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Do Short Sellers Affect Corporate Decisions?
Mahdi Nezafat, Tao Shen, Qinghai Wang∗
January, 2015
Abstract
We study the effects of short selling activities on corporate investment. In a modelwith short-term managerial incentives, we show that short sellers can cause firms tooverinvestment. The overinvestment is more severe for managers with low productivityand/or with high short-term incentives. Empirically, we find that short interest isstrongly and positively associated with subsequent corporate investment. The impactof short selling activities on investment is greater when a firm’s investment prospect ispoor and/or when the sensitivity of a CEO’s compensation to stock price performanceis strong. Additionally, both short interest and corporate investment are negativelyassociated with subsequent stock returns.
JEL Codes: G30, G31Keywords: Short Selling, Corporate Investment, Stock Returns
∗Mahdi Nezafat, Broad College of Business, Michigan State University, East Lansing, MI 48824. E-mail:nezafat@broad.msu.edu. Tao Shen, School of Economics and Management, Tsinghua University, China,Beijing 100084. Email: shentao@sem.tsinghua.edu.cn. Qinghai Wang, Lubar School of Business, Universityof Wisconsin-Milwaukee, Milwaukee, WI 53201. E-mail: wangq@uwm.edu. We thank Charles Hadlock andXu Jiang for helpful comments. We thank Lalitha Naveen and Alex Edmans for making their data publiclyavailable. We alone are responsible for any errors.
1 Introduction
Do short sellers affect corporate decisions? Lamont (2012) documents that the management
takes a variety of legal and regulatory actions in response to short selling pressure to impede
short selling and concludes that “firms are not just passively responding to market signals,
but are in fact actively trying to prop up their stock prices.”1 In this paper, we study the
effects of short selling on corporate investment. We show theoretically that short selling
activities, in combination with short-term managerial objectives, can cause managers to
overinvestment. The overinvestment is more severe for managers with low productivity
and/or with high short-term incentives. The empirical analysis provides strong support for
the model’s predictions.
We introduce short sellers in the model described in Bebchuk and Stole (1993) to highlight
how short sellers can play an important role in corporate decisions. In our two-period
model, there are a manager and two types of investors: long investors and short sellers.
The manager’s utility depends on both the first and the second period firm’s valuation.
The manager decides to allocate a limited capital to two projects: a short-term project,
and a long-term project. The payoff of the long-term project is a function the manager’s
unobservable productivity. The long and short investors have different priors about the
productivity of the manager.
We show that short-term managerial objectives cause the manager to overinvest in the
long-term project and the presence of short sellers exacerbates the overinvestment problem.
Why does a manager overinvest? In this model, the market can observe the level of invest-
ment, but it has incomplete information about the productivity of the manager. Since the
manager’s utility depends on firm’s valuations in both periods, a manager with high produc-
tivity wants to invest more in the long-term project (relative to the first-best) to signal to
the market that the long-term project is valuable and therefore boost the firm’s valuation1These actions mainly include legal maneuvers such as lawsuits or the threat of lawsuits, as well as
actions such as stock splits or appeals to shareholders to limit the supply of shares. Liu and Swanson (2011)document that the management also employs share repurchases to fight short sellers.
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in the first period. The existence of the short sellers reduces the market assessment of the
productivity of the manager and therefore the firm’s valuation in the short-term. This re-
duction in firm’s valuation reduces the total utility of the manager and hence increases his
incentive to overinvest even more (relative to a manager that does not face short sellers) in
the long-term project.
We also show that the overinvestment problem is more severe for managers with low
productivity. A manager with high productivity is already overinvesting to signal his high
productivity and due to resource constraints cannot increase his investment in the long-term
project aggressively in response to the short sellers. Whereas, a manager with low productiv-
ity is investing closer to the efficient investment level in the absence of short selling activities
and thus responds more aggressively to the short sellers. In addition, the overinvestment
problem is more severe for managers with strong short-term incentives. This is because a
manager whose utility is more sensitive to short-term firm’s valuation has a stronger incentive
to overinvest in the long-term project in order to increase the short-term firm’s valuation.
We find strong empirical support for the model’s predictions. We show that short interest
strongly and positively predicts subsequent firm’s investment over time periods of one quarter
to one year. For corporate investment over the next quarter, if the short interest of a
firm increases to the top 20th percentile in the sample, the investment to assets ratio will
increase by approximately five percent. For investment over the next year, the increase is
approximately three percent. The main results are robust with respect to different measures
of short selling activities, different time horizons, and different estimation methodologies.
We explore two predictions of the model to understand the cross-sectional differences of
short sellers’ roles in corporate decisions. The model suggests that the lower the produc-
tivity of a manager, the stronger the effects of short selling on investment. The manager’s
productivity in the model determines the payoff of the long-term project, thus the manager’s
productivity can be interpreted as the quality of the investment opportunities that the firm
has. We use Tobin’s Q as a proxy for the quality of a firm’s investment opportunity. We find
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that the effects of short interest on investment remain significant for firms with low Tobin’s
Q, whereas the effects are much weaker for firms with high Tobin’s Q. The model also sug-
gests that the higher the sensitivity of a manager’s utility to the short-term firm’s valuation,
the greater the effects of short selling on investment. We use a CEO’s pay-performance sen-
sitivity (PPS), i.e., dollar change in wealth associated with a 1% change in the firm’s stock
price, as a proxy for the sensitivity of a manager’s utility to the firm’s short-term valuation.
We find that the high PPS firms respond more strongly to short interest in their investment
decisions than the low PPS firms do.
We conduct several tests to address concerns that reverse causality and endogeneity
problems could drive the evidence we have documented. We first investigate the concern
that firms with high short interest are overpriced and a firm’s overvaluation rather than
short selling activities causes the firm to overinvestment (see, e.g., Polk and Sapienza 2009).
We follow Polk and Sapienza (2009) and use discretionary accruals as a measure of mispricing
and study the effects of short interest on investment while controlling for the overvaluation
effects. We find that the inclusion of discretionary accruals does not subsume the effects of
short interest on investment.
We next investigate the concern that (over)investment and the associated overvaluation
drive short selling activities, and because investment is persistent, we observe a spurious
relation between short interest and subsequent investment. We employ three different tests
to address this concern. In the first test, we directly include past investment in the baseline
regression model to control for the possible relation between past investment and short
interest. We find that the inclusion of past investment does not subsume the effects of
short interest on investment. In the second test, we employ a two-stage least-squares (2SLS)
regression to tease out the effects of short interest on investment. Again, the effects of short
interest on investment remains significant in most specifications.
We develop our third test based on a prediction of the reverse causality argument in the
presence of short-sale constraints. For the reverse causality argument, it is what drives the
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possible short selling, i.e., overinvestment or overvaluation, and not the actual short interest
that relates to the subsequent investment. Because short-sale constraints affect short selling
activities, if reverse causality explains our empirical findings, the relation between short
interest and investment should be stronger in firms that are short-sale constrained. We find
that short-sale constraints have a negative rather than a positive impact on the documented
relation between short interest and investment which is opposite to the prediction of the
reverse causality argument. Taken together, these three separate tests provide support on
the robustness of our main empirical finding as they show that even after controlling for the
possible confounding effects on short selling activities, short interest still exhibits substantial
influence on corporate investment decisions.
Lastly, we examine the relation between corporate investment and stock returns in the
presence of short selling activities. We find that both short interest and corporate investment
are negatively associated with subsequent stock returns. The literature refers to the negative
relation between investment and future return as investment or asset growth anomaly, and
different theories have been proposed to explain this anomaly (see, e.g., Titman, Wei, and
Xie 2004, Zhang 2005, Xing 2008, Cooper, Gulen, and Schill 2008, and Lam and Wei 2011).
Our model and empirical findings suggest a new mechanism in which overinvestment driven
by short-term managerial incentives leads to an inefficient allocation of capital and hence
the abnormal negative future returns. This mechanism is consistent with empirical findings
in Titman, Wei, and Xie (2004) and Cooper, Gulen, and Schill (2008) in which they show
that asset growth effect is weaker in times of increased corporate oversight.
Our paper is related to models in Goldstein and Guembel (2008) and Brunnermeier and
Oehmke (2013). Goldstein and Guembel (2008) present a model in which short sellers can
cause under-investment due to price manipulation and the feedback effect from the stock price
to the real investment decisions. Brunnermeier and Oehmke (2013) present a model in which
predatory short selling forces financial firms to liquidate long-term investment at a discount.
In contrast to these models, our model implies that short sellers can cause overinvestment
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and the presented empirical evidence supports the overinvestment prediction.
Our paper is also related to studies on the effects of short-sale constraints on corporate
decisions. Massa, Zhang, and Zhang (2013a) and Massa, Zhang, and Zhang (2013b) find
that stock lending supply, i.e., the amount of shares available to be lent for short selling,
has a negative relation with earnings manipulation and a positive relation with internal
governance. Chang, Lin, and Ma (2014) show a negative relation exists between stock
lending supply and investment spikes. The stock lending supply is an ex ante threat to
the firm, and this threat could discipline managers. Our paper focuses on impact of the
observed short selling activities which is an ex post action taken by investors. Grullon et al.
(forthcoming) study the effects of short-sale constraints on corporate decisions. They find
that the relaxation of short-sale constraints affects the investment and financing decisions
of only small firms. Our findings, along with the findings of Liu and Swanson (2011), differ
from Grullon et al. (forthcoming) as we investigate the impact of the observed short sellers’
decisions and not the constraints that can affect the short selling activities.
The rest of the paper is organized as follows. The model is presented in Section 2. Section
3 describes the data and Section 4 presents the empirical results. Section 5 offers concluding
remarks.
2 Model
In this section we develop a simple model to show how short sellers can affect corporate
investment decisions. Our model follows the theoretical framework described in Bebchuk
and Stole (1993) while introducing short sellers into the model. There are two periods, a
manager and a unit measure of two types of investors: a fraction of 1 − w investors are
equity holders who are holding one divisible outstanding share, and a fraction of w are short
sellers. We assume that w is exogenous and there are a sufficient number of long and short
investors for each type to take positions in the firm. The assumption that w is exogenous is
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not a restrictive assumption in our model as we are investigating the effects of short sellers
on the investment choice of a manager. The manager has capital K and he allocates this
capital to two projects. The first project, the short-term project, will realize a return in the
first period and the second project, the long-term project, will realize a return in the second
period.
Let x represent the investment in the long-term project. The realization of the short-term
project’s return is S̃ = S(K−x)+ εs, where S ′(.) > 0, S ′′(.) < 0, and εs is a random variable
with mean zero and unbounded support. The realization of the long-term project’s return
is L̃ = θL(x) + εl, where θ represents the productivity of the manager, L′(.) > 0, L′′(.) < 0,
and εl is a random variable with mean zero and unbounded support that is independent of
εs. It is common knowledge by the investors and the manager that the long investors believe
that θ is distributed according to the continuous probability function f(θ) on [θl, θl]. The
short sellers are in disagreement with the long investors and it is also common knowledge
by the investors and the manager that short sellers believe that θ is distributed according
to the continuous probability function g(θ) on [θs, θs] such that θs < θl and θs ≤ θl. These
differences in priors can be interpreted as arising rationally due to difference in information
acquired by the investors, or as irrational overconfidence (see, e.g., Scheinkman and Xiong
2003).
Let x∗(θ) represent the value-maximizing level of investment in the long-term project. In
particular x∗(θ) is the solution to the following maximization problem:
x∗(θ) = arg maxx∈[0,K]
W (x) = S(K − x) + θL(x). (1)
This first-best solution can be achieved in a principal-agent setting in which θ is publicly
observable and contractible.
Let Vt represent the stock market’s valuation of the firm in period t over both periods.
The manager’s utility depends on both the first and the second period firm’s valuation. In
particular, the manager’s utility is:
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U(V1, V2) = α0 + α1V1 + α2V2,
where α1 > 0 and α2 > 0 are respectively the sensitivity of the manager to the first and
second period firm’s valuation.
We assume that the manager knows his productivity, i.e., θ. The investors cannot observe
θ but they form rational expectations. The output of the short-term project will be known
by the manager and the investors in the first period, and the investors can observe the level
of investment in the long-term project. We consider separating equilibrium in which the
manager signals his productivity through the level of investment in the long-term project. A
pure strategy equilibrium will have that a manager of type θ who observe a short interest of
w chooses xw, and therefore we can represent the equilibrium by function xw(θ). Let Θw(xw)
be the set of all θ that choose xw for a given level of short interest w. The market will have
expectation of θ which will be a function of xw and w. In particular,
θwE(xw) = E[θ|xw, w] = (1− w)
´Θw(x)
θf(θ)dθ´Θw(x)
f(θ)dθ+ w
´Θw(x)
θg(θ)dθ´Θw(x)
g(θ)dθ.
The manager’s expected utility can be written as:
U(xw, w, θ) = α0 + α1[S(K − xw) + θwE(xw)L(xw)] + α2[S(K − xw) + θL(xw)].
In this framework, we can prove the following three propositions (see Appendix A for
detail).
Proposition 1. A manager that faces short sellers invests more than a manager that does
not.
Proposition 2. The lower the productivity of a manager, the more severe the overinvestment
problem caused by short sellers.
Proposition 3. The higher the sensitivity of a manager’s utility to the first period firm’s
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valuation, the more severe the overinvestment problem.
Figure 1 illustrates the solution of the model. We plot xw as a function of θ, for managers
that face short sellers, xo as a function of θ, for managers that do not face short sellers, and
x∗ as a function of θ. In all figures we set S(x) = log(x), L(x) = log(x), K = 10, θs = 1,
θs = 3, θl = 1.5, and θl = 3. In the top figure, we set α1 = 0.1 and α2 = 1. In the middle
figure, we set α1 = 1 and α2 = 1. In the bottom figure, we set α1 = 1 and α2 = 0.1. The
relative value of α1 and α2 highlights differences in the sensitivities of the manager’s utility
to the firm’s valuations in the two periods.
The figures and the comparison of the figures reveal the main results of the model: (1)
investment in the long-term project is higher in the presence of short sellers, (2) the effects
of short sellers on investment are stronger when the productivity of the manager is lower,
and (3) the larger the ratio of α1/α2, i.e., the greater the managerial utility’s sensitivity to
first period firm’s valuation, the higher the overinvestment in the long-term project,
Why does the manager overinvest in this model? The results here resemble those in
Bebchuk and Stole (1993). In this model, the market can observe the level of investment, but
it has incomplete information about the productivity of the manager. Since the manager’s
utility depends on firm’s valuations in both periods, a manager with high productivity wants
to invest more in the long-term project to signal to the market that the long-term project is
valuable (as it depends on the productivity of the manager) and therefore boost the firm’s
valuation in the first period. Whereas, a manager with low productivity prefers to invest
more efficiently and overinvest less than managers with high productivity. This is because
overinvestment is more costly for managers with low productivity. The comparison between
the first-best solution and the solution without short sellers in Figure 1 illustrates this point.
Why does the overinvestment problem become more severe when the manager faces short
sellers? The existence of the short sellers reduces the market assessment (the expected value)
of the productivity of the manager and therefore the firm’s valuation in the first period.
This reduction in firm’s value reduces the total utility of the manager and hence increases
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his incentive to overinvest in the long-term project. As Figure 1 illustrates, investment in
the long-term project is always higher in the presence of short sellers.
Moreover, the overinvestment problem due to short selling activities is more severe for
managers with low productivity. A manager with high productivity is already overinvesting
to signal its high productivity and due to resource constraints cannot increase his investment
in the long-term project aggressively in response to short selling. Whereas, a manager with
low productivity is investing closer to the efficient investment level in the absence of short
selling activities and thus responds more aggressively to the short sellers. In addition, the
overinvestment problem is more severe for managers with strong short-term incentives. This
is because a manager whose utility is more sensitive to short-term firm’s valuation has a
stronger incentive to overinvest in the long-term project in order to increase short-term
firm’s valuation.
This simple model provides us a framework to understand the roles that short sellers may
play in corporate decisions. The model further highlights that the channel that transmits
the effects of short selling activities on corporate decisions is the agency problems between
the shareholders and the managers. We organize our empirical tests on the relation between
short selling activities and corporate investment based on the propositions presented here
and discuss the results in Section 4.
3 Data
We obtain quarterly and annual accounting data from CRSP/Compustat Merged database.
The sample period is from 1987 to 2011. We exclude foreign firms, and firms with SIC
codes between 4900-4999 (utilities) and 6000-6999 (financial services). To control errors in
quarterly data file, we exclude firm-quarter with negative or missing values in total assets,
net property plant & equipment, sales, or book equity. Short selling is sometimes driven by
mergers and acquisitions (see, e.g., Mitchell, Pulvino, and Stafford 2004). First, we follow
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Whited and Wu (2006) and exclude any firm-quarter that experienced a merger accounting
for more than 15% of the book value of its assets. Second, we obtain the merger and
acquisition information from SDC and exclude any firm-year that has a match in SDC.
We use the capital expenditure as a proxy for the long-term project in our model. This
is due to the modeling assumption that the source of information asymmetry between the
investors and the manager is θ which only affects the long-term project and not the short-
term project. To investigate whether short selling activities affects capital expenditure over
different time horizons, we construct one-, two-, and four-quarter investment as Ii,t/Ki,t−1,
(∑1
m=0 Ii,t+m)/Ki,t−1, and (∑3
m=0 Ii,t+m)/Ki,t−1 respectively. Ii,t is firm’s i investment in
quarter t and Ki,t−1 is firm’s i total assets in quarter t. We construct one-, two-, and
four-quarter R&D in a similar way.
We obtain monthly short interest data from the New York Stock Exchange (NYSE),
the American Stock Exchange (AMEX), and NASDAQ for the period of January 1988 to
December 2011. The level of short interest in individual stocks is reported to the exchanges
by member firms. Exchanges report short interest twice per month since September 2007.
To be consistent with the short interest data from the earlier period we keep the data at the
monthly frequency. Nasdaq short interest data start from July of 1988.
Following the literature (see, e.g., Christophe, Ferri, and Angel 2004 and Henry, Kisgen,
and Wu 2014), we use abnormal change in short interest to measure short selling activities
in a stock. Let SIji be the short interest for firm i at the end of month j, where short
interest is defined as the number of shares that are shorted divided by the number of shares
outstanding. We define the relative short interest denoted by RSIji as:2
RSIji = SIji −1
3(SIj−3
i + SIj−2i + SIj−1
i ).
In other words, we subtract from a stock’s monthly short interest, its moving average2Here we omit the quarter subscript t which the month i belongs to, because the month j− 1, j− 2, and
j − 3 may be in quarter t or quarter t− 1.
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over the past three months to represent the change of a firm’s short interest. The implicit
assumption in this approach is that the average short interest over the past three months is
a fair representation of the firm’s typical short interest. This approach also corrects for time
invariant omitted variables that might lead to high short interest. A large increase suggests
abnormally high short interest relative to its own recent shorting activity.
In our regression models we use the following three measures for abnormal short selling
activities to ensure that our results are not driven by the specific choice of the short selling
measure. Suppose quarter t has months j−2, j−1, and j, then RSIji,t represents the relative
short interest at the end of the quarter t for firm i.
The first abnormal short interest measure, denoted by ABSI(1), is a dummy variable
which equals to one if RSIji,t is above the top 20th percentile cutoff point, and zero otherwise.
The second abnormal short interest measure, denoted by ABSI(2), is the relative short
interest at the end of each quarter, i.e., ABSI(2)i,t = RSIji,t. The third abnormal short
interest measure, denoted by ABSI(3), is the maximum of relative short interest in the
three months within each quarter, i.e., ABSI(3)i,t = max{RSIji,tRSIj−1i,t , RSIj−2
i,t }. In the
remainder of the paper, we drop the term ‘abnormal’ and refer to the three measures of
abnormal short selling activities as ‘short interest’.3
Table 2 provides summary statistics for our variables of interest. To reduce the impact
of outliers, all variables are winsorized at 1st and 99th percentile in each year. The mean
of one-quarter investment is about 2%, while the median is about 1%. Not surprisingly, the
one-year investment is about 4 times the one-quarter investment. The firm’s book value of
total assets is about 1200 millions in 2004 dollars, while the median is about 103 millions.
The size variable is highly skewed, so we use its logarithm value in the regressions.
The variable SI in Table 2 is the raw short interest ratio at the end of a quarter. It has
an average of 2.3%, and a median of 0.54%. This high skewness is well documented in the3 In addition to the three main variables for measuring abnormal short interest, we further construct
several alternative measures of abnormal short interest. Details of the alternative short selling activitymeasures are presented in Section 4.
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literature (see, e.g., Asquith, Pathak, and Ritter 2005). The three short interest measures
exhibit different characteristics. ABSI(1) is a dummy variable which by construction has
a mean of 0.2. ABSI(2) has a mean of 0.057% and ABSI(3) has a mean of 0.436%. The
standard deviations of these two measures are around 1%.
4 Empirical Results
4.1 Short Selling and Corporate Investment
We begin with a test of our first hypothesis which predicts that high short interest lead to
overinvestment. Following the literature (see, e.g., Kaplan and Zingales 1997, and Almeida
and Campello 2007), we augment the traditional investment equation with our measures of
short selling activities that we defined in Section 3. Given that we are interested in examining
the effects of short selling activities on investment over different horizons, we estimate the
following investment model.
∑nm=0 Ii,t+mKi,t−1
= fi + λt + β1Qi,t−1 + β2
∑nm=0CFi,t+mKi,t−1
+ β3Sizei,t+n + β4ABSIi,t−1 + εi,t. (2)
where i represents the firm, Ii,t+m is the one-quarter capital expenditure at the end of quarter
t+m, Ki,t−1 is total assets at the beginning of the quarter t, Qi,t−1 is the Tobin’s Q at the end
of quarter t− 1, CFi,t+m is the one-quarter cashflow at the end of quarter t+m, Sizei,t+n is
the logarithm of total assets (in 2004 constant dollar) at the end of quarter t+n, ABSIi,t−1 is
the short interest at the end of quarter t− 1. We set n = 0, n = 1, and n = 3 for investment
over one quarter, two quarters, and four quarters respectively. fi is the firm fixed effect, and
λt is year-quarter fixed effect. Our first hypothesis predicts that the coefficient β4 will be
positive.
Table 3 shows the quarterly results with different short interest measures and over dif-
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ferent investment horizons.4 In all columns, both firm and year-quarter fixed effects are
included, and the standard errors are clustered at firm level. Table 3 shows that there is
indeed a strong positive relation between short interest and investment over one-quarter to
one-year horizons. The coefficients of all three short interest measures for all investment
horizons are significant at 1% level.
Table 3 shows that for investment over one quarter, if the short interest of a firm increases
to the top 20th percentile in the sample, the investment to asset ratio will increase by 0.001.
The average of one-quarter investment is 0.02 in the sample, so that represents a 5% increase.
The economic impact of short interest is not trivial even after we control for some well-known
first order determinants of corporate investment. For investment over two quarters and four
quarters, if the short interest of a firm is in the top 20th percentile in the sample, the
investment to asset ratio will increase approximately 4% over two quarters and 3% over
four quarters for the average firm. For investment over two and four quarters, the economic
impact of short interest declines, as the magnitude of their coefficients increases less than
two- and four-folds. This is expected because short interest is less persistent than other
determinants, and corporate investment is likely to respond to the most recent changes in
short selling activities.
We conduct several robustness checks to confirm our main results. These additional tests
include alternative measures of short interest, different control variables and their lagging
schemes in the regressions. For example, for alternative measures of short selling activities,
we use different lagged values for short interest, different cutoff points, and employ different
methodologies to measure short selling activities.5 These tests produce no qualitative change4In Table 2, the logarithm of the firm’s size is much larger than one-quarter investment. To properly
display the estimates in tables, we multiply all investment by 10. The short interest measures are in theiroriginal level, not in percentage.
5We use RSIj−1i,t , RSIj−2i,t , the average of relative short interest∑2
n=0 RSIj−ni,t
3 , and the zero instead ofthe top 20th percentile as the cutoff for dummy. In addition, we construct benchmark portfolios to adjustrelative short interest. Specifically, we construct 27 (3 × 3 × 3) portfolios at the beginning of each monthby independently sorting stocks on market capitalization, book-to-market, and momentum, all measured atthe end of the prior month. Prior literature shows that short interest is related to these firm characteristics.Momentum is defined as a stock’s cumulative returns over the past 12 months. We take the differencebetween a firm’s relative short interest and its benchmark portfolio, and use the differences as the proxy.
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to our empirical findings and are omitted from the paper for space considerations. Next,
we report results from the tests that provide important information in addition to the main
findings.
Most corporate investment studies employ annual data in empirical analysis. Due to
the high frequency nature of the short interest data, it is more appropriate to use quarterly
investment in our setting though we show the results are consistent across time horizons from
one quarter to four quarters. In order to compare with other studies of corporate investment,
we also perform tests at annual frequency and report the panel regression results in Table
4.6 In columns (1) to (3), short interest all positively predicts next year’s investment and
the significance is at least at 5% level. The evidence from annual data is consistent with
our main results from quarterly data. The economic magnitude is also similar. If the short
interest of a firm is in the top 20th percentile in the sample, the annual investment to asset
ratio in next year will increase by 0.02.
The last question we address in our baseline tests is the concern that (over-)investment is
driven by investment opportunities for which Tobin’s Q fails to control for sufficiently (see,
e.g., Erickson and Whited 2000). Therefore, the positive relation between short interest
and investment could be spurious, and in fact may reveal a relation between short selling
and efficient investment. To address this concern, we study the effects of short interest
on research and development (R&D). Eberhart, Maxwell, and Siddique (2004) find that
high R&D firms have significantly positive long-term abnormal operating performance and
subsequent abnormal stock returns. Therefore, if short selling is positively related with
investment opportunities rather than overinvesting, then the short interest should also be
All measure give qualitatively similar results. To save space, we focus on the three short interest measuresthroughout the paper.
6At annual frequency, the relative short interest RSIji,t for firm i in month j and year t is defined asSji,t − Sj
i,t−1. We use three measures of annual short interest to predict next year investment. Assume in ayear the last month with RSIji,t available is December. The first is a dummy of the year-end relative shortinterest ABSI(1)i,t which equals to one if RSI12i,t is in top 20th percentile of the sample. The second is therelative short interest at the end of each year, ABSI(2)i,t = RSI12i,t . The third is the maximum in year t,ABSI(3)i,t = max{RSIji,t}j=1,..,12.
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positively related with R&D.
To test this hypothesis, we construct R&D expenditures over one quarter, two quarters
and four quarters and replace the left-hand-side of the regression model (2) with R&D
expenditures. Table 5 shows the quarterly results with different short interest measures and
R&D horizons.7 We can see that there is a strong negative relation between short interest
and R&D over both short term and long-term horizons. Short interest negatively predicts
R&D expenditure, except for the second measure which is not significant.
The results in Tables 3 and 5 illustrate striking differences on the relation between short
interest and two corporate investment decisions. Short selling activities are associated with
increases in capital expenditures but decreases in R&D expenditures. Even though R&D
investment can increase the quality of a firm in the long-term (see, e.g., Eberhart, Maxwell,
and Siddique 2004), R&D is classified as an expense (while capital expenditure increases
long-term assets) and may depress the earnings and thus the current stock price (see, e.g.,
McConnell and Muscarella 1985). The result on R&D provides evidence against the argument
that firms with high short interest may have good investment opportunities for which Tobin’s
Q fails to fully control for in the regressions, and further highlights the differences between
the two corporate decisions (see also Kumar and Li 2014).
In sum, investment in tangible assets, i.e., capital expenditure, increases significantly
in response to short selling activities, whereas investment in intangible assets, i.e., R&D,
decreases significantly in response to short selling activities. These findings are consistent
with the signalling model that we presented in Section 2.7There is a missing value problem in the R&D data, and some early studies (see, e.g., Himmelberg,
Hubbard, and Palia 1999) set missing R&D values to zeros. We drop the missing values in R&D from thesample and perform the analysis. Because our sample covers a relative long time period, this choice doesnot affect our results in a significant way. Our results remain unchanged when we set the missing values tobe zeros and include a dummy for the observations with missing values.
15
4.2 Short Interest, Investment, and Firms’ Characteristics
We next turn to our hypotheses which relate the severity of the overinvestment problem to the
quality of investment opportunities and to the managerial incentives. The empirical analyses
in this subsection provide direct tests on the predictions of the model. These predictions
and the associated tests help us to disentangle the effects of short selling on investment from
other confounding effects.
The second prediction of the model relates to the unobserved productivity of the manager,
i.e., the variable θ in the model. In our simple model, θ is the single variable that determines
the payoff of the long-term project. We showed that the effects of short selling on investment
are stronger when θ is lower. One interpretation of θ is that it summarizes the quality of the
investment opportunities that a firm has. Therefore, one testable prediction of the model
is that managers in firms with lower quality investment opportunities react more strongly
when facing short sellers.
We use Tobin’s Q as a proxy for the quality of a firm’s investment opportunity. Because
Tobin’s Q is highly significantly related to investment decisions, an interaction of Tobin’s
Q with our short selling measures may only capture the marginal effects of Tobin’s Q on
investment. We use a different approach to examine the effects of short selling on high and
low Tobin’s Q firms. We first divide the full sample into two sub-samples based on Tobin’s
Q in the previous quarter, and then examine the effects of short interest on investment in
the two sub-samples of firms.
Table 6 reports the results. The first and second panels report the results for low and
high Tobin’s Q firms respectively. The short selling activity affects the firms with low
Tobin’s Q, though two proxies become insignificant in the four-quarter horizon. For high
Tobin’s Q firms, the impact of short selling on investment is much weaker. The evidence
appears consistent with our hypothesis that managers in firms with lower quality investment
opportunities react more strongly when facing short sellers.
The third prediction of the model relates to the incentives of a manager. In the model
16
that we present in Section 2, we assumed that the manager’s expected utility is:
U(V1, V2) = α0 + α1V1 + α2V2,
where Vt represents the stock market’s valuation of the firm in period t over both periods.
We showed that the effects of short selling on investment are stronger if the sensitivity of
a manager’s utility to the first period firm’s valuation is higher (i.e., the value of α1/α2
is greater). Thus, one direct prediction of the model is that managers who have stronger
short-term incentives react more aggressively when facing short sellers.
We follow the empirical literature and quantify the sensitivity of a manager’s wealth
from his stock and options holdings to the stock price as a proxy for the sensitivity of the
manager’s utility to the firm’s performance (see, e.g., Hall and Liebman 1998). To test the
hypothesis that the greater the sensitivity of a manager’s wealth to the firm’s short-term
performance, the stronger the effects of short selling activities on investment, we use the
CEO pay-performance sensitivity (PPS), i.e., dollar change in wealth associated with a 1%
change in the firm’s stock price, as a proxy for the short-term incentive. We obtain CEO’s
PPS, or the delta, from Coles, Daniel, and Naveen (2006) which use the method in Core and
Guay (2002) to calculate the delta for the period 1992-2010 for executives in the Compustat
Execucomp database.
In each year, we sort firms into quintiles based on the previous year CEO’s PPS. The
variable “High PPS” is a dummy which equals to one if the PPS is in the highest quintile,
and the variable “Low PPS” is a dummy which equals to one if PPS is in the lowest quintile.
We interact those two dummies with our short interest measures. Because the PPS is firm
specific, we use two-digit industry SIC fixed effects in the regressions. The model predicts
that the loading on the interaction term of the high PPS firms is higher than that of the low
PPS firms.
Table 7 reports results in three panels for one-, two-, and four-quarter investment respec-
17
tively. The sample of firms for which we have executive compensation data is a subset of
our full sample firms. The estimates in columns (1), (3), and (5) in all three panels show
that the coefficients on the three measures of short interest are positive and significant in
this sub-sample, consistent with our full sample results.
The interaction terms in all three panels have the expected sign, and are all significant
except for the second measure of short interest. The high PPS firms tend to invest more,
while the low PPS firms invest less than average. For one-quarter investment, if the short
interest increases to the top 20th percentile in the sample, the investment to assets ratio of
the firms with high PPS will be about 0.0039, higher than that of the low PPS firms. The
coefficient magnitude on the interaction term of low PPS firms (-0.019) is larger than that
of unconditional short interest (0.015). It suggests that investment of firms in the low PPS
quintile do not respond significantly to short selling activities. Similar results are also found
for two- and four-quarter investment in the second and the third panels. The significance of
the first measure (a dummy) and the third measure (quarterly maximum) of short interest is
also consistent with the intuition that only the high short interest would attract managers’
attention. The second measure does not capture this intuition as well as the other two.
As a robustness check, we also use the scaled wealth-performance sensitivity proposed
by Edmans, Gabaix, and Landier (2009) as an alternative proxy for the managerial incen-
tive. This is the dollar change in CEO’s wealth for a 100 percentage point change in firm’s
value, divided by the annual flow compensation. We find that the results are qualitatively
unchanged.8 Overall, the results
In sum, we find strong evidence that the effects of short selling activities on investment
are stronger for firms with poor investment prospects measured by Tobin’s Q. In addition,
firms whose CEOs’ compensation is more sensitive to the stock price respond more strongly
to short selling activities. These results are broadly consistent with the predictions of the8Edmans, Gabaix, and Landier (2009) argue that “The key advantage of this incentive measure is that,
empirically, it is independent of firm size, and thus comparable across firms and over time. Theoretically, itis generated by a model where effort has a multiplicative effort on both firm value and CEO utility.”
18
model and provide insight on the agency problem channel that transmits the effects of short
selling activities into corporate decisions.
4.3 Addressing Concerns on Endogeneity and Reverse Causality
We now address concerns that the documented relation between short interest and invest-
ment is driven by forces other than those emphasized in our model. Although one cannot
completely rule out all the forces that can drive our main result, but the analyses in this sub-
section provide evidence that is broadly consistent with the forces emphasized in the model.
We focus on two closely related questions that are essential for establishing the causal effects
of short selling on investment decisions: (1) the effects of overvaluation on short interest and
overinvestment, and (2) the possible reverse causality between overinvestment and shorting
interest.
Overvaluation can lead to corporate overinvestment. Polk and Sapienza (2009) argue
that managers may try to boost short-term share prices by catering to temporary market
overvaluation. They use discretionary accruals as a proxy for mispricing and find that it
is positively related to investment. The overinvestment channel in our model is different
from the catering channel described in Polk and Sapienza (2009). However, it is possible
that short sellers react to overvaluation, and the observed short interest can be driven by
overvaluation. In this case, the relation between short interest and corporate investment
could be driven by overvaluation.
We first examine how short interest is directly related to the overvaluation measure. We
follow Polk and Sapienza (2009) and use discretionary accruals as a measure of overvaluation.
In particular, the discretionary accruals is:
DACCRi,t = ACCRi,t −NORMALACCRi,t,
where ACCRi,t = 4NCCAi,t − 4CLi,t − DPi,t represents accrual for firm i in year t,
19
4NCCAi,t is the change in noncash assets, 4CLi,t is the change in current liabilities minus
change in debt included in current liabilities and minus the change in income taxes payable,
and DPi,t is depreciation and amortization. Appendix B provides more details on the vari-
able construction. In unreported results, we find that the correlation between discretionary
accruals and short interest measures ranges from -5% to 3%, and the correlation among the
three short interest measures ranges from 33% to 61%. Given the low correlations between
discretionary accruals and short interest measures, it is unlikely that the short selling mea-
sures we employ in the study that are based on changes in short selling activities are driven
by the levels of mispricing.
To further see whether the inclusion of the mispricing proxy will subsume our results, we
include the discretionary accruals variable in our baseline regression model in equation (2).
Columns (4) to (6) in Table 4 report the estimates from annual data. The short interest
measure is from the previous year, while as in Polk and Sapienza (2009) the measure of
accruals is contemporaneous. These columns show that when we control for investment
opportunities, firm size, cashflow, and discretionary accruals, we still find that firms with
higher short interest invest more. This relation is significant at least at 5% level. Therefore,
the inclusion of discretionary accruals does not subsume the effects of short interest. The
coefficients on short interest are smaller than those in columns (1) to (3), except for the third
measure.
We also include discretionary accruals in quarterly investment regressions, and present
the results in Table 8. The coefficients on short interest are positive and significant in all
specifications. Again, the inclusion of discretionary accruals does not subsume the effects
of short interest. Nonetheless, the discretionary accruals do explain part of the investment
as the coefficients on short interest are smaller and the discretionary accruals are significant
in the regressions. This suggests that corporate overinvestment could be driven by both
channels. On the other hand, the results in this table should be read with some caution.
The accruals here are at the end of each year, while one- and two-quarter investment are
20
during the year. To avoid this time alignment issue, we also experiment with lagged accruals.
Though not reported, accruals are not significant in any of the specifications, whereas the
results are stronger for short interest.
In sum, our evidence on discretionary accruals alleviates the concern that short interest
is a proxy for overvaluation and the relation between short interest and investment is driven
by the overvaluation effects. Short interest and the mispricing measure have low correlation
and including overvaluation in our baseline regression model does not subsume the effects of
short interest on investment.
We next examine the possibility that reverse causality, i.e., the effects of (over)investment
on short interest, drives the evidence we have documented. Short sellers may target firms
that overinvest and hence, the relation that we document between the short interest and the
firm’s investment is simply a manifestation of the reaction of short sellers to overinvestment.
Ruling out, or adequately controlling for the reverse causality effects in our empirical tests is
a challenging task. We provide three different tests to assess how much the possible reverse
causality affects our results.
In our first test, we directly include the past investment in the baseline regression model
in equation (2). To the extent that past investment predicts future investment and may
affect short selling activities, including the past investment in the regression can at least
partly control for the possible relation between past investment and short interest. Table 9
reports the results from the regression model that include the lagged value of investment.
We measure the past investment over the same length of the time periods as we measure
the subsequent investment. Compared with the baseline results, the results on short selling
measures are weaker, but remain significant for most specifications.
For our second test, we employ a two-stage least-squares (2SLS) regression to tease out
the effects of short interest on investment. The challenge for this approach is the selection of a
valid instrumental variable. The industry median of each ABSIi,t−1 measure in each quarter
is used as the excluded instrumental variable for ABSIi,t−1. The intuition is that an industry
21
level common shock may affect the short interest of all firms and this common shock could
affect a firm’s investment through the firm’s short interest. The model is exactly identified
with one excluded instrumental variable. Table 11 reports the two-stage least-squares (2SLS)
regression results. To save space, only the second stage results are reported. The LM test
statistics for under-identification indicate that the excluded instrumental variable is strongly
correlated with the endogenous regressor. The effects of short interest remains significant,
except the last proxy in the four-quarter horizon.
We develop our third test based on a prediction of the reverse causality argument in
the presence of short-sale constraints. For the reverse causality argument, it is what drives
the possible short selling, i.e., overinvestment or overvaluation, and not the actual short
interest that relates to subsequent investment. Because short-sale constraints affect short
selling activities, if reverse causality explains our empirical findings, the relation between
short interest and investment should be stronger in firms that are short-sale constrained.
The difference in short-sale constraints across firms allows us to explore this prediction.
We use idiosyncratic risk obtained from the Fama-French three-factor model over the past
three-year period as a proxy for short-sales constraints (see, e.g., Pontiff 2006). We include
the variable of idiosyncratic risk and an interaction variable of idiosyncratic risk and short
interest in our baseline regression model in equation (2). Table 12 reports the results and
show that the interaction variable has a negative relation with subsequent investment which
is the opposite to the prediction of the alternative argument. This result suggests that the
alternative argument does not drive our findings.
Overall, the three separate tests provide support on the robustness of our main empirical
findings. Although we cannot completely rule out all the forces that can drive our main
result, the presented results in this subsection show that after controlling for the possible
confounding effects on short interest, short selling activities still exhibit substantial influence
on corporate investment decisions which is broadly consistent with our model.
22
4.4 Short Interest, Investment, and Stock Returns
We have shown that high short interest leads to corporate overinvestment. The inefficient
allocation of capital by a manager could have important implications for firm’s subsequent
performance. If the market recognizes, possibly with some delay, the overinvestment by self-
interest driven managers, those firms that overinvest will have subsequent negative abnormal
returns. We next investigate this hypothesis that relates investment and short interest to
subsequent stock returns.
The relation between investment and subsequent stock returns has been studied exten-
sively in the literature. Titman, Wei, and Xie (2004) and Cooper, Gulen, and Schill (2008),
among others, show that firms that invest more or grow their total assets more have lower
subsequent risk-adjusted returns. The relation between short interest and subsequent stock
returns has also been studied in the literature. Asquith and Meulbroek (1995) and Desai,
Ramesh, Thiagarajan, and Balachandran (2002), among others, show that firms with high
short interest have significant negative abnormal returns.
Our test is different from the two strands of the literature. First and foremost, we
argue that short interest could cause low subsequent stock return through its real effects on
corporate decisions. Existing studies on the relation between short interest and stock returns
largely focus on the informational role of short interest and examine whether short interest
predicts subsequent stock returns. Second, on the relation between corporate investment
and stock returns, we highlight the causes of such a relation by including short interest as
one of the possible causes of overinvestment.
Our return regression model controls for the firm’s characteristics and is analogous to
investment regression model of equation (2) which incorporates different investment horizons.
In addition, we test subsequent returns using the Fama and MacBeth (1973) method. In
23
particular, our specification is,
CumReti,(t+n+1, t+2n+1) = β0 + β1 log
(∑nm=0 Ii,t+mKi,t−1
)+ β2ABSIi,t−1 + β3 log(Qi,t−1)
+ β4
∑nm=0 CFi,t+mKi,t−1
+ β5MEi,t−1 + β6MOMi,t−1 + εi,j, (3)
where CumReti,(t+n+1, t+2n+1) is the firm i’s cumulative quarterly stock returns from the
quarter t+n+1 to the quarter t+2n+1. The variableMOMi,t−1 is the momentum, defined
as a stock’s cumulative returns over the past 12 months. The variable MEi,t−1 is the market
value of equity. Other variables are the same as those in equation (2). We set n = 0, n = 1,
and n = 3 for investment over one quarter, two quarters, and four quarters respectively.
Table 13 presents the Fama and MacBeth (1973) cross sectional results for investment and
subsequent stock returns. Consistent with our hypothesis, in the first panel, the subsequent
returns are strongly and negatively related with investment, after controlling for the short
interest and other firm characteristics. The choice of short interest measures does not change
the coefficients of the logarithm of investment to assets ratio. One standard deviation increase
in one-quarter investment leads to about a cumulative -0.44% abnormal returns in the next
quarter, equivalent to annualized abnormal returns of -1.77%. The overinvestment effect
diminishes in long horizon. One standard deviation increase in four-quarter investment leads
to about a cumulative -1.24% abnormal returns in the next year. This finding is consistent
with our evidence in Table 3 that the impact of short interest on investment diminishes
in long horizon. Overall, the result suggests that although managers try to counteract the
effects of short selling activities by signalling firms’ quality through overinvestment, over
time the market realizes the increase in investment has been inefficient.
Controlling for the short interest is important. Table 13 shows that if the short interest
of a firm increases to the top 20th percentile in sample, the cumulative abnormal returns in
the next quarter is about -0.6%, equivalent to annualized abnormal returns of -2.4%. This
magnitude is larger than that of the investment. It suggests that both short selling activities
24
and overinvestment lead to abnormal negative future returns.
The evidence on investment and returns is consistent with previous studies. In addition,
we show that the negative relation between investment and future returns is robust after
controlling for short selling activities, and the magnitude diminishes in long horizon. These
new findings can be explained by our model and are consistent with our baseline regression
results in Table 3.
The literature refers to the negative relation between investment and future return as
investment or asset growth anomaly, and different theories have been proposed to explain this
anomaly.9 Our model and empirical findings suggest a new mechanism in which signalling
through investment leads to an inefficient allocation of capital and hence the abnormal
negative future returns. This mechanism is consistent with empirical findings in Titman,
Wei, and Xie (2004) and Cooper, Gulen, and Schill (2008) in which they show that asset
growth effect is weaker in times of increased corporate oversight.
5 Conclusions
Investors who short stocks may have real impacts on corporate decisions. In this paper we
focus on one central corporate decision, namely the investment. In a simple model we show
that short sellers can cause firms to overinvestment. The overinvestment is more severe for
managers with low productivity and/or with high short-term incentives. Empirically, we
find that investment in tangible assets, i.e., capital expenditures, increases significantly in
response to an increase in short selling activities, whereas investment in intangible assets,
i.e., R&D expenditures, decreases significantly in response to an increase in short selling
activities. In particular, for corporate investment over the subsequent quarter, if the short
interest of a firm increases to the top 20th percentile in the sample, the investment to assets
ratio will increase approximately by five percent. For investment over the next year, the9For example, Zhang (2005), and Xing (2008), among others, provide q-theory based rational explana-
tions. Titman, Wei, and Xie (2004), and Cooper, Gulen, and Schill (2008) among others, provide behavioralexplanations. Lam and Wei (2011) find supporting empirical evidence for both.
25
increase is approximately three percent. We also find that the impact of short selling on
investment is larger for firms with poor investment prospects and for firms whose CEO’s
compensation is more sensitive to its stock performance.
Investment policy is not the only corporate decision that could be affected by short selling
activities. Firms may increase payout to shareholders, either through dividend or share
repurchase, to boost stock price and increase the cost of short selling. Liu and Swanson
(2011) indeed find that firms employs share repurchases to fight short sellers. In view of the
increased payout, the evidence on increased investment is even more striking. These results,
along with the argument we presented in the theoretical model, further suggest that short
selling activities can also affect firm’s financing decisions and capital structure. Exploring
the real effects of short selling activities on aspects of firm’s policies other than investment
remain a topic of future research.
26
Appendix A: Proofs
To prove Proposition 1, 2 and 3, we need to prove the following two propositions.
Proposition 4. In any Nash equilibrium of the signaling game and given level of short-
interest w, xw(θ) will be a nondecreasing function of θ.
Proof: We prove this proposition by contradiction. Let (xw, θ) and (x′w, θ′) be two investment-
type pairs used in equilibrium by the managers who faces the same level of short-interest
and θ > θ′ but x′w > xw. By revealed preference
U(xw, w, θ) > U(x′w, w, θ)
U(x′w, w, θ′) > U(xw, w, θ′)
which leads to
(θ − θ′)(L(xw)− L(x′w)) > 0
which contradicts the initial assumption.
Proposition 5. A unique fully separating Perfect Bayesian equilibrium exists which involves
over-investment in the second project relative to the first-best with probability one and where
the equilibrium choice of investment, xw(θ), is such that xw(θs) = x∗(θs) and for all θ ∈
(θs, θl]
dxw
dθ=
α1
α1 + α2
L(xw)
S ′(K − xw)− θL′(xw).
Proof: For simplicity of notation we drop the superscript w in xw. Any Perfect Bayesian
equilibrium must have beliefs that are a nondecreasing function of investments. Since
limx→0∂U(x,w,θ)
∂x= +∞ and limx→K
∂U(x,w,θ)∂x
= −∞, necessary conditions for the manager’s
choice of investment are
∂U(x,w, θ)
∂x= 0, and
∂2U(x,w, θ)
∂x26 0 (4)
27
Differentiating the first order condition we get that
∂2U(x,w, θ)
∂θ∂x+∂2U(x,w, θ)
∂x2
∂x
∂θ= 0
Therefore, the necessary local second-order condition can be restated as ∂2U(x,w,θ)∂θ∂x
> 0,
which is true by the assumption that L′(x) > 0. Furthermore, if x(θ) is nondecreasing, the
local conditions for a maximum is sufficient. To see that the monotonicity of x(θ) and the
first-order condition are sufficient for a separating equilibrium, suppose x(θ) satisfies these
conditions but the manager prefers to choose otherwise. Suppose that x′ = x(θ′) rather than
x is the chosen investment by a manager with productivity θ. Then, revealed preference
implies U(x(θ′), w, θ)− U(x(θ), w, θ) > 0. Therefore
ˆ θ′
θ
Ux(x(s), w, θ)dx(s)
dsds > 0
But by hypothesis, Ux(x(θ), w, θ) = 0 for all θ. Therefore,
ˆ θ′
θ
(Ux(x(s), w, θ)− Ux(x(s), w, s))dx(s)
dsds > 0
which implies that ˆ θ′
θ
ˆ θ
s
Uxθ(s, w, t)dx(s)
dsdtds > 0
But by assumption, the above double integral is always non-positive, which contradicts
our hypothesis. Therefore, if our solution satisfies the local first-order condition and the
manager’s investment function is a nondecreasing in θ, we have characterized the equilibrium
path of a Perfect Bayesian Nash equilibrium.
The first order condition is
∂U(x,w, θ)
∂x= (α1 + α2)[θL′(x)− S ′(K − x)] + α1
dθ
dxL(x) = 0
28
Or equivalentlydθ
dx=α1 + α2
α1
S ′(K − x)− θL′(x)
L(x)(5)
Let x∗(θ) be the efficient level of investment for a given productivity θ. In a fully sepa-
rating equilibrium, the worst inference which the investors can place on a manager is that
the productivity of the second project is θs, and consequently the worst firm’s manager must
earn at least U(x∗(θs), w, θs). Thus, in a fully separating equilibrium, x(θs) = x∗(θs) which
is an initial condition of differential equitation (5).
We must specify beliefs off the equilibrium path. Let X = [x, x] be the set of all investment
levels which arise with positive probability in the proposed equilibrium of signaling game.
One set of arbitrary beliefs which holds together the equilibrium has the market believing
that for any x ∈ [0, x) the firm’s type is θs, and for any x > x the firm’s type is θl.
Differential equation (5) implies that ∂x∂θ
= ∞ at θs and at any other points where
x(θ) = x∗(θ). Since x(θ) is monotonic in θ and x∗(θ) has finite slope, x(θ) must remain
above x∗(θ) for all θ ∈ [θs, θl]. Therefore, we have a uniquely defined fully separating
equilibrium which exhibit over-investment with probability one.
Proof of Proposition 1: Let xw(θ) denote the investment of a manager with productivity
θ that faces short sellers and let xo(θ) denote the investment of a manager with productivity
θ that does not face short-sellers. The functions xw(.) and xo(.) are characterized by the
following differential equations:
dxw
dθ=
α1
α1 + α2
L(xw)
S ′(K − xw)− θL′(xw), xw(θs) = x∗(θs) (6)
dxo
dθ=
α1
α1 + α2
L(xo)
S ′(K − xo)− θL′(xo), xo(θl) = x∗(θl) (7)
We need to show that xw(θ) ≥ xo(θ) for ∀θ. Dropping w and o in the above differential
equations, they are of the following form:
dθ
dx= h1(x)− θh2(x) (8)
29
where
h1(x) =
(1 +
α2
α1
)S ′(K − x)
L(x), h2(x) =
(1 +
α2
α1
)L′(x)
L(x)
The solution to differential equation (8) is of the form:
θ =
´h1(t)e
´h2(t)dt + c
e´h2(t)dt
or equivalently
θ = z1(x) + cz2(x)
where
z1(x) =
´h1(t)e
´h2(t)dt
e´h2(t)dt
, z2(x) =1
e´h2(t)dt
Therefore, the solutions to the differential equations (6) and (7) are characterized by
θw = z1(xw) + cwz2(xw)
θo = z1(xo) + coz2(xo)
where, cw and co are constant that are determined based on initial conditions xw(θs) = x∗(θs)
and xo(θl) = x∗(θl). For a given level of investment x,
θw(x)− θo(x) = z2(x)(cw − co)
Given that z2(.) > 0, in order to show that xw(θ) > xo(θ) we can equivalently show that
co > cw. We prove this by contradiction. Suppose that cw > co. Consider the level of
investment x∗ such that θo(x∗) = θl = z1(x∗) + coz2(x∗). Given that cw > co we have that
θw(x∗) = z1(x∗) + cwz2(x∗) > θl. Given the monotonicity of θw and x, this implies that
xw(θ1) < xo(θ1) = x∗. However, this is not consistent with Proposition 1 as we showed that
xw(θ) > x∗(θ).
30
Proof of Proposition 2: Let xw(θ) denote the investment of a manager with productivity
θ that faces short sellers and let xo(θ) denote the investment of a manager with productivity
θ that does not face short-sellers. The functions xw(.) and xo(.) are characterized by the
following differential equations:
dxw
dθ=
α1
α1 + α2
L(xw)
S ′(K − xw)− θL′(xw), xw(θs) = x∗(θs)
dxo
dθ=
α1
α1 + α2
L(xo)
S ′(K − xo)− θL′(xo), xo(θl) = x∗(θl)
Define f(θ) as f(θ) = xw(θ)− xo(θ). We need to show that f ′(θ) 6 0 for θ ∈ (θs, θl).
We know that xw(θ) and xo(θ) are increasing functions. To show that xw(θ)− xo(θ) is a
decreasing function, we need to show that θo(x)− θw(x) is a decreasing function.10
From proof of Proposition 1 we know that
θw = z1(xw) + cwz2(xw)
θo = z1(xo) + coz2(xo)
where, cw and co are constant that are determined based on initial conditions xw(θs) = x∗(θs)
and xo(θl) = x∗(θl). Therefore,
θo(x)− θw(x) = z2(x)(co − cw)
Since co > cw and z2(.) is a decreasing function, we get that θo(x) − θw(x) is a decreasing
function.
Proof of Proposition 3: We need to show that dxw
dα1> 0. We know that
10It is straightforward to show that if f(x) and g(x) are increasing functions, h(x) = f(x) − g(x) isdecreasing iff g−1(.)− f−1(.) is a decreasing function.
31
dxw
dθ=
α1
α1 + α2
L(xw)
S ′(K − xw)− θL′(xw)
Therefored2xw
dα1dθ=
α2
α1(α1 + α2)
dxw
dθ
Thereforedxw
dα1
=α2
α1(α1 + α2)xw
Given that xw > 0 we get that dxw
dα1> 0.
Appendix B: Variable Definitions
We obtain quarterly and annual firm accounting data from CRSP/Compustat Merged
database. The sample period is from 1987 to 2011. We exclude foreign firms, and firms
with SIC codes between 4900-4999 (utilities) and 6000-6999 (financial services). We exclude
firm-quarter with negative or missing values in total assets, net property plant & equipment,
sales, or book equity, and firm-quarter that experienced a merger accounting for more than
15% of the book value of its assets. We obtain the merger and acquisition information from
SDC and exclude any firm-year that has a match in SDC. Item names refer to Compustat
quarterly data items.
Variable Definition
IK CAPXYQ / Item ATQ. Data Item ATQ is lagged. CAPXYQ
is the difference between the current and previous quarter of
Item CAPXY in each fiscal year.
Size The logarithm of the 2004-dollar deflated Item ATQ
Tobin’s Q (Item PRCCQ × Item CSHOQ - Item CEQQ - Item TXDBQ)
/ Item ATQ
32
Variable Definition
CF (Item IBQ + Item DPQ)/ Item ATQ. Data Item ATQ is
lagged.
RnD Item XRDQ / Item ATQ. Data Item ATQ is lagged.
ABSI See Section Data for details.
DACCR See Table 4 for details.
33
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Fama, E. F., and J. D. MacBeth. 1973. Risk, return, and equilibrium: Empirical tests.Journal of Political Economy pp. 607–636.
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Grullon, G., S. Michenaud, and J. P. Weston. forthcoming. The real effects of short-sellingconstraints. Review of Financial Studies .
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Titman, S., K.-C. Wei, and F. Xie. 2004. Capital investments and stock returns. Journal ofFinancial and Quantitative Analysis 39:677–700.
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36
Figure 1: Solution to the Model
The figure plots the solution of the model for three set of parameters. In the top figureα1 = 0.1 and α2 = 1. In the middle figure α1 = 1 and α2 = 1. In the bottom figure α1 = 1and α2 = 0.1.
1.0 1.5 2.0 2.5 3.05
6
7
8
9
10
Productivity of the Manager HΘL
Inves
tmen
tin
the
Lon
g-
Ter
mP
roje
ctHxL
Without Short Sellers
1.0 1.5 2.0 2.5 3.05
6
7
8
9
10
Productivity of the Manager HΘL
Inves
tmen
tin
the
Lon
g-
Ter
mP
roje
ctHxL
With Short Sellers
First-Best
1.0 1.5 2.0 2.5 3.05
6
7
8
9
10
Productivity of the Manager HΘL
Inves
tmen
tin
the
Lon
g-
Ter
mP
roje
ctHxL
1.0 1.5 2.0 2.5 3.05
6
7
8
9
10
Productivity of the Manager HΘL
Inves
tmen
tin
the
Lon
g-
Ter
mP
roje
ctHxL
Without Short Sellers
1.0 1.5 2.0 2.5 3.05
6
7
8
9
10
Productivity of the Manager HΘL
Inves
tmen
tin
the
Lon
g-
Ter
mP
roje
ctHxL
With Short Sellers
First-Best
1.0 1.5 2.0 2.5 3.05
6
7
8
9
10
Productivity of the Manager HΘL
Inves
tmen
tin
the
Lon
g-
Ter
mP
roje
ctHxL
1.0 1.5 2.0 2.5 3.05
6
7
8
9
10
Productivity of the Manager HΘL
Inves
tmen
tin
the
Lon
g-
Ter
mP
roje
ctHxL
Without Short Sellers
1.0 1.5 2.0 2.5 3.05
6
7
8
9
10
Productivity of the Manager HΘL
Inves
tmen
tin
the
Lon
g-
Ter
mP
roje
ctHxL
With Short Sellers
First-Best
1.0 1.5 2.0 2.5 3.05
6
7
8
9
10
Productivity of the Manager HΘL
Inves
tmen
tin
the
Lon
g-
Ter
mP
roje
ctHxL
37
Table 2: Summary StatisticsWe obtain quarterly accounting data from CRSP/Compustat Merged data file. The sample period is from1988 to 2011. We drop the companies with a SIC code that is between 4900 and 4999, or between 6000and 6999. Firm investment I is calculated as the difference of the Item CAPXY between two consecutivequarters in each fisical year. The total assets K is Item ATQ. “Cashflow” is Item IBQ + Item DPQ. “To-bin’s Q” is the market-to-book ratio (Item ATQ + Item PRCCQ × Item CSHOQ - Item CEQQ - ItemTXDBQ)/ Item ATQ. The R&D expense RnD is Item XRDQ. The firm size is the Item ATQ in millionsof 2004 dollars. Data Item ATQ is lagged in denominator. I/K1Q, I/K2Q, and I/K4Q are Ii,t/Ki,t−1,(∑1
m=0 Ii,t+m)/Ki,t−1, and (∑3
m=0 Ii,t+m)/Ki,t−1 respectively. RnD/K1Q, RnD/K2Q, and RnD/K4Q areRnDi,t/Ki,t−1, (
∑1m=0 RnDi,t+m)/Ki,t−1, and (
∑3m=0 RnDi,t+m)/Ki,t−1 respectively. All accounting vari-
ables are winsorized at 1% level on each tail every year. ABSI(1) is a dummy variable which equals to oneif the relative short interest at the end of a quarter is above the top 20th percentile cutoff point, and zerootherwise. ABSI(2) is the relative short interest at the end of a quarter (in percentage). ABSI(3) is themaximum relative short interest among the three months in a quarter (in percentage). SI is the raw shortinterest level (in percentage). We obtain the relative short interest by subtracting the average short interestof previous three months from the current month short interest.
Mean Median Stn dev. 25th perc. 75th perc. No. Obs.Accounting VariablesI/K1Q 0.019 0.010 0.027 0.004 0.022 270,009I/K2Q 0.039 0.022 0.052 0.009 0.046 259,801I/K4Q 0.080 0.047 0.103 0.021 0.096 239,367RnD/K1Q 0.031 0.019 0.041 0.002 0.042 110,282RnD/K2Q 0.064 0.040 0.082 0.003 0.086 99,940RnD/K4Q 0.131 0.082 0.168 0.007 0.177 91,741Cashflow 0.000 0.017 0.067 -0.007 0.033 269,987Tobin’s Q 2.078 1.437 1.938 1.059 2.291 269,293Size 1191.7 103.4 4350.7 28.2 445.2 270,009
Short-Selling VariablesSI 2.332 0.539 4.359 0.066 2.635 195,591ABSI(1) 0.200 0.000 0.400 0.000 0.000 180,578ABSI(2) 0.057 -0.003 0.967 -0.121 0.153 180,568ABSI(3) 0.436 0.079 1.112 -0.001 0.472 185,006
38
Table3:
ShortSelling
andCorpo
rate
Investment
Thistablepresents
quarterlyinvestmentregression
resultswithdiffe
rent
shortinterest
measures(A
BSI(.) i,t−1)an
dinvestmentho
rizons
(one-,tw
o-,
andfour-qu
arters).
ABSI(1)is
adu
mmyvariab
lewhich
equa
lsto
oneiftherelative
shortinterest
attheendof
aqu
arteris
abovethetop20th
percentile
cutoffpo
int,
andzero
otherw
ise.
ABSI(2)is
therelative
shortinterest
attheendof
aqu
arter.
ABSI(3)is
themax
imum
relative
short
interest
amon
gthethreemon
thsin
aqu
arter.
Incolumns
(1)to
(3),
thedepe
ndentvariab
leis
I i,t/K
i,t−
1.In
columns
(4)to
(6),
thedepe
ndent
variab
leis
(∑ 1 m=0I i
,t+m)/K
i,t−
1,“C
ashfl
ow”is
(∑ 1 m=0CFi,t+
m)/K
i,t−
1,an
d“Size”
isfirm’s
size
t+1.In
columns
(7)to
(9),
thede
pend
entvariab
leis
(∑ 3 m=0I i
,t+m)/K
i,t−
1,“C
ashfl
ow”is
(∑ 3 m=0CFi,t+
m)/K
i,t−
1,an
d“Size”
isis
firm’s
size
t+3.In
allcolumns
theTob
in’s
Qis
thesame.
Firm
and
year-qua
rter
fixed
effects
areinclud
ed.The
stan
dard
errors
arerobu
stto
heteroskedasticity,a
ndclusteredat
firm
level.
One-Q
uarter
Two-Qua
rters
Four-Q
uarters
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
ShortInterest
Measure
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
Cashfl
ow0.14
4***
0.143*
**0.14
4***
0.23
8***
0.23
7***
0.23
6***
0.38
0***
0.37
9***
0.37
9***
(9.27)
(9.25)
(9.28)
(10.87
)(10.85
)(10.81
)(10.13
)(10.12
)(10.21
)
Tob
in’s
Q0.01
9***
0.019*
**0.01
9***
0.04
4***
0.04
4***
0.04
4***
0.10
0***
0.10
0***
0.10
0***
(24.42
)(24.54
)(24.68
)(25.08
)(25.17
)(25.30
)(24.80
)(24.83
)(24.97
)
Size
0.00
5**
0.00
6**
0.00
6**
0.01
6***
0.01
7***
0.01
7***
0.06
2***
0.06
3***
0.06
3***
(2.31)
(2.49)
(2.42)
(3.14)
(3.29)
(3.22)
(4.81)
(4.88)
(4.94)
ABSI
0.01
0***
0.236*
**0.35
5***
0.01
7***
0.49
6***
0.68
3***
0.02
4***
0.97
3***
0.83
4***
(7.25)
(5.13)
(6.58)
(6.65)
(5.67)
(6.40)
(4.36)
(5.61)
(3.72)
Yr-Qtr
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Firm
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N17
9710
179700
1841
3817
1238
1712
2917
5391
1549
1715
4908
1587
12Adj.R
20.43
70.437
0.43
40.51
10.51
10.50
90.58
40.58
40.58
3tstatistics
inpa
rentheses
∗p<
0.10,∗∗p<
0.05
,∗∗∗
p<
0.01
39
Table 4: Short Selling and Annual InvestmentThis table presents annual investment regression results with different short interest measures (ABSI(.)i,t−1).The dependent variable is Ii,t/Ki,t−1. In columns (1) and (4), we use a dummy of the year-end relativeshort interest ABSI(1)i,t which equals to one if RS12
i,t is in top 20th percentile of the sample. In columns(2) and (5), we use the relative short interest at the end of each year, ABSI(2)i,t = RS12
i,t. In columns(3) and (6), we use the maximum in year t, ABSI(3)i,t = max{RSj
i,t}j=1,..,12. Discretionary accruals isdefined as DACCRi,t = ACCRi,t − NORMALACCRi,t, where ACCRi,t =
4NCCAi,t−4CLi,t−ItemDPi,t
ItemATi,t−1,
and NORMALACCRi,t =ItemSale×
∑5j=1 ACCRi,t−j∑5
j=1 ItemSalei,t−j. The 4NCCAi,t is the change of NCCAi,t which is
(ItemACTi,t−ItemCHEi,t), and the 4CLi,t is the change of CLi,t which is (ItemLCTi,t−ItemDLCi,t−ItemTXPi,t). Item names refer to Compustat annual data names. Firm and year fixed effects are included.The standard errors are robust to heteroskedasticity, and clustered at firm level.
(1) (2) (3) (4) (5) (6)Short Interest Measure ABSI(1) ABSI(2) ABSI(3) ABSI(1) ABSI(2) ABSI(3)Cashflow 0.045*** 0.045*** 0.045*** 0.044*** 0.044*** 0.043***
(13.36) (13.33) (13.51) (11.51) (11.51) (11.54)
Tobin’s Q 0.062*** 0.062*** 0.062*** 0.051*** 0.051*** 0.051***(17.35) (17.44) (17.55) (12.22) (12.27) (12.35)
Size 0.010** 0.011** 0.010** 0.016*** 0.016*** 0.016***(2.06) (2.19) (2.00) (3.10) (3.20) (3.11)
ABSI 0.020*** 0.351*** 0.111** 0.014*** 0.235*** 0.132**(5.55) (6.60) (2.00) (3.73) (4.26) (2.33)
DACCR 0.110*** 0.109*** 0.110***(4.10) (4.09) (4.20)
Year Fixed Effect Yes Yes Yes Yes Yes YesFirm Fixed Effect Yes Yes Yes Yes Yes YesN 42378 42378 43244 31180 31180 31857Adj. R2 0.366 0.366 0.367 0.331 0.331 0.330t statistics in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
40
Table5:
ShortSelling
andR&D
Thistablepresents
quarterlyR&D
regression
resultswithdiffe
rent
shortinterest
measures(A
BSI(.) i,t−1)an
dR&D
horizons
(one-,tw
o-,a
ndfour-
quarters).
ABSI(1)is
adu
mmyvariab
lewhich
equa
lsto
oneiftherelative
shortinterest
attheendof
aqu
arteris
abovethetop20th
percentile
cutoffpo
int,
andzero
otherw
ise.
ABSI(2)is
therelative
shortinterest
attheendof
aqu
arter.
ABSI(3)is
themax
imum
relative
shortinterest
amon
gthethreemon
thsin
aqu
arter.
Incolumns
(1)to
(3),
thedepe
ndentvariab
leis
RnD
i,t/K
i,t−
1.
Incolumns
(4)to
(6),
thedepe
ndent
variab
leis
(∑ 2 t=1RnD
i,t)/K
i,t−
1,“C
ashfl
ow”is
(∑ 1 m=0CFi,t+
m)/K
i,t−
1,an
d“Size”
isfirm’s
size
t+1.In
columns
(7)to
(9),
thede
pend
entvariab
leis
(∑ 4 t=1RnD
i,t)/K
i,t−
1,“C
ashfl
ow”is
(∑ 3 m=0CFi,t+
m)/K
i,t−
1,an
d“Size”
isfirm’s
size
t+3.In
allcolumns
theTob
in’s
Qis
thesame.
Firm
and
year-qua
rter
fixed
effects
areinclud
ed.The
stan
dard
errors
arerobu
stto
heteroskedasticity,a
ndclusteredat
firm
level.
One-Q
uarter
Two-Qua
rters
Four-Q
uarters
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
ShortInterest
Measure
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
Cashfl
ow-1.191
***
-1.191
***
-1.178
***
-1.348
***
-1.348
***
-1.332
***
-1.611
***
-1.611
***
-1.598
***
(-26
.31)
(-26.31)
(-26
.35)
(-22
.11)
(-22.11)
(-22
.02)
(-17
.91)
(-17.90)
(-17
.83)
Tob
in’s
Q0.02
2***
0.022*
**0.02
2***
0.05
2***
0.05
1***
0.05
2***
0.12
0***
0.11
9***
0.12
0***
(17.57
)(17.49
)(17.72
)(19.20
)(19.13
)(19.44
)(19.62
)(19.52
)(19.78
)
Size
-0.086
***
-0.087
***
-0.086
***
-0.142
***
-0.143
***
-0.142
***
-0.169
***
-0.171
***
-0.169
***
(-17
.26)
(-17.31)
(-17
.32)
(-13
.81)
(-13.89)
(-13
.93)
(-7.39
)(-7.49
)(-7.46
)
ABSI
-0.004
**0.03
3-0.285
***
-0.012
***
-0.003
-0.723**
*-0.042
***
-0.013
-2.064**
*(-2.14
)(0.54)
(-3.89
)(-3.33
)(-0.02
)(-5.07
)(-5.32
)(-0.05
)(-6.52
)Yr-Qtr
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Firm
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N94
585
9458
596
472
8409
684
096
8568
875
309
7530
976
757
Adj.R
20.77
00.77
00.76
90.80
00.80
00.79
90.81
10.81
10.81
1tstatistics
inpa
rentheses
∗p<
0.10
,∗∗p<
0.05
,∗∗∗
p<
0.01
41
Table6:
ShortSelling
,Tob
in’s
Q,a
ndInvestment
Thistablepresents
quarterlyinvestmentregression
resultswithdiffe
rent
shortinterest
measures(A
BSI(.) i,t−1)an
dinvestmentho
rizons
(one-,tw
o-,
andfour-qu
arters)forhigh
andlow
Tob
in’s
Qfirms.
ABSI(1)is
adu
mmyvariab
lewhich
equa
lsto
oneiftherelative
shortinterest
attheendof
aqu
arteris
abovethetop20th
percentile
cutoffpo
int,
andzero
otherw
ise.
ABSI(2)is
therelative
shortinterest
attheendof
aqu
arter.
ABSI(3)is
themax
imum
relative
shortinterest
amon
gthethreemon
thsin
aqu
arter.
Incolumns
(1)to
(3),thedepe
ndentvariab
leisI i
,t/K
i,t−
1.In
columns
(4)
to(6),
thedepe
ndentvariab
leis
(∑ 1 m=0I i
,t+m)/K
i,t−
1,“Cashfl
ow”is
(∑ 1 m=0CFi,t+
m)/K
i,t−
1,a
nd“Size”
isthefirm’s
ize t
+1.In
columns
(7)to
(9),
thedepe
ndentvariab
leis
(∑ 3 m=0I i
,t+m)/K
i,t−
1,“Cashfl
ow”is
(∑ 3 m=0CFi,t+
m)/K
i,t−
1,a
nd“Size”
isfirm’s
size
t+3.In
allc
olum
nstheTob
in’s
Qis
thesame.
Ineach
quarterfirmsaresorted
into
twopo
rtfolio
sba
sedon
theirTob
in’sQ
intheprevious
quarter.
The
first
panelsho
wstheestimates
for
low
Tob
in’s
Qfirms.
The
second
panels
howstheestimates
forhigh
Tob
in’s
Qfirms.
Firm
andyear-qua
rter
fixed
effects
areinclud
ed.The
stan
dard
errors
arerobu
stto
heteroskedasticity,a
ndclusteredat
firm
level.
Low
Tob
in’s
QFirms
One-Q
uarter
Two-Qua
rters
Four-Q
uarters
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
ShortInterest
Measure
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
Cashfl
ow0.13
5***
0.134*
**0.13
5***
0.25
8***
0.25
7***
0.25
8***
0.64
5***
0.64
4***
0.64
5***
(7.05)
(7.01)
(7.06)
(9.16)
(9.15)
(9.19)
(11.83
)(11.84
)(11.84
)
Tob
in’s
Q0.10
8***
0.109*
**0.10
8***
0.21
6***
0.21
6***
0.21
6***
0.39
3***
0.39
4***
0.39
3***
(19.68
)(19.74
)(19.69
)(18.73
)(18.76
)(18.73
)(15.73
)(15.75
)(15.72
)
Size
0.01
5***
0.015*
**0.01
5***
0.03
5***
0.03
6***
0.03
5***
0.08
5***
0.08
6***
0.08
5***
(4.82)
(4.94)
(4.85)
(5.10)
(5.16)
(5.10)
(4.95)
(4.98)
(4.95)
ABSI
0.00
7***
0.202*
**0.21
1***
0.00
7**
0.32
9***
0.31
7**
0.01
00.84
3***
0.39
7(3.55)
(3.14)
(2.78)
(2.00)
(2.58)
(2.18)
(1.38)
(3.45)
(1.36)
Yr-Qtr
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Firm
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N89
243
8924
389
243
8505
585
055
8505
576
533
7653
376
533
Adj.R
20.45
00.45
00.45
00.53
00.53
00.53
00.61
60.61
60.61
6tstatistics
inpa
rentheses
∗p<
0.10
,∗∗p<
0.05
,∗∗∗
p<
0.01
42
HighTob
in’s
QFirms
One-Q
uarter
Two-Qua
rters
Four-Q
uarters
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
ShortInterest
Measure
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
Cashfl
ow0.01
80.01
80.01
80.08
5***
0.08
4***
0.08
4***
0.15
2***
0.15
2***
0.15
2***
(0.94)
(0.93)
(0.93)
(3.35)
(3.33)
(3.34)
(3.81)
(3.81)
(3.80)
Tob
in’s
Q0.01
4***
0.014*
**0.01
4***
0.03
3***
0.03
3***
0.03
3***
0.07
6***
0.07
6***
0.07
6***
(19.26
)(19.29
)(19.21
)(20.15
)(20.19
)(20.14
)(20.55
)(20.55
)(20.58
)
Size
0.00
9***
0.009*
**0.00
9***
0.02
2***
0.02
2***
0.02
2***
0.07
1***
0.07
1***
0.07
1***
(2.93)
(2.98)
(2.89)
(3.27)
(3.32)
(3.25)
(4.32)
(4.33)
(4.33)
ABSI
0.00
30.06
40.13
6**
0.00
7**
0.18
2*0.26
2**
0.00
30.28
7-0.117
(1.64)
(1.06)
(2.14)
(2.09)
(1.65)
(2.13)
(0.43)
(1.35)
(-0.45
)Yr-Qtr
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Firm
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N89
193
8919
389
193
8499
984
999
8499
977
596
7759
677
596
Adj.R
20.49
50.49
50.49
50.57
70.57
60.57
70.64
50.64
50.64
5tstatistics
inpa
rentheses
∗p<
0.10,∗∗p<
0.05
,∗∗∗
p<
0.01
43
Table 7: Short Selling, CEO Pay-Performance Sensitivity, and InvestmentThis table presents quarterly investment regression results in three panels. We obtain the data of CEOpay-performance sensitivity (PPS) from Coles et al. (2006). In each year firms are sorted into quintiles onthe previous year CEO’s PPS. The variable “High PPS” is a dummy which equals to one if the PPS is inthe highest quintile, and the variable “Low PPS” is a dummy which equals to one if PPS is in the lowestquintile. We interact those two dummies with our short interest measures (ABSI(.)i,t−1). ABSI(1) is adummy variable which equals to one if the relative short interest at the end of a quarter is above the top 20thpercentile cutoff point, and zero otherwise. ABSI(2) is the relative short interest at the end of a quarter.ABSI(3) is the maximum relative short interest among the three months in a quarter. In the first panel,the dependent variable is Ii,t/Ki,t−1. In the second panel, the dependent variable is (
∑1m=0 Ii,t+m)/Ki,t−1,
“Cashflow” is (∑1
m=0 CFi,t+m)/Ki,t−1 and “Size” is firm’s size t+1. In the third panel,the dependent variableis (∑3
m=0 Ii,t+m)/Ki,t−1, “Cashflow” is (∑3
m=0 CFi,t+m)/Ki,t−1, and “Size” is firm’s sizet+3. The Tobin’s Qis the same for all columns in each panel. Two-digit industry and year-quarter fixed effects are included.Robust standard errors are used.
One-Quarter(1) (2) (3) (4) (5) (6)
Short Interest Measure ABSI(1) ABSI(2) ABSI(3)
Cashflow 0.738*** 0.731*** 0.737*** 0.737*** 0.740*** 0.736***(21.36) (20.72) (21.33) (20.85) (21.49) (20.91)
Tobin’s Q 0.015*** 0.014*** 0.015*** 0.015*** 0.015*** 0.015***(16.91) (16.23) (17.01) (16.93) (16.82) (16.29)
Size -0.006*** -0.007*** -0.006*** -0.006*** -0.006*** -0.006***(-9.94) (-10.67) (-10.19) (-9.88) (-9.68) (-9.82)
ABSI 0.015*** 0.015*** 0.349*** 0.324*** 0.589*** 0.622***(7.91) (6.81) (4.89) (3.53) (8.59) (7.41)
ABSI × High PPS 0.020*** 0.354 0.496**(4.53) (1.53) (2.55)
ABSI × Low PPS -0.019*** -0.014 -0.506***(-4.34) (-0.08) (-3.23)
Constant 0.203*** 0.225*** 0.206*** 0.226*** 0.132*** 0.136***(8.72) (9.81) (8.85) (9.61) (6.65) (6.90)
Yr-Qtr Fixed Effect Yes Yes Yes Yes Yes YesIndustry Fixed Effect Yes Yes Yes Yes Yes YesN 37972 35889 37972 35889 38095 36012Adj. R2 0.322 0.319 0.321 0.317 0.322 0.319
44
Two-Quarters(1) (2) (3) (4) (5) (6)
Short Interest Measure ABSI(1) ABSI(2) ABSI(3)
Cashflow 1.004*** 0.999*** 1.002*** 1.004*** 1.005*** 1.003***(23.53) (22.85) (23.48) (22.96) (23.62) (23.01)
Tobin’s Q 0.029*** 0.029*** 0.030*** 0.030*** 0.029*** 0.029***(16.96) (16.37) (17.07) (17.00) (16.83) (16.37)
Size -0.013*** -0.014*** -0.013*** -0.014*** -0.013*** -0.013***(-11.43) (-11.98) (-11.68) (-11.32) (-11.17) (-11.25)
ABSI 0.030*** 0.031*** 0.751*** 0.640*** 1.261*** 1.269***(8.47) (7.19) (5.49) (3.65) (9.46) (7.88)
ABSI × High PPS 0.036*** 0.877** 1.140***(4.31) (2.02) (3.03)
ABSI × Low PPS -0.029*** 0.180 -0.771**(-3.46) (0.53) (-2.45)
Constant 0.405*** 0.307*** 0.415*** 0.298*** 0.279*** 0.300***(9.31) (8.72) (9.47) (8.44) (7.33) (8.43)
Yr-Qtr Fixed Effect Yes Yes Yes Yes Yes YesIndustry Fixed Effect Yes Yes Yes Yes Yes YesN 37411 35343 37411 35343 37531 35463Adj. R2 0.363 0.360 0.363 0.359 0.364 0.360
45
Four-Quarters(1) (2) (3) (4) (5) (6)
Short Interest Measure ABSI(1) ABSI(2) ABSI(3)
Cashflow 1.378*** 1.376*** 1.376*** 1.380*** 1.380*** 1.379***(25.42) (24.95) (25.35) (25.06) (25.51) (25.11)
Tobin’s Q 0.061*** 0.061*** 0.062*** 0.063*** 0.060*** 0.060***(15.03) (14.67) (15.15) (15.12) (14.90) (14.61)
Size -0.028*** -0.030*** -0.029*** -0.029*** -0.028*** -0.029***(-11.83) (-12.26) (-12.10) (-11.84) (-11.62) (-11.73)
ABSI 0.062*** 0.064*** 1.556*** 1.516*** 2.679*** 2.687***(8.65) (7.37) (5.56) (4.38) (10.01) (8.46)
ABSI × High PPS 0.056*** 1.077 1.977***(3.41) (1.21) (2.67)
ABSI × Low PPS -0.043** 0.038 -1.210*(-2.50) (0.06) (-1.92)
Constant 0.249*** 0.606*** 0.271*** 0.596*** 0.402*** 0.800***(3.24) (8.68) (3.58) (8.57) (4.40) (9.20)
Yr-Qtr Fixed Effect Yes Yes Yes Yes Yes YesIndustry Fixed Effect Yes Yes Yes Yes Yes YesN 35266 34068 35266 34068 35381 34183Adj. R2 0.403 0.402 0.403 0.401 0.404 0.403t statistics in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
46
Table8:
ShortSelling
,Accruals,
andInvestment
Thistablepresents
quarterlyinvestmentregression
resultswith
diffe
rent
shortinterest
measuresan
dinvestmentho
rizons
(one-,
two-,an
dfour-
quarters).
Lettrepresentqu
arter.
Three
proxiesareused
forABSI i
,t−1.ABSI(1)is
adu
mmyvariab
lewhich
equa
lsto
oneiftherelative
short
interest
attheendof
aqu
arteris
abovethetop20th
percentile
cutoffpo
int,
andzero
otherw
ise.
ABSI(2)is
therelative
shortinterest
attheend
ofaqu
arter.
ABSI(3)is
themax
imum
relative
shortinterest
amon
gthethreemon
thsin
aqu
arter.
Incolumns
(1)to
(3),
thedepe
ndentvariab
leis
I i,t/K
i,t−
1.In
columns
(4)to
(6),
thedepe
ndentvariab
leis
(∑ 1 m=0I i
,t+m)/K
i,t−
1,“C
ashfl
ow”is
(∑ 1 m=0CFi,t+
m)/K
i,t−
1,an
d“Size”
isfirm’s
size
t+1.In
columns
(7)to
(9),thedepe
ndentvariab
leis(∑ 3 m
=0I i
,t+m)/K
i,t−
1,“Cashfl
ow”is(∑ 3 m
=0CFi,t+
m)/K
i,t−
1,a
nd“Size”
isfirm’ssize
t+3.In
allcolumns
theTob
in’s
Qis
thesame.
Foreach
year
j,discretion
aryaccrua
lsaredefin
edas
DACCR
i,j=
ACCR
i,j−
NORM
ALACCR
i,j,where
ACCR
i,j=4
NCCA
i,j−4
CL
i,j−Item
DP
i,j
Item
ATi,j
−1
,and
NORM
ALACCR
i,j=
Item
Sale×∑ 5 n
=1ACCR
i,j
−n
∑ 5 n=
1Item
Sale
i,j
−n
.The4NCCA
i,jis
thechan
geof
NCCA
i,jwhich
is(Item
ACTi,j−
Item
CHE
i,j),
andthe4CLi,jis
thechan
geof
CLi,jwhich
is(Item
LCTi,j−
Item
DLC
i,j−
Item
TXPi,j).
Item
names
referto
Com
pustat
annu
alda
tana
mes.Firm
andyear-qua
rter
fixed
effects
areinclud
ed.The
stan
dard
errors
arerobu
stto
heteroskedasticity,a
ndclustered
atfirm
level.
One-Q
uarter
Two-Qua
rters
Four-Q
uarters
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
ShortInterest
Measure
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
Cashfl
ow0.16
5***
0.165*
**0.16
3***
0.29
0***
0.29
0***
0.28
7***
0.52
4***
0.52
4***
0.51
2***
(7.33)
(7.34)
(7.30)
(8.98)
(8.99)
(8.92)
(9.41)
(9.41)
(9.20)
Tob
in’s
Q0.01
8***
0.018*
**0.01
8***
0.03
9***
0.04
0***
0.04
0***
0.09
1***
0.09
1***
0.09
2***
(12.91
)(12.96
)(12.96
)(13.64
)(13.68
)(13.64
)(13.68
)(13.71
)(13.71
)
Size
0.00
50.00
50.00
50.01
3*0.01
4*0.01
3*0.05
1***
0.05
1***
0.05
2***
(1.29)
(1.35)
(1.34)
(1.79)
(1.84)
(1.79)
(2.93)
(2.96)
(2.97)
DACCR
0.04
1***
0.041*
**0.04
1***
0.07
5***
0.07
5***
0.07
6***
0.14
2***
0.14
1***
0.14
4***
(4.54)
(4.54)
(4.63)
(3.93)
(3.92)
(3.99)
(3.29)
(3.29)
(3.38)
ABSI
0.00
6***
0.170*
**0.19
3***
0.01
1***
0.37
8***
0.38
0***
0.01
6***
0.64
4***
0.42
8*(4.05)
(3.59)
(3.24)
(3.92)
(4.12)
(3.23)
(2.73)
(3.52)
(1.79)
Yr-Qtr
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Firm
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N90
900
9089
392
985
8923
189
224
9126
883
818
8381
185
763
Adj.R
20.44
70.44
70.44
50.52
60.52
60.52
30.60
30.60
30.60
1tstatistics
inpa
rentheses
∗p<
0.10
,∗∗p<
0.05
,∗∗∗
p<
0.01
47
Table9:
ShortSelling
,LaggedInvestment,an
dInvestment
Thistablepresents
quarterly
investmentregression
resultswith
diffe
rent
shortinterest
measures(A
BSI(.) i,t−1)an
dinvestmentho
rizons
(one-,
two-,an
dfour-qu
arters).
ABSI(1)is
adu
mmyvariab
lewhich
equa
lsto
oneif
therelative
shortinterest
attheendof
aqu
arteris
abovethe
top20th
percentile
cutoff
point,
andzero
otherw
ise.
ABSI(2)is
therelative
shortinterest
attheendof
aqu
arter.
ABSI(3)is
themax
imum
relative
shortinterest
amon
gthethreemon
thsin
aqu
arter.
Incolumns
(1)to
(3),
thedepe
ndentvariab
leis
I i,t/K
i,t−
1,an
d“Laggedinvestment”
isI i
,t−1/K
i,t−
2.In
columns
(4)to
(6),
thede
pend
entvariab
leis
(∑ 1 m=0I i
,t+m)/K
i,t−
1,“La
gged
investment”
is(∑ 1 m
=0I i
,t+m−2)/K
i,t−
3,“Cashfl
ow”
is(∑ 1 m
=0CFi,t+
m)/K
i,t−
1an
d“Size”
isfirm’s
size
t+1.In
columns
(7)to
(9),
thedepe
ndentvariab
leis
(∑ 3 m=0I i
,t+m)/K
i,t−
1,“Laggedinvestment”
is(∑ 3 m
=0I i
,t+m−4)/K
i,t−
5,“C
ashfl
ow”is
(∑ 3 m=0CFi,t+
m)/K
i,t−
1,an
d“Size”
isfirm’s
size
t+3.In
allcolumns
theTob
in’s
Qis
thesame.
Firm
and
year-qua
rter
fixed
effects
areinclud
ed.The
stan
dard
errors
arerobu
stto
heteroskedasticity,a
ndclusteredat
firm
level.
One-Q
uarter
Two-Qua
rters
Four-Q
uarters
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
ShortInterest
Measure
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
Lagg
edinvestment
0.35
8***
0.358*
**0.35
6***
0.31
2***
0.31
2***
0.31
0***
0.23
7***
0.23
7***
0.23
3***
(44.29
)(44.30
)(44.44
)(31.87
)(31.87
)(32.00
)(20.53
)(20.53
)(20.35
)
Cashfl
ow0.11
0***
0.110*
**0.11
1***
0.20
7***
0.20
6***
0.20
4***
0.38
4***
0.38
4***
0.38
8***
(8.71)
(8.69)
(8.75)
(11.18
)(11.17
)(11.09
)(9.98)
(9.98)
(10.17)
Tob
in’s
Q0.01
4***
0.014*
**0.01
4***
0.03
4***
0.03
4***
0.03
4***
0.08
4***
0.08
4***
0.08
4***
(23.42
)(23.54
)(23.65
)(22.80
)(22.89
)(23.04
)(20.49
)(20.51
)(20.63
)
Size
0.00
10.00
10.00
10.00
40.00
50.00
50.03
1***
0.03
1***
0.03
3***
(0.52)
(0.66)
(0.65)
(1.12)
(1.19)
(1.20)
(2.88)
(2.89)
(2.99)
ABSI
0.00
5***
0.107*
**0.17
9***
0.00
7***
0.21
2***
0.31
3***
0.00
40.46
6***
0.19
0(4.29)
(2.58)
(4.13)
(2.90)
(2.65)
(3.43)
(0.91)
(2.82)
(0.95)
Yr-Qtr
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Firm
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N17
5105
1750
9617
9419
1610
0616
0997
1648
9713
6012
1360
0513
9355
Adj.R
20.51
60.51
60.51
30.56
70.56
70.56
50.61
70.61
80.61
6tstatistics
inpa
rentheses
∗p<
0.10
,∗∗p<
0.05
,∗∗∗
p<
0.01
48
Table10
:So
rting
Ineach
year-qua
rter
werunan
investmentregression
inwhich
thedepe
ndentvariab
leis
theinvestmentcapitalratioan
dtheindepe
ndentvariab
les
includ
eTob
in’sq,
cash
flow,a
ndfirm
size.Werecord
theregression
residu
alan
drank
firmsinto
over-a
ndun
der-investmentgrou
psby
theirresidu
als.
Withineach
grou
p,weindepe
ndentlysort
firmsinto
high
andlow
ABSI
subg
roup
sby
thedu
mmyvariab
leABSI(1).
The
averageinvestmentin
each
subg
roup
ineach
year-qua
rter
iscompu
ted.
The
tablebe
low
show
stheaverageinvestmentan
daveragenu
mbe
rof
firmsin
each
subg
roup
from
1988
Q1to
2011
Q4.
The
diffe
rences
ofinvestmentbe
tweenhigh
andlow
ABSI
subg
roup
sarealso
compu
ted.
One-Q
uarter
Two-Qua
rter
Four-Q
uarter
ABSI
Ave.
Invt.
No.
ofFirms
ABSI
Ave.
Invt.
No.
ofFirms
ABSI
Ave.
Invt.
No.
ofFirms
Over-investment
Over-investment
Over-investment
High
0.03
319
5High
0.06
7186
High
0.13
816
8
Low
0.02
975
0Lo
w0.05
871
3Lo
w0.11
864
8
High-Lo
w0.00
4***
High-Lo
w0.009*
**High-Lo
w0.020*
**Und
er-in
vestment
Und
er-in
vestment
Und
er-in
vestment
High
0.00
617
8High
0.01
3171
High
0.03
015
5
Low
0.00
574
8Lo
w0.01
171
3Lo
w0.02
664
7
High-Lo
w0.00
1***
High-Lo
w0.002*
**High-Lo
w0.005*
**∗p<
0.10,∗∗p<
0.05,∗∗∗
p<
0.01
49
Table11
:2S
LS:S
hort
Selling
andInvestment
Thistablepresents
thesecond
stageresultsof
thetw
o-stageleast-squa
res(2SL
S)regression
withdiffe
rent
shortinterest
measures(A
BSI(.) i,t−1)an
dinvestmentho
rizons
(one-,tw
o-,an
dfour-qu
arters).
Inthefirst
stage,
theindu
stry
medianof
each
ABSI i
,t−1proxyin
each
quarteris
used
asthe
exclud
edinstrumentvariab
leforABSI i
,t−1,an
dthereforethemod
elis
exactlyidentified.
ABSI(1)is
adu
mmyvariab
lewhich
equa
lsto
oneifthe
relative
shortinterest
attheendof
aqu
arterisab
ovethetop20th
percentile
cutoffpo
int,an
dzero
otherw
ise.
ABSI(2)istherelative
shortinterest
attheen
dof
aqu
arter.
ABSI(3)isthemax
imum
relative
shortinterest
amon
gthethreemon
thsin
aqu
arter.
Incolumns
(1)to
(3),thedepe
ndent
variab
leis
I i,t/K
i,t−
1.In
columns
(4)to
(6),
thedepe
ndentvariab
leis
(∑ 1 m=0I i
,t+m)/K
i,t−
1,“C
ashfl
ow”is
(∑ 1 m=0CFi,t+
m)/K
i,t−
1,an
d“Size”
isfirm’s
size
t+1.In
columns
(7)to
(9),
thedepe
ndentvariab
leis
(∑ 3 m=0I i
,t+m)/K
i,t−
1,“C
ashfl
ow”is
(∑ 3 m=0CFi,t+
m)/K
i,t−
1,an
d“Size”
isfirm’s
size
t+3.In
allc
olum
nstheTob
in’sQ
isthesame.
Firm
andyear-qua
rter
fixed
effects
areinclud
ed.The
LMtest
statistics
forun
der-identificationare
repo
rted.The
stan
dard
errors
arerobu
stto
heteroskedasticity,a
ndclusteredat
firm
level.
Second
Stag
e.Dep
endent
Variable:
Investment
One-Q
uarter
Two-Qua
rters
Four-Q
uarters
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
ShortInterest
Measure
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
Cashfl
ow0.14
4***
0.143*
**0.14
4***
0.23
8***
0.23
7***
0.23
6***
0.38
0***
0.37
9***
0.37
9***
(9.27)
(9.23)
(9.28)
(10.88
)(10.85
)(10.82
)(10.14
)(10.13
)(10.20
)
Tob
in’s
Q0.01
9***
0.019*
**0.01
9***
0.04
4***
0.04
4***
0.04
4***
0.09
9***
0.10
0***
0.10
0***
(24.08
)(24.42
)(24.47
)(24.89
)(25.12
)(25.15
)(24.68
)(24.81
)(24.94
)
Size
0.00
5**
0.006*
*0.00
6**
0.01
6***
0.01
7***
0.01
7***
0.06
1***
0.06
3***
0.06
3***
(2.17)
(2.48)
(2.37)
(3.05)
(3.28)
(3.14)
(4.70)
(4.87)
(4.86)
ABSI
0.01
5***
0.336*
**0.42
0***
0.02
4***
0.65
1***
0.82
1***
0.04
0**
1.40
6***
1.01
8(3.73)
(2.86)
(2.85)
(3.03)
(3.01)
(2.58)
(2.39)
(3.16)
(1.49)
Yr-Qtr
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Firm
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N17
9710
1797
0018
4138
1712
3817
1229
1753
9115
4917
1549
0815
8712
LMTest
850.00
287.06
327.42
826.82
277.64
317.05
759.19
246.40
288.48
tstatistics
inpa
rentheses
∗p<
0.10
,∗∗p<
0.05
,∗∗∗
p<
0.01
50
Table12
:Sh
ortSelling
,Idiosyn
cratic
Risk,
andInvestment
Thistablepresents
quarterlyinvestmentregression
resultswithdiffe
rent
shortinterest
measures(A
BSI(.) i,t−1),
idiosyncraticrisk,an
dinvestment
horizons
(one-,
two-,an
dfour-qu
arters).
ABSI(1)is
adu
mmyvariab
lewhich
equa
lsto
oneiftherelative
shortinterest
attheendof
aqu
arter
isab
ovethetop20th
percentile
cutoffpo
int,
andzero
otherw
ise.
ABSI(2)is
therelative
shortinterest
attheendof
aqu
arter.
ABSI(3)is
the
max
imum
relative
shortinterest
amon
gthethreemon
thsin
aqu
arter.
“IdioR
isk”
isthestan
dard
deviationof
theresidu
alfrom
theFa
ma-French
3-factor
mod
el.In
columns
(1)to
(3),
thedepe
ndentvariab
leis
I i,t/K
i,t−
1.In
columns
(4)to
(6),
thedepe
ndentvariab
leis
(∑ 1 m=0I i
,t+m)/K
i,t−
1,
“Cashfl
ow”is(∑ 1 m
=0CFi,t+
m)/K
i,t−
1,a
nd“Size”
isfirm’ssize
t+1.In
columns
(7)to
(9),thedepe
ndentvariab
leis(∑ 3 m
=0I i
,t+m)/K
i,t−
1,“Cashfl
ow”
is(∑ 3 m
=0CFi,t+
m)/K
i,t−
1,a
nd“Size”
isis
firm’ssize
t+3.In
allc
olum
nstheTob
in’s
Qis
thesame.
Firm
andyear-qua
rter
fixed
effects
areinclud
ed.
The
stan
dard
errors
arerobu
stto
heteroskedasticity,a
ndclusteredat
firm
level.
One-Q
uarter
Two-Qua
rters
Four-Q
uarters
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
ShortInterest
Measure
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
Cashfl
ow0.15
7***
0.157*
**0.156*
**0.26
1***
0.26
1***
0.25
9***
0.42
3***
0.42
3***
0.42
2***
(9.52)
(9.51)
(9.43)
(10.85
)(10.84
)(10.75
)(9.98)
(9.98)
(10.03
)
Tob
in’s
Q0.01
8***
0.018*
**0.019*
**0.04
1***
0.04
1***
0.04
1***
0.09
4***
0.09
4***
0.09
4***
(19.41
)(19.52
)(19.58
)(19.76
)(19.88
)(19.97
)(19.68
)(19.74
)(19.79
)
Size
0.00
8***
0.008*
**0.008*
**0.02
1***
0.02
2***
0.02
2***
0.07
3***
0.07
3***
0.07
4***
(2.89)
(2.97)
(3.03)
(3.65)
(3.73)
(3.78)
(5.24)
(5.26)
(5.35)
ABSI
0.01
4***
0.374*
**0.481*
**0.02
0***
0.69
7***
0.88
5***
0.04
9***
1.72
3***
1.85
3***
(5.66)
(4.57)
(5.45)
(4.42)
(4.56)
(5.20)
(5.01)
(5.95)
(5.32)
ABSI×
IdioRisk
-0.042
***
-1.131
**-1.322
***
-0.050
*-1.931
**-2.254
***
-0.194
***
-5.841
***
-7.126
***
(-3.01
)(-2.37
)(-3.09
)(-1.81
)(-2.16
)(-2.75
)(-3.31
)(-3.46
)(-4.14
)
IdioRisk
-0.036
**-0.042
**-0.038
**-0.056
-0.062
-0.053
-0.003
-0.031
0.00
2(-2.03
)(-2.32
)(-2.11
)(-1.46
)(-1.61
)(-1.38
)(-0.03
)(-0.36
)(0.02)
Yr-Qtr
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Firm
Fixed
Effe
ctYes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N17
5105
1750
9617
9419
1610
0616
0997
1648
9713
6012
1360
0513
9355
Adj.R
20.44
00.44
00.43
80.51
50.51
50.51
20.59
00.59
00.58
8tstatistics
inpa
rentheses
∗p<
0.10
,∗∗p<
0.05
,∗∗∗
p<
0.01
51
Table13
:Sh
ortSelling
,Inv
estm
ent,an
dSu
bsequent
StockReturns
Thistablepresents
mon
thly
Fama-MacBeth
regression
resultsforshortinterest,investmentan
dsubsequent
returns.
Incolumns
(1)to
(3),
the
depe
ndentvariab
leisthestockreturnsover
thequ
artert+1,
theinvestmentisI i
,t/K
i,t−
1,a
nd“C
ashfl
ow”isCFi,t/K
i,t−
1.In
columns
(4)to
(6),the
depe
ndentvariab
leisthecumulativequ
arterlystockreturnsfrom
thequ
artert+1to
thequ
artert+2,
theinvestmentis(∑ 1 m
=0I i
,t+m)/K
i,t−
1,a
nd“C
ashfl
ow”is(∑ 1 m
=0CFi,t+
m)/K
i,t−
1.In
columns
(7)to
(9),thedepe
ndentvariab
leisthecumulativequ
arterlystockreturnsfrom
thequ
artert+1
tothequ
artert+4,the
investmentis(∑ 3 m
=0I i
,t+m)/K
i,t−
1,a
ndthe“C
ashfl
ow”is(∑ 3 m
=0CFi,t+
m)/K
i,t−
1.In
allc
olum
nstheQ
i,t−
1,m
arketvalue
ofequity
“ME′′ i,t−
1,a
ndthemom
entum
“MOM′′ i,t−
1arethesame.
ABSI(1)isadu
mmyvariab
lewhich
equa
lsto
oneiftherelative
shortinterest
attheendof
aqu
arteris
abovethetop20th
percentile
cutoffpo
int,
andzero
otherw
ise.
ABSI(2)is
therelative
shortinterest
attheendof
aqu
arter.
ABSI(3)is
themax
imum
relative
shortinterest
amon
gthethreemon
thsin
aqu
arter.
New
ey-W
eststan
dard
errorareused
withfour-periodlag.
Subseque
ntReturns
One-Q
uarter
Two-Qua
rters
Four-Q
uarters
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
ShortInterest
Measure
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
ABSI(1)
ABSI(2)
ABSI(3)
ln(I/K
)-0.005
***
-0.005
***
-0.005
***
-0.007
**-0.008
***
-0.008**
*-0.015
**-0.015
***
-0.015**
*(-3.91
)(-3.93
)(-3.79
)(-2.56
)(-3.15
)(-3.11
)(-2.62
)(-2.68
)(-2.66
)ABSI
-0.006
*-0.365
**-0.484
***
-0.008
*-0.251
-0.648
***
-0.013
-0.934
*-0.837
**(-1.71
)(-2.20
)(-3.11
)(-1.78
)(-1.28
)(-2.71
)(-1.62
)(-1.95
)(-2.03
)log(Tob
in’s
Q)
-0.002
-0.000
-0.001
-0.009
-0.011
-0.008
-0.010
-0.022
-0.022
(-0.20
)(-0.03
)(-0.19
)(-0.67
)(-0.77
)(-0.55
)(-0.35
)(-0.83
)(-0.84
)Cashfl
ow0.63
2***
0.568*
**0.55
8***
0.30
6***
0.28
2***
0.27
6***
-0.024
-0.014
-0.007
(7.95)
(12.63
)(12.70
)(4.10)
(4.26)
(4.21)
(-0.31
)(-0.18
)(-0.09
)M
E-0.008
***
-0.008
***
-0.007
***
-0.011
***
-0.010
***
-0.010
***
-0.010
*-0.008
-0.008
(-4.44
)(-4.53
)(-4.37
)(-2.92
)(-2.71
)(-2.79
)(-1.82
)(-1.56
)(-1.56
)M
OM
-0.022
**-0.024
**-0.023
**-0.027
***
-0.024
***
-0.024
***
-0.048
***
-0.037
***
-0.038
***
(-2.28
)(-2.61
)(-2.54
)(-3.10
)(-2.96
)(-2.88
)(-2.64
)(-2.98
)(-3.20
)Con
stan
t0.06
1***
0.062*
**0.06
2***
0.11
6***
0.10
6***
0.11
0***
0.20
7***
0.20
2***
0.20
0***
(4.06)
(4.11)
(4.16)
(3.44)
(3.19)
(3.38)
(3.37)
(3.23)
(3.26)
N99
9898
9998
9896
9595
R2
0.04
40.03
90.03
90.04
70.04
10.04
10.04
80.04
00.04
0tstatistics
inpa
rentheses
∗p<
0.10
,∗∗p<
0.05
,∗∗∗
p<
0.01
52
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