP payment date (PAYDT) occurs after the prior earnings
report date, but before the earnings report date as reported in COMPUSTAT. If the earnings report date is
missing, a split is assigned to a fiscal quarter if it occurs within the fiscal quarter begin and end dates.
A key prediction in our study centers on the link between shares outstanding and the volatility of earnings.
We create three measures of earnings volatility. Net Income Volatility is calculated as the standard deviation
of net income over the past 12 quarters.
This directly measures the variance in net income, however it
does not capture predictable, seasonal net income variation. Net Income Volatility - Naive Forecast is the
standard deviation of seasonally adjusted net income over the past 12 quarters. This proxy captures the
variance around a time-varying mean using a simple forecast for the mean based on seasonality and prior
growth in net income. Net Income Volatility - Analysts Forecast is calculated as the standard deviation of
(Net Income - median IBES forecasted earnings) over the past 12 quarters, where median IBES forecasted
earnings is the median EPS forecast multiplied by shares outstanding. The benefit of this measure is that it
captures actual earnings expectations in each period. However, the drawback is that it requires data from
IBES which reduces the sample.
[Insert Table 1 Here]
13

Table 1 presents the summary statistics of the sample. The key dependent variable used in this study is
shares outstanding (median = 23.55 million, mean = 83.85 million). EPS has a median of $0.19 and mean
of $0.20. This translates to a median and mean earnings target size of ±2.6% and ±2.5% of expected net
income.
3.2 Results
We begin by examining if data are consistent with the view that managers recognize the effects of rounding
and the earnings target size, and in particular the lower bound of earnings required to meet forecasts.
Evidence in prior literature is consistent with this.
For example, Das and Zhang (2003) document an
abnormally large number of net income realizations that round upwards when translating net income to
EPS. Given this evidence, we expect that an abnormal number of net income realizations will be just above
the minimum that will round to the EPS forecast.
We present a figure that is similar in spirit to analyses presented in Burgstahler and Dichev (1997)
and Degeorge et al. (1999), who find an abnormal number of EPS outcomes that are just enough to clear
certain thresholds. Instead of examining EPS outcomes, we plot net income realizations around the threshold
E[EP S] ∗ s −
s
200
, which is the minimum net income required to meet the median analyst EPS forecast.
We scale each firm’s realized net income by E[EP S] ∗ s − s
200
and plot frequencies in Figure 2. Any value
< 1 means the firm missed the EPS forecast, and a value of 1 indicates that the firm reported just enough
net income such that it rounds to the EPS forecast.
[Insert Figure 2 Here]
The red line (left line) in the figure indicates the minimum net income that meets forecasts - the lower
bound of the target size. The green line (right line) indicates, for the average firm, the net income implied by
analysts’ forecasts (E[EP S] ∗ s). The figure shows a disproportionate occurrence of net income realizations
that are just enough to meet the minimum net income required to satisfy the EPS forecast.
In what follows, we examine if managers recognize that the location of this threshold is a choice variable
and choose the number of shares accordingly.
Our main hypothesis is that managers of firms with
unpredictable net income will choose high levels of shares outstanding so that a wide range of net income
realizations will meet forecasts. We also expect that managers with high incentive compensation will choose
more shares outstanding for similar reasons. We briefly examine these relationships using multivariate sorts.
Figure 3 presents the average median shares outstanding across deciles of net income volatility in Panel
14

A and incentive compensation in Panel B. We present medians to alleviate concerns of extreme outliers. 14 In
each quarter, we first sort the sample into 20 groups based on net income, then within each net income group
we sort into deciles based on net income volatility or incentive compensation. This allows us to compare
firms with roughly equivalent net income. We plot median shares (bar height) across net income deciles. We
also report median net income (line) to confirm that we are comparing firms of similar size.
[Insert Figure 3 Here]
We find a strong association between shares outstanding and both net income volatility and incentive
compensation. Shares outstanding monotonically increases across net income volatility deciles. We also
observe a positive trend in shares outstanding across incentive compensation deciles, although the pattern
is weaker. In both figures, the average net income (line-plot) is stable across the decile ranks. 15
While the
extreme deciles have similar net income, the top net income volatility decile has three times as many shares
outstanding (in thousands) than its bottom decile counterpart (33,162 vs. 10,037, p-value < 0.01). In Panel
B, the top incentive compensation decile has nearly 40% more shares outstanding than the bottom decile
(49,774 vs. 70,898, p-value < 0.01).
3.2.1 Regression Analysis
Results from the dependent sorts indicate that firms with similar mean net income but different variance
have drastically different shares outstanding. In this section, we examine cross sectional variation in shares
outstanding in more detail.
Table 2 presents pooled OLS regression models of shares outstanding as a function of firm characteristics.
These results are suggestive of the cross sectional determinants of the level of shares outstanding. Regression
coefficients are standardized to represent standard deviation effects in shares outstanding for a one standard
deviation difference in a given covariate. All determinants of shares outstanding are lagged one period. Column
1 presents a basic specification, including variables representing size (Market Cap), liquidity (Amihud),
and ownership (Percent Institutional Ownership). These determinants have previously been associated with
stock splits and, as such, we expect them to be related to the level of shares outstanding. This specification
includes a proxy for earnings volatility, Net Income Volatility t−1 , defined as the standard deviation of Net
Income over the last twelve quarters. These results are robust to using various income definitions including
Operating Income Before Depreciation as well as Income Before Extraordinary Items.
14 The patterns in both figures are stronger using averages.
15 The higher level of average net income in Panel B reflects the fact that the ExecuComp sample of firms are larger.
15

Column 2 presents the same specification as column 1, but uses an earnings volatility proxy adjusted
for expectations based on prior earnings. Specifically, Net Income Volatility - Naive Forecast t−1 is measured
as the standard deviation of the difference between actual earnings and a seasonally adjusted proxy for
expected earnings. The expected earnings is earnings from 4 quarters prior, plus the difference between the
earnings 4 quarters and 8 quarters before. Column 3 presents another specification using a third proxy for
earnings volatility, Net Income Volatility - Analyst Forecast t−1 . This is the volatility of earnings adjusted for
analysts’ forecasts over the last twelve quarters. Finally, column 4 presents the same specification as column
1, but includes a measure for the level of incentive compensation. This is measured as 1 − (
salary
totalcompensation )
and is meant to capture both explicit EPS incentives (through bonuses) and implicit incentives including
sensitivity to market reactions due to unexpected earnings (through grants and options). This measure is
available only for firms in the ExecuComp database.
[Insert Table 2 Here]
The hypothesis described in Section 2 suggests that the number of shares outstanding should be related
to the volatility of earnings relative to expectations as well as to the payoffs to managers, conditional on
meeting earnings. We examine both of these aspects. The higher the volatility, the more likely a firm
misses earnings by chance, while the lower the volatility, the higher the probability of meeting or beating
earnings. In column 1, we see that the higher the level of Net Income Volatility t−1 , the higher the number
of shares outstanding. This is strongly significant, both economically and statistically. A firm with earnings
volatility one standard deviation above the mean has 0.21 standard deviations more shares outstanding.
The association is consistent across columns 1-3 using different proxies for earnings volatility. In fact, when
looking at volatility relative to analyst forecasts, the effect is even larger. One standard deviation higher
earnings volatility is associated with 0.30 standard deviations more shares.
We also examine payoffs to managers conditional on meeting or beating earnings. Under our hypothesis,
we expect that the stronger the incentives for managers to avoid missing earnings forecasts, the more shares
outstanding. In column 4, we proxy for these incentives with the fraction of CEO compensation that is
performance based. Stock and option ownership should be associated with strong incentives to meet or beat
earnings due to the strong negative stock market reaction to missing forecasts. Bonuses paid to managers
are often paid based on meeting EPS targets (De Angelis and Grinstein (2011), Young and Yang (2011),
Kim and Yang (2012)). The measure of total incentive compensation should capture both of these aspects
of a manager’s incentive to meet earnings. Consistent with this, we see a small but significantly positive
16

elationship between incentive compensation and shares outstanding. Specifically, a one standard deviation
larger incentive compensation is associated with 0.05 standard deviations more shares outstanding.
Consistent with the nominal price puzzle (Weld et al. (2009)), we see that larger firms have more shares
outstanding.
A one standard deviation change in size is associated with 0.76 standard deviations more
shares outstanding. We also find that a one standard deviation larger Amihud measure is associated with a
small (0.11 of a standard deviation), but statistically significant lower number of shares outstanding. This
is consistent with the evidence that liquidity tends to improve after a stock splits. In column 1, we see
no evidence of Institutional Ownership relating to the share structure of the firm. However, in column 4,
controlling for incentive compensation (which reduces the sample due to data requirements), we see that
Institutional Ownership is negatively related to shares outstanding. This is consistent with Dyl and Elliott
(2006) who find that smaller share price stocks have lower institutional ownership.
While our evidence on the volatility of earnings and incentive compensation is consistent with our hypothesis,
we find evidence that the level of net income is negatively associated with shares outstanding.
This is not entirely surprising. After controlling for size, there is significantly less variation in net income.
Moreover, these findings highlight the thorny fact that these firm characteristics are jointly determined and
are likely related to other, unobserved characteristics. Therefore, fully understanding what is driving the
the shares outstanding choice requires a different identification strategy.
To the extent that firms have unobserved characteristics that determine share structure and managerial
incentives, the simple pooled OLS estimates will be biased and inconsistent. The first step we take to mitigate
these issues is to examine a simple first difference model. This specification will measure the relationship
between changes in firm characteristics and changes in shares outstanding. To the extent that a firm’s level
of shares is determined by some variety of unobserved firm characteristics, focusing on changes will allow us
to identify the effect of firm observable characteristics that change over time. While the specification itself
mitigates issues with unobserved time invariant heterogeneity, it does not rule out the possibility of reverse
causality.
In Table 3, we present three specifications, one for each of the earnings volatility proxies described in
Table 2. Consistent with prior results, earnings volatility is an important determinant of shares outstanding.
In this case, a one standard deviation change in earnings volatility is associated with between 0.03 and 0.07
standard deviations of changes in shares outstanding. This effect is statistically significant at the 1% level
and is still economically large when considering it is an estimate of changes.
[Insert Table 3 Here]
17

While Table 2 and Table 3 establish a relationship between earnings volatility and shares outstanding
in both the cross section and time series, they do not establish a clear causal link due to the presence of
unobserved firm characteristics that likely change through time. In order to examine this question more
carefully and test the explicit hypotheses outlined above, we use exogenous variation in the volatility of
earnings around the expectation to establish a causal link between incentives and share structure.
In Table 4 we use an instrumental variable approach for the first difference model described above. We
instrument for the volatility of earnings (proxied for in Table 2 using the volatility of earnings relative to
analyst forecasts) by using exogenous drops in analyst coverage. Our identification strategy is similar to
those used in Hong and Kacperczyk (2010), Kelly and Ljungqvist (2012), and Derrien and Kecskés (2012)
who argue that the consolidation of analyst coverage following brokerage house mergers leads to exogenous
drops in overall coverage. When brokerage houses merge, the combined houses will often have more than
one analyst covering a stock. As brokerages reduce coverage to eliminate this duplication of effort, the total
number of analysts following certain stocks drops; however, this drop in coverage is exogenous to the firm’s
fundamentals.
[Insert Table 4 Here]
We use a slight variation in the brokerage house strategy employed by Degeorge et al. (2012). We use
drops in analyst coverage brought on by analysts that leave the IBES database permanently in that period.
As shown in Degeorge et al. (2012), these drops match the distribution of those from brokerage mergers.
After a drop in analyst coverage, the consensus forecasts will be noisier because the consensus is formed over
a smaller sampling of analysts - the variance of the sample mean is decreasing in n. Therefore, it is less
likely that realized EPS will meet forecasts solely as a result of the drop.
In Table 4, we show results from the second stage of a 2SLS regression using the drop in a analyst
coverage as an instrument for Net Income Volatility-Analyst Forecast t−1 . Our instrument is strong. In the
first stage regression, the t-statistic on the instrument is > 5 and the F-statistic is > 25, both well above
the benchmarks established in Stock et al. (2002). Using the instrumental variable approach, we see still
see a strong causal relationship between changes in the volatility of forecast errors and shares outstanding.
Specifically, a one standard deviation increase in Net Income Volatility-Analyst Forecast t−1 is associated
with a 0.53-0.58 standard deviation increase in the number of shares outstanding. This is an economically
large effect, as one standard deviation is measured over the entire cross sectional distribution of shares
outstanding. Given the exogenous nature of the instrument, we can now document evidence consistent with
18

the view that increases in forecast volatility cause managers to increase the number of shares outstanding.
Comparing these coefficients to Table 3 we see a much larger effect. This difference provides strong evidence
of the endogenous relationship between these variables and shows the importance of the exogenous shock in
terms of measuring magnitudes.
We also see a clearer relationship with respect to other incentives and share structures. Changes in Market
to Book are negatively related to shares outstanding. A one standard deviation increase in Market to Book
is associated with 0.03 standard deviation decrease in shares outstanding, but this effect is insignificant
when we control for incentive compensation. We also find a positive effect of 0.08 standard deviations due
to a change in Market Cap. These two results are consistent with De Angelis and Grinstein (2011) who
show that small, high growth firms compensate managers less on accounting based criteria. We also observe
that as Net Income grows, shares outstanding increase. Finally, in column 2 of Table 4 there is a small
but significant positive relationship between increases in incentive compensation and the change in shares
outstanding. Overall, we find that changes in forecast error volatility cause an increase in shares and that
net income growth and incentive compensation increases are also associated with an increase in shares. This
evidence supports our hypothesis H1A described in Section 2.
In Table 5, we explore in more detail the mechanism by which managers increase their shares outstanding.
In order to compare across columns, we use standardized independent variables and unstandardized measures
for changes in shares outstanding.
This allows us to interpret the coefficients as the number of shares
increased (or decreased) due to a one standard deviation change in a given independent variable. We do
this to compare across different sources of share increases which have different cross sectional distributions.
Column 1 reports the effect of changes in characteristics on increases in shares from sources other than stock
splits. While the point estimate for changes in Net Income Volatility as instrumented by analyst coverage
drops shows an increase in shares outstanding from a combination of issuances, treasury shares, and stock
awards, the effect is not statistically significant. In contrast, column 2 shows a large and significant increase
in shares due to an increase in Net Income Volatility (as instrumented by analyst coverage) as a result of
stock splits. These results suggest that the channel managers use to increase the range of Net Income that
will round to analyst expectations is through stock splits, not through issuances or use of treasury stock.
This evidence is consistent with hypothesis H4.
To provide further evidence that managers engage in target size management, we explore a unique feature
of the relationship between shares, net income, and target size. The size of the earnings target is a function of
the magnitude of the EPS forecast, not the sign. Therefore, earnings growth has opposite effects, depending
19

on whether the firm has positive or negative earnings. As such, we expect differential results depending on
whether firms have positive or negative EPS (see Section 2 H5).
[Insert Table 5 Here]
Columns 3 and 4 test this discontinuity in our prediction explicitly. We split the sample based on firms
that have negative earnings (column 3) and firms with positive earnings (column 4). The effect of Net Income
Volatility is driven largely by the positive EPS firms. Consistent with our predictions, the coefficient on Net
Income growth is negative for those firms with negative EPS. The net income of these firms is growing (i.e.
getting closer to zero) which suggests that the rounding range is actually increasing. As a result, these firms
are less likely to split.
In columns 5 and 6, we examine in further detail the effect that compensation structure has on the response
of firms to volatility shocks. We split the sample based on Incentive Compensation. We expect that
the stronger the EPS incentives, the stronger the observed effect of forecast volatility on stock splits (hypothesis
H2a). We see that the coefficient is substantially larger for firms with high incentive compensation
(column 5) compared to low incentive compensation (column 6), for which the coefficient is not statistically
different from zero. While we cannot reject the null that these two coefficients are statistically the same,
the point estimates suggest a strong relationship between incentive compensation and the magnitude of our
effect.
3.2.2 Costs of Splitting
The evidence so far is consistent with managers adjusting shares to manage the size of the EPS target. In
this section, we examine if target size management is conditional on other costs or benefits relating to shares.
However, we also recognize that a change in the quantity of tradeable securities affects things other than
just the target, and that managers likely trade off other costs or benefits when choosing to adjust shares. In
certain cases, the manager might find it too costly to increase the target size for other share-related reasons,
such as liquidity/delisting.
In Table 6, we estimate models the using same specification presented in Table 5. Motivated by the
“optimal trading range” (see, e.g., Baker and Gallagher (1980)), we include indicator variables for high
priced stocks (above $80) and low priced stocks (below $20). While we control for price (market value) in
all previous regressions, the optimal trading range suggests a non-linear relationship. High priced stocks are
much more likely to split, but our results are not driven by these firms. The results are robust to using other
price level cutoffs as well.
20

In columns 2 and 3, we measure our effect conditional on illiquidity. We split the sample based on median
Amihud. We expect the cost of splitting to be significantly higher for less liquid stocks due to microstructure
constraints (hypothesis H3). Consistent with this, we see little effect in the highly illiquid stocks. Conversely,
we see a large effect in column 3 for those that are highly liquid.
[Insert Table 6 Here]
3.2.3 Changes in shares, earnings management, and EPS outcomes
If managers increase shares in order to increase the size of the earnings target, then increases in shares should
be associated with an increase in the frequency with which the firms meets EPS expectations (H6) and with
a decrease in the usage of other earnings management tools (H7). To examine potential associations, we
distinguish quarters in which the firm’s shares increased by at least 25% (a split ratio of at least 5-for-4).
In Table 7, we examine changes in EPS outcomes over time and distinguish between changes around share
increases from those without.
[Insert Table 7 Here]
In Panel A, we compare the frequencies with which firms meet, beat, or miss EPS targets at quarter
t − 1 (the “pre” period) to those at quarter t + 1 (“post”). We compute the difference in the pre and post
period, and then differentiate firms that increase shares at t = 0 (the treatment group) from those that do
not (control) and compute the difference in the sample mean differences.
Among firms that increase shares in quarter t = 0, we find that they meet EPS forecasts 71% on average
in quarter t − 1 and this increases to 76% in the quarter after the share increase. This is statistically and
economically different from the difference among the control group. We also find that the treatment firms
miss and beat EPS forecasts less frequently following share increases. These differences relative to those
of the control group are also significant - firms miss EPS forecasts 22% of the time in the quarter prior to
the share increase and this drops to 18% in the quarter following the increase. Firms beat EPS 7.3% pre
increase, and this drops to 6.1%. We find similar effects in Panel B which uses four quarter averages for the
pre and post periods.
We also examine the association between increases in shares and the usage of accruals and real earnings
management tools in a similar manner. We use two measures of accruals and three measures of real earnings
management. Discretionary accruals are residuals from industry total accruals regressions including performance
controls following Ecker et al. (2011). Total accruals are defined as the change in current assets,
21

adjusted for the change in cash, minus the change in current liabilities, adjusted for current liabilities used
for financing, minus depreciation expense. Measures of real earnings management are estimated by abnormal
cash flow, production costs, and expenditure following the methodology in Roychowdhury (2006). We do
not have predictions on the sign of accruals or real earnings management, only on the magnitude of their
usage because increasing the target size makes it easier to meet EPS forecasts from above as well as from
below. Therefore, we examine changes in the absolute values of these earnings management tools. Results
are reported in Table 8.
[Insert Table 8 Here]
We find evidence that the usage of accruals and real earnings management drops after the manager
increases shares outstanding. This is broadly consistent with Cheong and Thomas (2012) who show that
higher accruals are associated with higher EPS levels. For example, among firms that increase shares, the
usage of total accruals drops from 3.76% of assets over t − 1 to 3.30% over t + 1. This is compared to a slight
increase (3.09% to 3.10%) over time among the control group. There are similar drops in the usage of other
measures of accounting and real earnings management surrounding increases in shares, and these hold using
four quarter averages as well (Panel B). Overall, the results indicate that an increase in the target size is
associated with significant, real effects on EPS outcomes and the usage of other earnings management tools.
3.2.4 Short term rounding effects
As discussed in Section 2, managers might choose the amount by which they change shares in light of current
period earnings. To examine this, we distinguish splits by the timing in which they are declared and the
magnitude of the split factor. First, we identify a split as late if it occurs after the quarter end but before
the earnings report date. Also, for each split we set a dummy variable atypical equal to one if the split factor
is not in (1.25, 1.33, 1.5, 1.75, 2, 2.5, 3, 4, 5, 10).
Similar to Bens et al. (2003) and Hribar et al. (2006), we determine if each split had an accretive or
dilutive effect (or neither) on that quarter-end’s EPS by comparing the post-split EPS to what the EPS
would have been had the firm not split. We compute post-split as IBADJQ/CSHPRQ (from Compustat)
rounded to the penny. We compute pre-split EPS as IBADJQ/CSHPRQ*FACSHR, rounded to the penny,
then divided by the split factor. If the post-split EPS is greater than the pre-split EPS then the split is
accretive. The split is dilutive if the post-split EPS is less than pre-split, and neither if there is no difference.
We expect that, if firms choose the magnitude of the split out of concern for its accretive or dilutive
effects on current period EPS, these splits will occur late in the quarter, and will, on average, be in an
22

atypical amount. In Table 9, we report the percentage of splits that are accretive, dilutive, or neither for
the full sample and subsamples. We find little evidence that managers use atypical split ratios and timing
to generate accretive rounding effects. Given the lack of economic significance, we do not formally report
statistical significance. Across all splits, 31.8% have an accretive effect and 29% have a dilutive effect. This
difference is roughly the same whether the split occurred during the quarter or after quarter end. Similarly,
we see no meaningful difference between accretive and dilutive when distinguishing between typical and
atypical split ratios.
[Insert Table 9 Here]
When we look exactly where we expect to see an effect - late splits that are of atypical split factors -
we see a large difference. However, only 13 splits satisfy these criteria, far from an economically meaningful
effect. To summarize, we find very little evidence that splits are used to have an accretive effect on current
period EPS.
3.3 Additional Implications
In this section, we discuss a few additional implication of TSM. Because TSM is achieved by changing shares,
any per-share metric will be affected. This suggests that cross sectional variation in a variety of per share
metrics such as analyst forecast error or dispersion, and even stock prices, may be the endogenous outcome
of TSM. We briefly examine how TSM may relate to i) analysts’ forecast errors, ii) the nominal stock price
puzzle, and iii) idiosyncratic return volatility.
3.3.1 Scale invariance of forecast volatility
The observation that firms with higher EPS levels have lower variance in forecast errors than what would
otherwise be expected was first documented in Degeorge et al. (1999). More recent work has attempted to
understand why this scale invariance exists. Cheong and Thomas (2011) test three potential explanations
and find results that, on net, suggest managers suppress the natural variation due to scale. Importantly,
forecast error variance is computed at the per-share level, which means it is a function of the magnitude
of rounding. Ball (2011) describes how rounding net income at the share level can introduce noise, and
suggests that this could contribute to a lack of variance with scale. We build on this by positing that scale
invariance is the endogenous outcome of TSM. In fact, the lack of variation with scale is essentially our main
prediction. To see this, consider a simple example.
23

Two firms are the same in all ways except for their distributions of net income. Firm A’s net income is
distributed uniformly over [9, 11), and Firm B’s net income is uniformly distributed over [8, 12). So both firms
have the same expected net income but B is more volatile than A. If both managers equally value meeting
EPS forecasts, then each will choose shares outstanding such that the probability of meeting expectations is
the same across both firms. If Firm A has 100 shares outstanding, then the probability that the firm meets
earnings is 1/2. 16 If the manager of B also wants to meet forecasts half of the time, the firm will need 200
shares outstanding. 17
From here it is easy to show that the two firms will have identical variance in forecast errors.
For
each firm, one fourth of the time the firm will miss EPS forecasts by one penny, one-half of the time they
meet expectations, and one-fourth of the time they beat expectations by a penny. 18
In this way, the scale
invariance of forecast errors is the equilibrium outcome of managers’ incentive to meet EPS forecasts.
Furthermore, we would expect forecast error variance to drop after a split. If nothing changes about
Firm A other than that it issues a two-for-one stock split, the variance in forecast errors drops to zero (all
possible net income outcomes generate EPS = 0.05).
We do not think our results completely explain the puzzle of scale invariant forecast errors. Cheong and
Thomas (2011) find that the scale invariance is not present in per share cash flow forecasts, for example.
A simple rounding based explanation is not consistent with this important finding.
Therefore, it seems
reasonable to conclude that target size management can explain some of the scale invariance results, but the
active smoothing of earnings by managers also plays an important role.
3.3.2 Nominal price puzzle
Weld et al. (2009) document that nominal per-share stock prices have remained remarkably constant across
time (1933-2007). This is surprising given significant inflation over the same period. The authors estimate
that if real stock prices had remained constant over this period, prices today would average around $450.
Furthermore, the authors make the observation that existing theories of stock splits fail to predict that
nominal share prices would remain constant. The authors conclude that social norms drive managers to use
stock splits to keep nominal prices at some fixed level.
While our results may not fully explain the nominal price puzzle, TSM may contribute to the constant
16 For simplicity assume that forecasts are unbiased. The firm needs net income within ± 0.5 = 5%, or any net income
|E[EP S]|
∈ [9.5, 10.5). The firm will generate net income in this range 10.5−9.5 = 1 of the time.
11−9 2
s
17 Set the probability of meeting forecasts equal to 1/2 and solve for s: 1/2 = 100
12−8 .
18 For Firm A, Var = 1 4 (0.09 − 0.10)2 + 1 2 (0)2 + 1 4 (0.11 − 0.10)2 = 1 2 (0.01)2 . For Firm B, Var = 1 4 (0.04 − 0.5)2 + 1 2 (0)2 +
1
4 (0.06 − 0.05)2 = 1 2 (0.01)2 .
24

price levels observed in the data. Firms are required to round EPS to the penny, and this remains true
despite the penny declining in real value. Because the norm of rounding to the penny has been stable, so
should nominal EPS levels. If managers choose shares outstanding to maintain a constant nominal level of
EPS, then it may not be surprising to also find constant nominal price levels over time.
In each quarter, we compute the median price-per-share and median earnings-per-share. We plot these
median values over time in Figure 3. Due to Compustat earnings data limitations, we limit the sample to
post 1970. Weld et al (2009) argue that managers choose shares outstanding to keep prices constant, whereas
we argue that managers choose shares outstanding to keep earnings per share constant. The figure shows
that, not surprisingly, prices and earnings levels are strongly related. It is also evident that there is variation
in both price-per-share and earnings-per-share medians.
[Insert Figure 4 about here]
It is difficult to distinguish between the incentive for constant nominal EPS generating constant nominal
prices from the incentive for constant nominal prices generating nominal EPS. We attempt to provide some
evidence that the incentive for constant EPS does affect aggregate price levels. To do so, we use time series
variation in net income volatility. Our earlier results suggest that firms respond to increases in net income
volatility by reducing EPS levels.
Therefore, we predict that changes in aggregate net income volatility
should predict changes in aggregate EPS levels.
If managers are choosing constant EPS levels and not
constant price levels, then this variation should also show up in price levels. Otherwise, it is less clear why
aggregate per share price levels should be a function of lagged aggregate net income volatility.
We compute correlations between median price-per-share, median earnings-per-share, and median Net
Income volatility (measured for each firm using the prior 12 quarters) over time. Median prices and median
earnings are highly correlated, 0.68. The correlation between median EPS and median NI volatility is -0.38,
and significant at the 1% level. This is consistent with our cross-sectional results which suggest that firms
decrease EPS as a response to an increase in volatility. More interestingly, median nominal prices are also
negatively correlated with trailing 12-quarter NI volatility (ρ = −0.16, pvalue = 0.025). This suggests that
managers’ incentives for certain EPS levels contribute to variation in price levels.
Our results do not suggest that social norms have no role. In fact norms may be the primary determinant
of constant nominal prices. We merely suggest that TSM is an explanation for stock splits that is consistent
with constant nominal price levels.
25

3.3.3 Stock price levels and idiosyncratic volatility
Target Size Management has implications for the relationship between per share stock price levels and return
volatility. One result documented in Brandt et al. (2010) is that lower priced stocks have higher return
volatility. An interpretation of this relationship is that low priced stocks have higher volatility because they
have a low price, and that this is a result of a retail trader clientele effect. TSM suggest that causality may
run in the opposite direction. Firms with high earnings volatility may choose low prices as a result of EPS
incentives. To the extent that earnings volatility and return volatility are correlated, we would expect to see
similar empirical outcomes but with causality running in the opposite direction.
In unreported tests, we observe a nearly identical relationship between per share price levels and return
volatility (Brandt et al. (2010)) and per share price level and net income volatility (TSM). Distinguishing
between these two possible explanations is beyond the scope of this paper.
However, this highlights an
example of potential implications of target size management that are beyond financial reporting and EPS
outcomes.
4 Conclusion
A range of net income numbers will generate the same EPS number. This is because earnings per share
are rounded to the nearest penny. So, for any given EPS forecast, there is a range of total earnings that
will meet that forecast. We refer to the magnitude of this range as the size of the earnings target. The
size of the earnings target is a function of the number of shares outstanding. We find evidence consistent
with the view that managers engage in target size management - adjusting the firm’s quantity of tradeable
securities to affect the size of the range of net income numbers that meet EPS forecasts. We find that an
exogenous decrease in the probability of meeting earnings estimates causes managers to split their stocks,
thereby increasing the earnings target size. We find that this effect is stronger among firms whose managers’
compensation is highly sensitive to EPS surprises, and weaker among firms for which an increase in shares
would be highly costly (e.g., highly illiquid firms).
Target size management has real effects. We find that firms are more likely to meet EPS expectations
following an increase in shares. Simultaneously, these firms use less accounting and real earnings management
tools. Both of these associations are consistent with an increase in shares increasing the earnings target size.
Our results suggest that the magnitude of the firm’s long run usage of earnings management tools is a
managerial choice. This has implications for research examining the determinants of traditional earnings
26

management tools.
27

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30

A
Appendix
We show that a drop in analyst coverage decreases the probability of meeting the earnings forecast. Consider
a firm with s shares outstanding and net income uniformly distributed [−e, e]), where e is in dollars. Assume
that each analyst issues a forecast that is independently drawn from a uniform distribution over [−e, e]), and
that the consensus forecast is the sample mean. With infinite analysts, the forecast equals the mean and
there is no variance. In this benchmark case the forecast is unbiased and has no noise, and the probability
that the firm meets earnings forecasts is
s
200e .
For simplicity, we compare to the case in which there is only one analyst. The variance in the estimate
will therefore be much higher than the benchmark case (the variance of the sample mean is decreasing in
N). Because the variance is higher, the probability of meeting the forecast is lower. The intuition for this is
straightforward. If the forecast is relatively close to the mean, then P r(meet) =
is close to one of the tails of the distribution, then P r(meet) <
s
200e
. But if the forecast
s
200e
. No matter where the forecast is, the
target size around the forecast is always ± s
200
, but integrating over this range results in different probabilities
depending on where in the distribution the forecast is. When the forecast deviates from the mean, the result
is a lower probability simply because the outcomes in the tails are less likely to occur.
With probability 1 −
With probability
P r(meet) =
s
200e
the forecast will be close enough to the mean such that P r(meet) =
s
200e .
s
400e
the forecast will be on the left tail of the uniform distribution such that in expectation
3s
800e
. Because the forecast is unbiased the effect is the same on the right tail. Therefore, with
a noisy, unbiased forecast:
E[P r(meet)] = (1 −
s
200e ) s
200e + 2( s
400e ) 3s
400e =
s
200e (1 −
s
800e ).
We can compare this probability to the case in which the forecast is not noisy (infinite analysts). It
is easy to show that if the manager prefers the same Pr(meet), shares need to increase in response to
a drop in analyst coverage.
Using s ∗ to denote the shares in the case of a forecast without noise, then
s
200e (1 −
s
800e ) =
s∗
200e → s > s∗ .
The result shown above assumes analysts are unbiased. It can be shown that an increase in forecast bias
has the same qualitative effect. Intuitively, integrating over the ± s
200
range results in a lower probability
when the forecast is farther away from the mean. In this way an increase in bias has an effect similar to an
increase in forecast variance.
31

Table 1: Summary Statistics
This table presents summary statistics of the key variables used in this study. Shares outstanding (millions) is
the total number of shares outstanding (CRSP) at the end of the quarter. EPS is the primary earnings per share
(COMPUSTAT). Net Income is the reported net income at the fiscal quarter end. Net Income Vol is the standard
deviation of net income over the past 12 qtrs. Net Income Vol - Naive is the standard deviation of seasonally adjusted
net income over the past 12 qtrs. Net Income Vol - Analyst is the standard deviation of net income minus the consensus
IBES median forecast of net income over the previous 12 qtrs. Stock Volatility is the standard deviation of daily
stock returns over the past year. Market Capitalization is the total market capitalization in millions at the quarter
end. Institutional Ownership is the % of institutional ownership from Thomson 13(f). Incentive Compensation is
calculated as 1-(Salary/TDC1). Num of Analysts is the number of analysts cover the stock during the quarter.
Annual Stock Return is the past 12 month stock return. Amihud is the log of the Amihud ratio calculated over the
past year. Split ratio is the ratio to adjust shares at stock split announcement. Share price is the stock price at the
end of the quarter. Age is the years since IPO. The sample is from 1984-2012.
Variable Mean P25 Median P75 STD
Shares Outstanding 83.85 10.16 23.55 56.75 346.78
EPS 0.20 -0.02 0.19 0.47 1.19
Net Income 34.48 -0.30 3.05 17.65 388.95
Net Income Vol 51.48 1.59 5.23 20.57 347.76
Net Income Vol - Naive 40.38 1.47 4.75 18.20 264.06
Net Income Vol - Analyst 32.04 0.58 2.38 11.01 250.83
Stock Volatility 3.30 1.82 2.68 4.04 2.35
Market Capitalization 2766 95 338 1316 13069
Institutional Ownership 47.97 24.34 46.85 70.22 27.78
Incentive Compensation 66.65 54.04 73.24 85.19 24.46
Num of Analysts 4.24 1 3 5 4.35
Annual Stock Return 15.74 -21.13 5.96 34.78 81.12
Amihud -1.05 -2.90 -0.98 0.80 2.57
Split Ratio 1.64 1.50 1.50 2.00 0.68
Share Price 22.68 7.70 17.25 30.75 24.94
Age 16.1 5.5 11.2 21.2 15.2
32

Figure 1: Example of the relationship between earnings growth, shares outstanding and EPS.
This figure shows the mechanical relationship between earnings growth, shares outstanding, and EPS as a result
of EPS rounding. The Base Case presents an example of a firm with $100 of expected earnings and 1000 shares
outstanding with a target size of ±5% of expected earings. Earnings Growth (1000 shares) presents an example of
the same 1000 shares outstanding and expected earnings of $200. The target size is ±2.5% of expected earnings.
Earnings Growth and 2:1 Split presents the same example but with 2000 shares outstanding. The target size returns
to ±5%.
Base Case (1000 Shares)
EPS= $0.10
Earnings=$95
E[Earnings]=$100
+/- 5% of E[Earnings]
Earnings=$105
Earnings Growth (1000 Shares)
EPS= $0.20
E[Earnings]=$200
Earnings=$195
Earnings=$205
+/- 2.5% of E[Earnings]
Earnings Growth and 2:1 Split (2000 Shares)
EPS= $0.10
Earnings=$190
E[Earnings]=$200
+/- 5% of E[Earnings]
Earnings=$210
33

Figure 2: Histogram of net income scaled by the minimum necessary to meet the median analyst forecast.
This figure presents a histogram of earnings outcomes. For each firm-quarter, we compute the minimum net income
needed to meet the median forecast. We scale each firm-quarter reported net income by this minimum. The dark
vertical line that intersects the x-axis at a value of 1 indicates the point at which the firm generates just enough net
income to meet the median forecast. The lighter line that intersects the x-axis near 1.02 reflects the average amount
of net income that would equal the forecasted net income (EPS forecast times shares).
34

Figure 3: Median Shares Outstanding across Net Income Volatility and Incentive Compensation Deciles
This figure presents median shares outstanding (bar chart) and median net income (line-plot) across deciles sorted
on Net Income Volatility (Panel A) and Incentive Compensation (Panel B). Shares outstanding are adjusted for net
income by first sorting the sample firms into 20 groups based on net income each quarter, and then sorting into deciles
based on Net Income Volatility or Incentive Compensation. Net Income Volatility is the standard deviation of the
previous 12 quarters of net income. Incentive Compensation is calculated as 1-(Salary/TDC1). Shares outstanding
is represented on the left axis and net income is on the right axis. The sample period is 1984-2011.
Panel A. Shares Outstanding across Net Income Volatility Deciles
Shares Outstanding
40,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
0
Bottom Net
Income Volatility
Decile
2 3 4 5 6 7 8 9
Net Income
5
Top Net Income
Volatility
Decile
4
3
2
1
0
Shares Outstanding
Net Income
Panel B. Shares Outstanding across Incentive Compensation Deciles
Shares Outstanding
80,000
70,000
60,000
50,000
40,000
30,000
20,000
Bottom
Incentive
Comp Decile
2 3 4 5 6 7 8 9
Net Income
50
40
30
20
10
0
Top
Incentive
Comp Decile
Shares Outstanding
Net Income
35

Figure 4: Median nominal price-per-share and earnings-per-share, 1971-2011.
This figure shows median nominal price-per-share and earnings-per-share, 1971-2011 for all US firms with price and
earnings data in Compustat.
36

Table 2: Determinants of Shares Outstanding
This table presents OLS cross sectional regression models of shares outstanding as a function of firm characteristics. Shares outstanding
is measured as the total number of shares outstanding (1000’s) from CRSP at the end of the quarter. Net Income Volatility is the
standard deviation of Net Income over the previous 12 quarters. Net Income Forecast Error Volatility - Naive is the standard deviation of
the the difference between actual earnings and an expectation of earnings based on the earnings from 4 quarters prior plus the difference
between the earnings 4 quarters and 8 quarters prior. Net Income Forecast Error Volatility - Analyst is the standard deviation of the
the difference between actual earnings and median IBES forecast of earnings. Market to Book is total market equity plus the book value
of total debt divided by total assets. Net Income is from Compustat at quarter end. Market Cap is the total market capitalization in
millions at the quarter end. Institutional ownership is percent ownership of all institutions. Return Volatility is the standard deviation
of daily stock returns over the prior 90 days. Annual Return is the past 12 month stock return. The Amihud measure of illiquidity
calculated over the previous 90 days. Incentive Comp is the percent of total compensation made up by bonus, stock, and option grants.
(1) (2) (3) (4)
Shares Shares Shares Shares
VARIABLES Outstanding Outstanding Outstanding Outstanding
Net Income Volatility t−1 0.21*** 0.25***
(0.01) (0.01)
Net Income Volatility - Naive Forecast t−1 0.21***
(0.01)
Net Income Volatility - Analyst Forecast t−1 0.30***
(0.02)
Market to Book t−1 0.01*** 0.01*** -0.01** -0.02**
(0.00) (0.00) (0.00) (0.01)
Net Income t−1 -0.11*** -0.11*** -0.09*** -0.07***
(0.01) (0.01) (0.01) (0.01)
Institutional Ownership t−1 0.01** 0.01*** 0.00 -0.14***
(0.00) (0.00) (0.01) (0.02)
Market Cap t−1 0.84*** 0.85*** 0.77*** 0.76***
(0.01) (0.01) (0.01) (0.01)
Annual Return t−1 -0.04*** -0.04*** -0.05*** -0.10***
(0.00) (0.00) (0.00) (0.01)
Amihud t−1 -0.05*** -0.06*** -0.11*** -0.43***
(0.00) (0.00) (0.00) (0.13)
Return Volatility t−1 0.05*** 0.06*** 0.06*** 0.12***
(0.00) (0.00) (0.00) (0.01)
Incentive Comp t−1 0.05***
(0.01)
Constant -0.04*** -0.03*** 0.03** 0.11*
(0.01) (0.01) (0.02) (0.06)
Year Effects Y Y
Observations 582,754 486,137 332,578 120,635
R-squared 0.81 0.81 0.81 0.82
Standard errors clustered by firm in parentheses
*** p

Table 3: Shares Outstanding: First Differences
This table presents First Differences regression models of changes in shares outstanding as a function of changes in firm characteristics.
Shares outstanding is measured as the total number of shares outstanding (1000’s) from CRSP at the end of the quarter. Net Income
Volatility is the standard deviation of Net Income over the previous 12 quarters. Net Income Forecast Error Volatility - Naive is the
standard deviation of the the difference between actual earnings and an expectation of earnings based on the earnings from 4 quarters
prior plus the difference between the earnings 4 quarters and 8 quarters prior. Net Income Forecast Error Volatility - Analyst is the
standard deviation of the the difference between actual earnings and median IBES forecast of earnings. Market to Book is total market
equity plus the book value of total debt divided by total assets. Net Income is from Compustat at quarter end. Market Cap is the total
market capitalization in millions at the quarter end. Institutional ownership is percent ownership of all institutions. Return Volatility
is the standard deviation of daily stock returns over the prior 90 days. Annual Return is the past 12 month stock return. The Amihud
measure of illiquidity calculated over the previous 90 days.
(1) (2) (3)
∆ Shares ∆ Shares ∆ Shares
VARIABLES Outstanding Outstanding Outstanding
∆ Net Income Volatility t−1 0.04***
(0.00)
∆ Net Income Volatility - Naive Forecast t−1 0.03***
(0.00)
∆ Net Income Volatility - Analyst Forecast t−1 0.07***
(0.01)
∆ Market to Book t−1 0.01*** 0.02*** 0.02***
(0.00) (0.00) (0.00)
∆ Net Income t−1 0.00 0.00 0.01***
(0.00) (0.00) (0.00)
∆ Institutional Ownership t−1 0.12*** 0.13*** 0.13***
(0.00) (0.00) (0.00)
∆ Market Cap t−1 0.10*** 0.10*** 0.10***
(0.00) (0.00) (0.00)
∆ Annual Return t−1 0.00 -0.00 -0.00
(0.00) (0.00) (0.00)
∆ Amihud t−1 -0.01*** -0.01*** -0.02***
(0.00) (0.00) (0.00)
∆ Return Volatility t−1 0.01*** 0.01*** 0.02***
(0.00) (0.00) (0.00)
∆ Incentive Comp t−1
Constant 0.02 0.02 0.24
(0.02) (0.02) (0.29)
Year Effects Y Y Y
Observations 543,355 454,258 313,297
R-squared 0.03 0.03 0.03
Standard errors clustered by firm in parentheses
*** p

Table 4: Shares Outstanding: First Differences and IV
This table presents IV regression models of changes in shares outstanding as a function of changes in firm characteristics. Net Income
Forecast Error Volatility - Analyst is instrumented for using exogenous changes in analyst coverage. Shares outstanding is measured as
the total number of shares outstanding (1000’s) from CRSP at the end of the quarter. Net Income Forecast Error Volatility - Analyst
is the standard deviation of the the difference between actual earnings and median IBES forecast of earnings. Market to Book is total
market equity plus the book value of total debt divided by total assets. Net Income is from Compustat at quarter end. Market Cap is
the total market capitalization in millions at the quarter end. Institutional ownership is percent ownership of all institutions. Return
Volatility is the standard deviation of daily stock returns over the prior 90 days. Annual Return is the past 12 month stock return.
The Amihud measure of illiquidity calculated over the previous 90 days.
(1) (2)
∆ Shares ∆ Shares
VARIABLES Outstanding Outstanding
∆ Net Income Volatility - Analyst Forecast t−1 0.53*** 0.58**
(0.17) (0.26)
∆ Market to Book t−1 0.03*** 0.02
(0.01) (0.01)
∆ Net Income t−1 0.03*** 0.04**
(0.01) (0.02)
∆ Institutional Ownership t−1 0.15*** 0.20***
(0.00) (0.01)
∆ Market Cap t−1 0.08*** 0.08***
(0.01) (0.01)
∆ Annual Return t−1 0.01 0.01
(0.01) (0.02)
∆ Amihud t−1 -0.02*** -0.03
(0.00) (0.05)
∆ Return Volatility t−1 0.02*** 0.04***
(0.00) (0.01)
∆ Incentive Comp t−1 0.01**
(0.00)
Constant 0.02 -0.14***
(0.02) (0.03)
Year Effects Y Y
Observations 246,077 105,571
R-squared 0.04 0.04
Standard errors clustered by firm in parentheses
*** p

Table 5: Changes in Shares Outstanding: Stock Splits and EPS
This table presents IV regression models of shares outstanding as a function of firm characteristics. In these specifications, Net Income Error Volatility is instrumented for using
exogenous changes in analyst coverage. Columns 1 presents standardized regression coefficients. Columns 1 and 2 show changes in shares outstanding due to splits and other
than splits respectively. Column 3 controls for high and low stock prices where High is defined as stocks above $80 and Low is defined as below $20. Columns 4 and 5 show
results for share changes due to splits for firms with negative EPS and positive EPS. Column 6 and 7 shows results for share changes do to splits for firms with above median
incentive compensation and below median incentive compensation. Shares outstanding is measured as the total number of shares outstanding (1000’s) from CRSP at the end of
the quarter. Net Income Error volatility is the standard deviation of the the difference between actual earnings and median IBES forecast of earnings. Market to Book is total
market equity plus the book value of total debt divided by total assets. Operating income is defined as operating income before interest and depreciation from Compustat at
quarter end. Market Cap is the total market capitalization in millions at the quarter end. Institutional ownership is percent ownership of all institutions. Return Volatility is the
standard deviation of daily stock returns over the prior 90 days. Annual Return is the past 12 month stock return.
(1) (2) (3) (4) (5) (6)
∆ Shares ∆ Shares s ∆ Shares ∆ Shares ∆ Shares ∆ Shares
VARIABLES non-Splits from Splits from Splits from Splits from Splits from Splits
Full Sample Full Sample Negative EPS Positive EPS Low Incent. Comp High Incent. Comp
∆ Net Income Volatility - Analyst Forecastt−1 136 6,676*** 2,115 7,204*** 4,142 15,867*
(268) (1,709) (1,714) (1,907) (3,146) (9,302)
∆ Market to Bookt−1 -11 241*** 38 458*** 989*** 312*
(9) (61) (31) (112) (223) (182)
∆ Net Incomet−1 13 408*** 51 536*** 412* 632*
(14) (106) (43) (145) (230) (332)
∆ Institutional Ownershipt−1 196*** 282*** -36 422*** 752*** 307***
(6) (44) (37) (63) (169) (102)
∆ Market Capt−1 114*** 587*** 412*** 547*** 635*** 332
(10) (72) (107) (95) (112) (277)
∆ Annual Returnt−1 3 -45 -32 -30 -239 162
(10) (62) (25) (94) (249) (297)
∆ Amihudt−1 -40*** 1 11 -20 44 147
(6) (22) (24) (21) (481) (532)
∆ Return Volatilityt−1 22*** 150*** 27* 244*** 464*** 117
(5) (23) (14) (37) (100) (113)
Constant 246*** 255* 281 39 99 713
(28) (139) (204) (184) (271) (738)
Year Effects Y Y Y Y Y Y
Observations 245,267 245,281 60,781 184,144 55,820 51,195
Standard errors clustered by firm in parentheses
*** p

Table 6: Changes in Shares Outstanding: High Cost to Splitting
This table presents IV regression models of shares outstanding as a function of firm characteristics. In these specifications, Net Income
Error Volatility is instrumented for using exogenous changes in analyst coverage. Column presents the regression specification from table
5 and controls for high and low stock prices where High is defined as stocks above $80 and Low is defined as below $20. Columns 2 and 3
show show results for share changes due to splits for firms with above median illiquidity and below median illiquidity respectively.Shares
outstanding is measured as the total number of shares outstanding (1000’s) from CRSP at the end of the quarter. Net Income Error
volatility is the standard deviation of the the difference between actual earnings and median IBES forecast of earnings. Market to Book
is total market equity plus the book value of total debt divided by total assets. Operating income is defined as operating income before
interest and depreciation from Compustat at quarter end. Market Cap is the total market capitalization in millions at the quarter end.
Institutional ownership is percent ownership of all institutions. Return Volatility is the standard deviation of daily stock returns over
the prior 90 days. Annual Return is the past 12 month stock return.
(1) (2) (3)
∆ Shares ∆ Shares ∆ Shares
VARIABLES Full Sample High Illiquidity Low Illiquidity
∆ Net Income Volatility - Analyst Forecast t−1 4,796** -1,295 6,263**
(1,882) (4,037) (2,477)
∆ Market to Book t−1 204*** 21 482***
(60) (15) (119)
∆ Net Income t−1 301*** 27 446***
(110) (82) (159)
∆ Institutional Ownership t−1 280*** 43*** 561***
(43) (10) (88)
∆ Market Cap t−1 451*** 424*** 569***
(57) (51) (90)
∆ Annual Return t−1 -56 -27 -40
(61) (18) (155)
∆ Amihud t−1 5 -9 58,847
(16) (8) (59,775)
∆ Return Volatility t−1 118*** 14** 417***
(19) (6) (66)
High Price t−1 13,008*
(1,335)
Low Price t−1 -101
(244)
Constant -155 -87 2,924
(155) (381) (2,886)
Year Effects Y Y Y
Observations 280,067 146,010 134,048
Standard errors clustered by firm in parentheses
*** p

Table 7: Changes in Shares and EPS Outcomes
This table presents results from a difference-in-difference analysis examining the association between increases in
shares outstanding and EPS outcomes, and earnings management. We distinguish firms that significantly increase
the number of shares outstanding in quarter t from those that do not. We define a significant increase as any change
that results in a 25% increase or greater (a split factor of 5-for-4 or greater). Then we compare how changes in EPS
outcomes differs across samples. Miss, Beat and Meet are dummies set to one if the firm’s reported EPS was below,
above, or equal to the median analyst forecast, respectively, zero otherwise. Panel A reports the average of these
dummy variables over quarter t − 1 (the ‘pre’ period) and that over quarter t + 1 (post). We distinguish firms that
increased shares at t = 0 from those that did not, and report the difference across these two groups in the differences
across time. Panel B uses the firm average over the 4 quarters prior to t = 0 and compares this to the firm average
over the t + 1 to t + 4. t-statistics on the differences in differences are clustered at the firm-level.
Panel A: 1 quarter pre and post evaluation period
split? pre post dif t-stat
Miss N 16.70% 16.83% 0.13%
Y 21.97% 17.94% -4.03%
-4.16% (-6.64)
Beat N 4.98% 5.01% 0.03%
Y 7.32% 6.08% -1.24%
-1.27% (-3.04)
Meet N 78.33% 78.16% -0.17%
Y 70.71% 75.99% 5.28%
5.45% (7.80)
Panel B: 4 quarter pre and post evaluation period
split? pre post dif t-stat
Miss N 17.71% 17.54% -0.17%
Y 19.75% 18.43% -1.32%
-1.15% (-3.34)
Beat N 4.71% 4.68% -0.03%
Y 7.03% 5.68% -1.35%
-1.32% (-5.86)
Meet N 77.58% 77.78% 0.20%
Y 73.22% 75.89% 2.67%
2.47% (6.29)
42

Table 8: Changes in Shares and Accounting and Real Earnings Management
This table presents results from a difference-in-difference analysis examining the association between increases in
shares outstanding and measures of accounting and real earnings management. We distinguish firms that significantly
increase the number of shares outstanding in quarter t from those that do not. We define a significant increase as
any change that results in a 25% increase or greater (a split factor of 5-for-4 or greater). Then we compare how
changes in the usage of earnings management tools differs across samples. Discretionary accruals are residuals from
industry total accruals regressions including performance controls following Ecker et al. (2011). Total accruals are
defined as the change in current assets, adjusted for the change in cash, minus the change in current liabilities,
adjusted for current liabilities used for financing, minus depreciation expense. Measures of real earnings management
are estimated by abnormal cash flow (RealEM CF ), production costs (RealEM P rod ), and expenditure (RealEM CF )
following the methodology in Roychowdhury (2006). In Panel A report the average of the absolute value of these
variables over quarter t − 1 (the ‘pre’ period) and compare it to that over quarter t + 1 (post). We distinguish firms
that increased shares at t = 0 from those that did not, and report the difference across these two groups in the
differences across time. Panel B uses the firm average over the 4 quarters prior to t = 0 and compares this to the
firm average over the t + 1 to t + 4. t-statistics on the differences across samples are clustered at the firm-level.
Panel A: 1 quarter pre and post evaluation period
split? pre post dif
|Accruals T otal | N 3.09% 3.10% 0.01%
Y 3.76% 3.30% -0.46%
-0.47% (-7.07)
|Accruals Disc | N 6.66% 6.67% 0.01%
Y 7.38% 6.59% -0.79%
-0.80% (-4.21)
|RealEM CF | N 2.83% 2.83% 0.01%
Y 3.31% 3.03% -0.28%
-0.29% (-5.50)
|RealEM P rod | N 3.62% 3.63% 0.01%
Y 4.31% 3.96% -0.34%
-0.35% (-6.31)
|RealEM Exp | N 3.43% 3.45% 0.02%
Y 3.84% 3.40% -0.43%
-0.45% (-8.62)
Panel B: 4 quarter pre and post evaluation period
split? pre post dif
|Accruals T otal | N 2.97% 2.88% -0.09%
Y 3.49% 3.17% -0.32%
-0.23% (-3.98)
|Accruals Disc | N 6.14% 6.34% 0.20%
Y 6.65% 6.23% -0.42%
-0.62% (-4.88)
|RealEM CF | N 2.67% 2.63% -0.05%
Y 3.18% 2.89% -0.29%
-0.24% (-6.63)
|RealEM P rod | N 3.52% 3.43% -0.09%
Y 4.21% 3.87% -0.34%
-0.25% (-4.19)
|RealEM Exp | N 3.30% 3.29% -0.01%
Y 3.79% 3.35% -0.44%
-0.43% (-8.86)
43

Table 9: Short-term Accretive and Dilutive Effects
This table presents summary statistics on the accretive and dilutive effect of stock splits on quarter-end EPS. A split
is determined to be accretive if the firm’s EPS (measured as Compustat IBADJQ/CSHPRQ rounded to the penny)
is greater than the EPS had the firm not split (measured as IBADJQ/CSHPRQ*facshr, rounded to the penny, then
divided by the split factor). The split is dilutive if the post-split EPS is less than pre-split, and neither if there is no
difference. Atypical split ratios are defined as any split factor not in (1.25,1.33,1.5,1.75,2,2.5,3,4,5,10). A split is late
if it occurs after the quarter end but before the earnings report date. Accretive, neither, dilutive, atypical, and late
are all indicator variables.
Sample Means
all splits late=0 late=1 atypical=0 atypical=1
N 11447 11016 431 11148 299
accretive 0.318 0.319 0.309 0.315 0.431
neither 0.393 0.392 0.415 0.401 0.097
dilutive 0.290 0.290 0.276 0.285 0.472
atypical 0.026 0.026 0.030
late 0.037 0.043
late=0 late=1 late=0 late=1
atypical=0 atypical=0 atypical=1 atypical=1
N 10730 418 286 13
accretive 0.316 0.300 0.423 0.615
neither 0.400 0.426 0.098 0.077
dilutive 0.285 0.275 0.479 0.308
44