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Ownership breadth:

Investor recognition or short-sale constraint

Zhiqi Cao

Antai College of Economics and Management

Shanghai Jiao Tong University, Shanghai, 200030 China

Wenfeng Wu*

Antai College of Economics and Management

Shanghai Jiao Tong University, Shanghai, 200030 China

Abstract: The competing theories of Miller (1977)’s short-sale constraint and Merton (1987)’s investor

recognition infers opposite association between ownership breadth and future stock returns. We find the

mixed empirical evidence in the prior literature comes from the opposite effects of positive and negative

breadth changes on stock returns. The breadth-future return relationship is positive only when breadth

decreases, whereas the relationship becomes negative when breadth increases. Our findings suggest that

investor recognition hypothesis holds only when breadth increases, whereas short-sale constraints

hypothesis holds when breadth decreases. This reconciles not only the conflicting evidences but also

the competing prediction of Miller (1977) and Merton (1987).

Keywords: Ownership breadth; stock returns; investor recognition; short-sales constraints

JEL Classification: G12; G14; M41

* Corresponding author at: Antai College of Economics and Management, Shanghai Jiao Tong University,

Shanghai, China. Address: Rm. B1521 Antai Building, No. 1954 Huashan Road, Shanghai, 200030 China.

Email: wfwu@sjtu.edu.cn. Tel: 8621-52301194

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1. Introduction

The relationship between ownership breadth (the percentage of number of investors with long

positions) and future stock return is puzzling. It is related to two competing theories: Miller (1977)’s

short-sale constraint and Merton (1987)’s investor recognition. Miller (1977) argues that when a stock

faces short-sale constraints, negative opinions held by pessimistic investors cannot be fully incorporated

into stock prices, thus lead to the stock’s overpricing. A lower ownership breadth indicates more

pessimistic investors, so the stronger short-sale constraints brings higher overpricing, as a consequence

of lower future stock return. In opinion of Miller (1977), the association between the ownership breadth

and future return is positive.

However, Merton (1987) argues that a stock’s market value is increasing in the degree of investor

recognition as of investors’ limited attentions. A higher ownership breadth represents a higher investor

recognition of the stock, so a higher stock’s current market value. In view of Merton (1987), the

ownership breadth is positively associated with contemporaneous return, but negatively associated

future return. This investor recognition-based prediction is contrary to Miller (1977)’s theory based on

the short-sale constraints.

Empirical evidence on the relationship between ownership breadth and stock return is also mixed.

Some literature supports investor recognition theory, such as Arbel, Carvell, and Strebel (1983), Lehavy

and Sloan (2008), and Bodnaruk and Ostberg (2009). They all find a negative association between the

change of ownership breadth and future stock returns1. Other literature provides the opposite evidence,

which supports the short-sale constraints theory. Chen, Hong and Stein (2002) find that the change of

ownership breadth positively predicts future stock returns. Lehavy and Sloan (2008) point out that it is

the autocorrelation of the change of ownership breadth that leads to a positive association between the

change of ownership breadth and future stock return. After controlling the autocorrelation of the change

1 Grullon, Kanatas, and Weston (2004) and Green and Jame (2013) propose that ownership breadth is a proxy for

investor recognition when examining what causes increase of investor recognition and liquidity, but they don’t

test how investor recognition affects stock returns. Foerster and Karolyi (1999) find that non-U.S. firms cross-

listing shares on U.S. exchanges earn cumulative abnormal returns of 1.20 percent during the listing week, but

incur a loss of 14 percent during the year following listing and is related to an expansion of the shareholder base.

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of ownership breadth, they find the association between the ownership breadth and future stock returns

is still negative. Cen, Lu, and Yang (2013) develop a dynamic multi-asset model and argue that the

relationship between the ownership breadth and future return is negative when the investor sentiment

variation is high, but becomes positive when the sentiment effect is small.

In this paper, we argue that that short-sale constraints effect dominates when ownership breadth

decreases, whereas investor recognition effect dominates for the increase of ownership breadth. The

decrease of ownership breadth comes from the exit of original shareholders, which does not mean the

disappearance of these investors’ recognition, so investor recognition does not decrease. Thus, short-

sales constraint effect should dominate as ownership breadth decreases, which will keep the stock price

at a high level and lead to higher contemporaneous returns and lower future returns. However, the

increase of ownership breadth represents expanding of investor recognition as more investors hold the

stock. As more investors incentivize to buy the stock, this push up stock price and lead to higher

contemporaneous returns and lower future returns. In this case, investor recognition effect dominates.

Using U.S. stock markets data covering the period from 1976 through 2017, we test our above

argument and find an asymmetric effect between positive and negative changes of ownership breadth

on the stock returns. Specifically, for the subsample of increase of ownership breadth, the change of

ownership breadth is positively associated with contemporaneous stock returns but negatively

associated with future stock returns. As to the subsample of decrease of ownership breadth, the

association is the opposite. That is, when breadth decreases, the change of ownership breadth is

negatively associated with contemporaneous returns but positively with future returns.

Our findings suggest that the investor recognition hypothesis holds only when ownership breadth

increases. As Lehavy and Sloan (2008) report that financing and investing activities increase in

investors’ recognition, we conduct regressions of financing and investing activities on the change of

ownership breadth. The results show that financing and investing activities are significantly positively

associated with the breadth change in the subsample of positive change of breadth, but the associations

are insignificant in the subsample of negative change of breadth. This further supports our above

argument.

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In addition, the short-sale constraints hypothesis holds only when the breadth decreases. To support

this argument, we examine the relationship between short-sales constraints and change of ownership

breadth. Our results confirm our above conjecture. Following Figlewski (1981), Asquith, Pathak, and

Ritter (2005) and Boehme, Danielsen, and Sorescu (2006), we use relative short interest, calculated as

the percentage of shares held short scaled by the total shares outstanding, as a proxy for the short-sale

constraints. We find that in the subsample of negative breadth change, the short-sale constraints are

negatively associated with the change of breadth, but the association is insignificant when ownership

breadth increases.

We also conduct some robustness tests. First, as Lehavy and Sloan (2008) argue, changes in

investor recognition might be driven by news about earnings, we apply three measures of earning news

as control variables to test the possibility. The result shows that innovations in ownership breadth appear

to be more important than earnings news in explaining contemporaneous and future stock returns, and

the asymmetric effect of increase and decrease of breadth change does not change.

Second, there is possibility that the asymmetry shown in our paper is an implication of the

sentiment story in Cen, Lu, and Yang (2013), who report a positive relationship between breadth change

and future returns when market sentiment variation is low and a negative one at periods of high market

sentiment variation. If it is the case, increase of ownership breadth should concentrate in high sentiment

variation period, whereas decrease of ownership breadth in low sentiment variation period. However,

we classified full sample into deciles by the level of market sentiment variation of the corresponding

year. We find that there is no significant difference in each decile on the percentage of firms with

increase and decrease of ownership breadth and mean of their breadth. We further separate the full

sample into high sentiment variation group and low sentiment variation group, and the regression result

also shows a significant asymmetry in both high and low sentiment variation period.

We also construct breadth change measure based on the number of institutional investors following

Chen, Hong and Stein (2002), and Lehavy and Sloan (2008) for robustness tests. The result shows that

after controlling autocorrelation of breadth change, the association between breadth change and future

return is negative when breadth increases, whereas it is positive when breadth decreases. This indicates

our conclusion holds whether we measure ownership breadth based on total number of all investors or

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that of institutional investors.

Our paper contributes to the literature in the following ways. First, we find an asymmetric effect

of ownership breadth on the stock return by demonstrating that the effect of positive breadth changes

on stock returns is the opposite to that of negative breadth changes, which is different from the examined

unidirectional relationship in the prior literature (Arbel, Carvell, and Strebel, 1983; Chen, Hong, and

Stein, 2002; Lehavy and Sloan, 2008; Bodnaruk and Ostberg, 2009; Choi, Jin, and Yan, 2013; Cen, Lu,

and Yang, 2013).

Second, this study helps to reconcile conflicting evidences on the relationship between the

ownership breadth and stock returns in previous studies. Based on the theory of Miller (1977), some

literature find a positive association between changes in ownership breadth and future stock return

(Chen, Hong, and Stein, 2002; Choi, Jin, and Yan, 2013), whereas negative association based on Merton

(1987) is also supported by other literature (Lehavy and Sloan, 2008; Bodnaruk and Ostberg, 2009).

We find that the conflicting evidence comes from the opposite effects between positive breadth change

and negative breadth change on the stock return. This not only reconcile the mixed empirical evidence,

but also reconciles the theory of Miller (1977) and Merton (1987).

The remainder of this paper is organized as follows. Section 2 describes the data and methodology.

Section 3 presents empirical results of the effect of breadth change on future stock returns and

contemporaneous returns and discusses the implications of breadth change. Section 4 shows the

robustness tests. Section 5 concludes the paper.

2. Data and Methodology

2.1 Data

Our sample includes all common stocks listed on the NYSE, AMEX, and Nasdaq from the CRSP

(Center for Research in Securities Price) database. The accounting information used to construct

common factors, such as number of outstanding shares, total assets, total liabilities and equity, is from

Compustat database. The sample period is from 1976 to 2017. To mitigate the concern that our stock

return tests might be influenced by return outliers, stocks with negative book value and with price less

than 1 dollar are excluded. Our measure of ownership breadth change is constructed from annual

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common/ordinary shareholders item in Compustat database, which represents the actual number of

shareholders of common/ordinary capital. All data is winsorized at 99% level. Finally, we have 117,390

firm-year observations.

The information on analysts’ forecast on earnings, which is used to construct dispersion of opinion,

is extracted from the I/B/E/S-unadjusted summary historical file2. Data used to construct measures of

corporate financing and investing activities are obtained from Compustat database. Information on

short-sales constraint is obtained from Thomson Reuters database. Measures of earning news are

constructed based on data from Compustat database and I/B/E/S-unadjusted summary historical file.

Sentiment indices are downloaded from Jeffrey A. Wurgler’s website3.

2.2 Construction of ownership breadth change

Our main measure of ownership breadth change, is given in Eq. (1):

𝐵𝑅𝐸𝐴𝐷𝑇𝐻𝑖,𝑡 = |𝐼𝑛𝑣𝑒𝑠𝑡𝑜𝑟 𝐵𝑎𝑠𝑒𝑖,𝑡 − 𝐼𝑛𝑣𝑒𝑠𝑡𝑜𝑟 𝐵𝑎𝑠𝑒𝑖,𝑡−1

𝐼𝑛𝑣𝑒𝑠𝑡𝑜𝑟 𝐵𝑎𝑠𝑒𝑖,𝑡−1| (1)

where Investor Basei,t is the number of shareholders of stock i in year t. As Merton (1987) proposes

that investors buy the stock only when they know the stock, the number of shareholders is referred to

as investor base. This measure considers all the investors who hold a long position in the stock,

including institutional investor and retail investors. We apply change level instead of absolute level here

is due to the consideration that absolute level of ownership breadth is influenced by a lot of other factors,

such as firm size, and change specification should be applied to control those factors.

Since some literature, such as Chen, Hong and Stein (2002) and Lehavy and Sloan (2008), uses

the number of institutional investors from 13-F file to calculate the ownership breadth change, we also

use the number of institutional investors as investor base to calculate ownership breadth change as a

robustness check.

2 It is argued that I/B/E/S summary historical file is embedded with many errors, while Diether, Malloy, and

Scherbina (2002) compare the summary file and detail file and find that the result given by summary file is almost

the same to that of detail file in empirical studies, thus we adopt summary file as data source here.

3 See http://people.stern.nyu.edu/jwurgler/

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2.3 Major regression models

(1) Ownership breadth change and stock return

We test the relationship between future and contemporaneous returns and ownership breadth

change applying Fama and MacBeth (1973) regressions. The dependent variable RET is annual stock

return adjusted by one-month treasury bill rate (Boehme, Danielsen, and Sorescu, 2006). The key

variable is ownership breadth change BREADTH described in Section 2.2. The control variables are

given as follows. SIZE is log of market capitalization in June of each year. B/M is log of book-to-market

ratio, of which book value is measured in June of each year and market capitalization is measured in

December of the previous year. LEV is leverage, calculated as the ratio of total liabilities to total assets.

Dispersion of analysts’ forecast ANALYST is calculated as standard deviation of fiscal year one analysts’

earnings forecast scaled by mean of analysts’ earnings forecast.

(2) Breadth change and corporate financing and investing activities

To further check different implications between increase of ownership breadth and decrease of

ownership breadth, we conduct some additional tests. As discussed above, Merton (1987) argues that

changes in investor recognition will be positively correlated with corporate financing and investing

activities. If change in ownership breadth represents change in investor recognition, it should also be

positively related to corporate financing and investing activities. Following Lehavy and Sloan (2008),

we define corporate financing activities FIN as net cash from financing activities, and corporate

investing activities INV as capital expenditures plus acquisitions less depreciation and sales of property

and equipment. Thus, we take FIN and INV as dependent variables, respectively. Independent variables

include breadth change BREADTH and control variables used in the return-breadth change regressions.

As we argue above, if breadth increase represents expansion of investor recognition, but breadth

decrease does not, we would expect a positive coefficient of breadth change in the regression with

subsample of positive breadth change and an insignificant coefficient of breadth change for subsample

of negative breadth change.

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(3) Breadth change and short-sales constraints

Prior literature proposes that when short-sales is constrained, stock’s prices are more likely to be

overvalued (Miller, 1977; Hong and Stein, 2003; Chang, Cheng, and Yu, 2007; Boehmer and Wu,

2013).4 Chen, Hong and Stein (2002) argue that lower ownership breadth indicates tighter short-sale

constraints. Thus, we take short-sale constraint as dependent variable to see its relationship with breadth

change. Following Figlewski (1981), Asquith, Pathak, and Ritter (2005) and Boehme, Danielsen, and

Sorescu (2006), we use relative short interest SSI, calculated as the percentage of shares held short of

the total shares outstanding, as a proxy for the short-sale constraints to investigate the association

between the breadth change and short-sale constraint. Larger relative short interest represents tenser

short-sale constraint. As Boehme, Danielsen, and Sorescu (2006) argue, high relative short interest

represents less stocks available to be short. This explanation can also be confirmed by Kelly and Tetlock

(2017) that short sellers are in fact informed and can predict future returns. In this case, those who still

hold the stock and can lend the stock are not clear about the future movement of the price, and those

who have already sold the stock and those who don't own the stock and short the stock are pessimistic

about the stock. As more investors sell the stock, more stocks are held by those who are not informed,

which is accompanied with more hidden investors that want to sell the stock. Therefore, higher relative

short interest means less stocks available to be short, thus tenser short-sales constraint.

3. Empirical results

3.1 Summary statistics

Panel A of Table 1 reports the summary statistics of the major variables used in our analysis.

Averagely, each stock has an annual breadth change of 3.13%, with standard deviation of 22.13%. It

4 Hong and Stein (2003) build a model to show that because of short-sales constraints, bearish investors do not

initially participate in the market and their information is not revealed in prices. Therefore, stock price tends to be

higher than the intrinsic value. Bris, Goetzmann, and Zhu (2007) find that prices incorporate negative information

faster in countries where short sales are allowed and practiced. Boehmer and Wu (2013) find that stock prices are

more accurate when short sellers are more active. Jones and Lamont (2002), Chang, Cheng, and Yu (2007) and

Autore, Billingsley, and Kovacs (2011) all find that short-sales constraints tend to cause stock overvaluation using

other measures of short-sales constraint.

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indicates that the investor base of each stock will increase by 313 for every 10000 people and is with

huge variation, which is not a trivial quantity that can be neglected. But the median of breadth change

is -2.40%, which implies a negatively-skewed pattern and that there are more stocks with negative

breadth change than stocks with positive change.

We further separate the sample into two groups by the sign of each stock’s breadth change and

show the summary statistics of each group in Panel B of Table 1. The positive and negative group show

the statistics of stocks with positive and negative breadth change, respectively. As Panel B shows,

averagely there are more stocks with negative breadth change than stocks with positive change. The

negative group consists of 60.7% of full sample, whereas the positive group covers 39.3%. But the

absolute value of the positive breadth change is 0.20, which is much larger than that of the negative

breadth change, and this pattern leads to the averagely positive breadth change over full sample. The

mean of return of positive breadth change group is 10.6%, whereas that of negative breadth change

group is 17.9%. The difference of returns between both groups is significant, which indicates that stocks

of negative breadth change are associated with higher return than stocks with positive breadth change.

All the other control variables also show a similar pattern, except financing activities FIN and revision

of analysts’ forecast REVISION.

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Insert Table 1 here

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Table 2 reports the time-series average of cross-sectional Pearson-correlation coefficients among

major variables. The Pearson-correlation coefficient between RET and BREADTH is statistically

significantly negative, implying that higher breadth change, to some extent, can indeed predict lower

future returns. Common factors such as Book-to-market ratio B/M is positively related to future returns,

and SIZE is negatively related to future returns, as expected. B/M and SIZE has the largest correlation

efficient of -0.357. BREADTH is shown to be negatively related to SIZE and B/M, which indicates that

small and value firms have larger breadth change. Of course, these correlations are only suggestive, and

we conduct more rigorous tests to formalize this observation.

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Insert Table 2 here

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3.2 Ownership breadth and stock return

Previous literatures all assume a monotonic relationship between ownership breadth and stock

returns. However, no final conclusion has been made due to the complexity of investors’ behavior and

psychology (e.g. Hirshleifer, 2001). For example, Chen, Hong, and Stein (2002) and Opie and Zhang

(2013) predict positive association between ownership breadth change and future returns, while Lehavy

and Sloan (2008) and Choi, Jin, and Yan (2013) predict negative relationship between them. Therefore,

in the following we investigate whether there exist different patterns between ownership breadth and

future returns when ownership breadth increases or decreases. We first conduct two regressions for the

full sample: one with quadratic term of breadth change and another without. Then we do regressions

for the subsample of breadth increase and that of breadth decrease, respectively. Table 3 reports the

regression results of future stock returns.

As Column (1) of Table 3 shows, for the full sample the coefficient of breadth change is -0.08

with standard error of 0.01, which indicates that the relationship between future returns and breadth

change is negative and significant. However, when we add a quadratic term of breadth change into the

regression, as shown in Column (2), the coefficient of quadratic term of breadth change is significantly

negative, which shows an invert-U shape between future returns and breadth change. In addition, the

coefficient of the breadth change is insignificant, which shows that the turning point of the invert-U

shape is around the zero point of breadth change. Therefore, we separate the full sample into two groups

and conduct regressions for the two subsamples, respectively.

Columns (3) and (4) of Table 3 report the results for the positive and negative breadth change and

subsamples, respectively. As Column (3) shows, the coefficient of breadth change of the positive group

is significantly negative at -0.09. This indicates that when ownership breadth increases, or more

investors buy the stock, the stock will realize lower future returns. However, in Columns (4), the

coefficient of breadth change of the negative group is significantly positive at 0.15, which means that

when ownership breadth decreases, or more investors sell the stock, the stock will realize lower future

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return instead of higher return.

Due to the consideration that ownership breadth change may can contain information of dispersion

of opinion, we add analysts’ forecast ANALYST as a control variable to proxy for dispersion of opinion

mentioned in Diether, Malloy, and Scherbina (2002) and Yu (2011). The results are presented in

Columns (5)-(8), which are similar to Column (1)-(4). Although the absolute value of coefficients of

breadth change in Column (5), (6) and (8) decrease a bit, the statistical significance doesn’t change. The

asymmetric effect of breadth change on the future stock return still holds. For the ANALYST itself, the

coefficients of ANALYST in the Columns (5)-(8) are all significantly negative, which indicates that the

dispersion of opinion of analysts has a negative effect on the future stock return. It is also consistent

with prior literature (Diether, Malloy, and Scherbina, 2002; Boehme, Danielsen, and Sorescu 2006; Yu,

2011).

For the other control variables, the coefficients of SIZE in the Columns (1)-(8) are all significantly

negative, which indicates small firms have higher future returns. In addition, the coefficients of B/M

and LEV in Columns (1)-(8) are all significantly positive. These results are consistent with prior

literature (Fama and French, 1992; Ang et al., 2006; Birru and Wang, 2016). As for L.RET, the

coefficients are all significantly positive, which can be explained as long-term reversal and is

consistent with McLean (2010).

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Insert Table 3 here

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To have a clearer picture of how breadth change affects future returns, we sort stocks by stocks’

breadth change into 20 groups in each year and calculate the time-series mean of future returns in each

group in Figure 1. The red dash line in Figure 1 represents the group that contains zero breadth change.

As the figure shows, there is a significant quasi-parabolic relationship between ownership breadth

change and future returns. When breadth change is positive, future returns decreases in breadth change,

but when breadth change is negative, future returns increases in breadth change. And it is easy to see

that the highest return group appears around the zero breadth change. Even though, the return of the

group with lowest breadth change is still 4% higher than the group with highest breadth change, thus

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the negative relationship between future return and breadth change is still significant for the full

sample as a whole, which is consistent with the result of Column (1).

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Insert Figure 1 here

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As prior literature documents (e.g. Lehavy and Sloan, 2008), the association between breadth

change and future returns is related to the contemporaneous stock price change. So we test the

relationship between contemporaneous returns and breadth change and report regression results in

Table 4. As Column (1) of Table 4 shows, for the full sample the coefficient of breadth change is

significantly negative at -0.104, which indicates that as a whole the firm value will contemporaneously

decrease with increase of ownership breadth. The result is similar to Grullon, Kanatas, and Weston

(2004), who argue this may be attributed to the existence of a ‘‘disposition effect’’ whereby investors

hold past losers and sell past winners. When we add the quadratic term of breadth change in the

regression, both the coefficients of the breadth change and the quadratic term are significant, and the

sign of the quadratic term is positive, which implies that there might also be a U-shape relationship

between ownership breadth change and contemporaneous returns.

Column (3) and (4) of Table 4 report the results for the subsample with positive breadth change

and negative breadth change, respectively. As Column (3) of the positive breadth change subsample

shows, the coefficient of breadth change is significantly positive, which means that increasing

ownership breadth will cause increasing contemporaneous return5. However, the result in Columns (4)

shows a different pattern. The coefficient of breadth change is significantly negative at -0.71, which

indicates that decreasing ownership breadth will lead to overvaluation instead of undervaluation. These

results are consistent with U-shape relationship between breadth change and contemporaneous return

as shown in Column (2).

We also add the control variable ANALYST into the regression models and report the results in

5 The explanation of overvaluation can be related to the literatures about investors’ herding behavior. For example,

Barber, Liu, Odean, and Zhu (2009) study retail investors’ trading data and show that stocks heavily bought

underperform stocks heavily sold by 4.4 percentage points the following year.

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Columns (5)-(8) of Table 4. As Table 4 shows, the pattern is similar with Columns (1)-(4), though the

coefficients of ANALYST are not significant. Overall, the result suggests that the relationship between

contemporaneous returns and breadth change is U-shape instead of monotonic. The negative

relationship between breadth change and futures returns when breadth change is positive can be

attributed to that increase of ownership breadth leads to contemporaneous overvaluation, and the

positive relationship between breadth change and futures returns when breadth change is negative can

be attributed to that decrease of ownership breadth leads to contemporaneous overvaluation.

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Insert Table 4 here

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Similar to Figure 1, Figure 2 shows the mean of contemporaneous returns of 20 groups sorted by

their breadth change in each year, and the red dash line represents the group that contains zero breadth

change. Figure 2 shows a U-shape pattern between the breadth change and contemporaneous stock

return. In addition, lowest returns appear in groups with lowest absolute value of breadth change. But

the return of the highest group is also 8% higher than that of the lowest group, which show a monotonic

pattern for the full sample as a whole.

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Insert Figure 2 here

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Overall, these results suggest that the relationship between stock returns and breadth change is not

monotonic. Increase of ownership breadth is positively related to contemporaneous returns and

negatively related to future returns, whereas decrease of ownership breadth is negatively related to

contemporaneous returns and positively related to future returns.

3.3 Breadth change and corporate financing/ investing activities

The above results suggest that we should study the positive breadth change and negative breadth

change separately, instead of considering it as a monotonic pattern. In the following sections we present

results to differentiate different meaning that positive and negative breadth change represent. Table 5

reports the regressions results of corporate financing and investing activities on breadth change.

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Columns (1)-(4) report the results of financing activities, whereas Columns (5)-(8) for investing

activities.

As Column (1) in Table 5 shows, for the full sample the coefficient of breadth change is

significantly positive, which is consistent with Lehavy and Sloan (2008). Column (2) with quadratic

term of breadth change shows, the coefficient of the quadratic term of breadth change is insignificant.

This means that the relationship between corporate financing activities and breadth change does not

have a quadratic pattern. However, if we separate the full sample into the positive and the negative

group, a different image is revealed. The positive relationship is still significant in the positive group in

Column (3), whereas for the negative group, the coefficient of breadth change is insignificant in Column

(4). These results show that the positive relationship between corporate financing activities and breadth

change only exits when ownership breadth increases.

For corporate investing activities, as Columns (5)-(8) in Table 5 show, the results are broadly

consistent with those in Columns (1)-(4). The coefficient of breadth change in full sample is

significantly positive, and that of quadratic term of breadth change is insignificant. For the separated

subsample, the coefficient of breath change in the positive group is significantly positive, whereas the

coefficient of breadth change in the negative group is insignificant yet. Therefore, corporate investing

activities increase with the increase of ownership breadth only when breadth change is positive.

Overall, the results above indicate that ownership breadth is positively related to corporate

financing and investing activities only when breadth change is positive. It supports our previous

conjecture that increase in ownership breadth indeed represents expansion of investor recognition,

whereas decrease in ownership breadth does not reflect reduction in investor recognition. It is

reasonable as investor may don’t know the stock before they buy it, but they can’t forget it after they

sell it. In other words, the breadth change can be used to proxy for investor recognition only when

breadth increases.

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Insert Table 5 here

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3.4 Breadth change and short-sales constraint

In this section, we regress relative short interest on breadth change and report the results in Table

6. As Table 6 shows, for the full sample, the coefficients of breadth change and its quadratic term are

neither significant, which indicates that breadth change may not be a suitable proxy for short-sale

constraint. However, when we separate the full sample into the positive group and the negative group,

we find that the coefficient of breadth change in the negative group becomes significantly negative,

whereas that in the positive group is insignificant. Overall, these results suggest that breadth change can

proxy for the short-sale constraints only when breadth decreases instead of breadth increases.

This finding helps to explain the results of Table 3 and Table 4 for the association between breadth

change and stock return. As Dechow et al. (2001) argue, short sellers take positions in stocks that

experience price run-ups and then cover as prices decline. Hence, less shareholders with long positions

indicates that the stock is overvalued more heavily and will face lower future returns, accompanied with

more severe short-sales constraints, as the results shown in Table 3 and Table 4.

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Insert Table 6 here

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4. Robustness tests

In this section, we run some robustness tests. First, we control some factors, such as earning news

and investor sentiment, which may be correlated with breadth change and lead to the results above.

Then we examine whether investor sentiment is highly correlated with the asymmetric effect of

ownership breadth change to rule out sentiment explanation. In addition, we report results on the breadth

change measure based on institutional investors.

4.1 Controlling earning news

As Lehavy and Sloan (2008) argue, earning news is a non-negligible concern if increase of

ownership breadth is due to expectations of higher future earnings, which reflects information

incorporation, and higher contemporaneous returns are indeed related to the incorporation of earning

news instead of pricing errors caused by investors. For example, Boehme, Danielsen, and Sorescu (2006)

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find that changes in expectations of future abnormal earnings are able to explain up to 30% of the

variation in stock returns. If earning news is incorporated into the market, more positive earning news

may cause overreaction to stock price and induce increase of ownership breadth, which may be

positively related to contemporaneous returns and negatively related to future returns. However, the

mechanism of earning news is only related to the situation of increasing ownership breadth, as more

negative earning news is related to more negative breadth change and lower contemporaneous return,

which is contradictory to the empirical result.

To rule out the possibility that change in ownership breadth is driven by earning news, following

Lehavy and Sloan (2008), we include measures of earnings news as control variables in the Fama and

MacBeth (1973) regressions. Three measures, EARN, ERROR, REVISION, are used to proxy for earning

news. The first earning news proxy, EARN, is calculated as difference of earnings before extraordinary

items between two fiscal years scaled by average total assets. ERROR is calculated as the actual reported

earnings minus the consensus earnings forecast outstanding prior to the earnings announcement divided

by price at the beginning of the period. The revision in annual earnings forecast REVISION equals the

change in the consensus annual earnings forecast scaled by price at the beginning of the period.

Both contemporaneous term EARN, ERROR, REVISION and lagged term L.EARN, L.REVISION

are applied to control the effect of earning news6. We first conduct the regression of contemporaneous

returns for the full example and separated subsamples, and then conduct the regression of future returns.

Table 7 reports the regression results. Columns (1)-(4) present results for the contemporaneous return,

whereas Columns (5)-(8) for the future stock return.

As Column (1) and (3) in Table 7 show, the coefficients of breadth change in the positive group

are significantly positive after controlling earnings news EARN, L.EARN, Forecast errors ERROR, and

forecast REVISION, L.REVISION. At the same time, for the negative breadth change group, the

coefficients of breadth change in Column (2) and (4) are significantly negative after controlling earning

news variables. These results indicates that after incorporating earning news, breadth change is

6 We follow the procedure of Lehavy and Sloan (2008) and do not include the lagged term of ERROR in the

regression model. However, our conclusion hold when we include the lagged term of ERROR.

17

positively associated with contemporaneous return when breadth increases, but negatively associated

with contemporaneous return when breadth decreases. These results are consistent with Table 4.

For the future return, as Column (5) and (7) in Table 7 show, the negative coefficients of breadth

change indicate that higher breadth change can forecast lower future returns after controlling earning

news variables when breadth increases. The positive coefficients of breadth change in Column (6) and

(8) suggest that higher breadth change leads to higher future return when breadth decreases. These

results are consistent with Table 3. Overall, these results in Table 7 suggests that our conclusion holds

after we control earning news variables.

We also find that the coefficients of earning news control variables EARN, L.EARN, ERROR, and

REVISION in Columns (1)-(8) are all significantly positive, which suggests that earning news not only

helps incorporate the fundamental information into contemporaneous price, but also is able to predict

higher future returns. It means that the effect of earning news on stock returns is momentum instead of

reversal. In other words, the reversal pattern of breadth change and returns can’t be attributed to earning

news. Furthermore, as more positive earning news is expected to be related to higher breadth change,

it is reasonable to argue that earning news can’t explain the relationship between ownership breadth

and stock returns when breadth change is negative. In summary, the results above confirm that even

though earning news is highly correlated with stock price, breadth change contains information of the

variation of stock returns that earning news can’t explain.

******************************

Insert Table 7 here

******************************

4.2 Market sentiment and the ownership breadth-return relationship

Investor sentiment is an important driving factor to explain variation in stock returns7. Baker and

Wurgler (2006) propose that investors behave differently in high investor sentiment and low investor

sentiment periods, and stocks that are highly speculative and difficult to arbitrage are more likely to be

7 Yu and Yuan (2011) find that stock market’s expected excess return is positively related to the market’s

conditional variance in low-sentiment periods but unrelated to variance in high-sentiment periods, which suggests

that sentiment traders undermine an otherwise positive mean–variance tradeoff during the high-sentiment periods.

18

overvalued. Cen, Lu, and Yang (2013) further show that the relationship between ownership breadth

and future returns depends on the investor sentiment. When investor sentiment is high, stocks are more

likely to be overvalued and breadth change is negatively related to future returns. When investor

sentiment is low, the relationship between breadth change and future returns is positive. Thus, they

argue that the positive relationship between breadth change and future returns in Chen, Hong, and Stein

(2002) is in fact due to low investor sentiment when the firm-level variation in sentiment is small.

To mitigate the concern that our results overlap with Cen, Lu, and Yang (2013), which indicates

that the asymmetric effect between ownership breadth change and stock returns are driven by investor

sentiment, we first check whether breadth changes are different between high and low sentiment periods.

In addition, we run Fama and MacBeth (1973) regressions of returns on ownership breadth change in

high and low sentiment periods, respectively to examine whether our asymmetric effect still exists in

different sentiment periods. Our measure of investment sentiment is the orthogonalized change of

sentiment indices ∆𝑆𝐸𝑁𝑇𝐼𝑀𝐸𝑁𝑇⊥ from Baker and Wurgler (2006, 2007). We obtain the original data

set that contains monthly 𝑆𝐸𝑁𝑇𝐼𝑀𝐸𝑁𝑇⊥ values to compute monthly ∆𝑆𝐸𝑁𝑇𝐼𝑀𝐸𝑁𝑇⊥ values, and

then compute the sums of ∆𝑆𝐸𝑁𝑇𝐼𝑀𝐸𝑁𝑇⊥ (change) within each year to get the corresponding annual

indices. Due to data availability, we get sentiment indices during periods from 1981 to 2015.

We sort 35 years into 5 sentiment groups based on each year’s ∆𝑆𝐸𝑁𝑇𝐼𝑀𝐸𝑁𝑇⊥, thus there are 7

years in each group. Then we divide the stocks into the positive group and the negative group in each

year. For each year in each sentiment group, we calculate the percentage of the number of all stocks

and mean of breadth change for the positive and negative group, respectively. Table 8 reports the

summary statistics. As Table 8 shows, the percentage of stocks and mean of breadth change are stable

across all sentiment groups in the positive and negative group. The percentage of the number of all

stocks is around 40% in the positive group and around 60% in the negative group, and the mean of

breadth change is around 0.2 in the positive group and around -0.08 in the negative group. The result

doubtlessly alleviates the concern that investor sentiment drives the asymmetry of the relationship

between stock returns and breadth change.

19

******************************

Insert Table 8 here

******************************

To further study the role of investor sentiment, we apply Fama and MacBeth (1973) regressions in

high and low investor sentiment periods, respectively. We divide the full sample years into two

sentiment groups. The high sentiment group contains years in the highest quintiles, and the low

sentiment contains years in other quintiles. Then in each sentiment group, we divide the stocks into the

positive breadth change group and the negative breadth change group. Table 9 reports the regression

results. Columns (1)-(4) present results for the high-sentiment period, whereas Columns (5)-(8) for the

low-sentiment period.

As Table 9 shows, the asymmetry of positive and negative breadth change group is still significant.

It is also noteworthy that the absolute value of coefficients of control variables, such as B/M and LEV,

in the high sentiment group is a bit larger, which may be explained by that those factors are more easily

to be priced during high sentiment period. Meanwhile, the absolute value of coefficients of L.BREADTH

is also much larger in the high sentiment group, indicating that the relationship between breadth change

and future returns are aggravated by investor sentiment, to some extent. Overall, these results indicate

that our conclusion is not totally driven by investor sentiment, although it can’t be denied that investor

sentiment has some impacts on our results, but at least, the concern of investor sentiment is not critical.

******************************

Insert Table 9 here

******************************

4.3 Breadth change measure based on institutional investors

Although institutional investors cannot represent all investors in the market, following prior

literature, such as Chen, Hong, and Stein (2002), Lehavy and Sloan (2008), and Cen, Lu, and Yang

(2013), we use number of institutional investors from 13-F files to calculate ownership breadth change.

Since quarterly number of institutional investors is available, we conduct regressions using quarterly

data. Following Lehavy and Sloan (2008), we calculate breadth change IBREADTH as the difference

of the number of institutional investors between quarter t and t-1, scaled by the total number of

20

institutional investors in the market in quarter t-1, with number of newcomer funds and liquidated

funds in each quarter adjusted. The dependent variable is quarterly size-adjusted stock return RET. We

also control size, book-to-market ratio, leverage, and lagged quarterly size-adjusted return. Table 10

reports the regression results.

As Column (1) in Table 10 shows, the coefficient of lagged breadth change L.IBREADTH is

significantly positive for the full sample. In addition, the coefficient of IBREADTH in Column (2) is

significantly positive. These results indicate that breadth change has positive effects both on

contemporaneous return and on future return. It is consistent with Lehavy and Sloan (2008). As

Lehavy and Sloan (2008) argue that there is a strong autocorrelation between contemporaneous

breadth change and lagged breadth change, we include both L.IBREADTH and IBREADTH into

regression model and report the result in Column (3). As Column (3) of Table 10 shows, the coefficient

of L.IBREADTH becomes significantly negative after controlling IBREADTH, which is also consistent

with Lehavy and Sloan (2008).

We separate the full sample into two subsamples: positive breadth change and negative breadth

change and run similar regression with Column (3). The results are reported in Column (4) and (5),

respectively. The coefficients of L.IBREADTH in Column (4) is significantly negative, which indicates

a negative relationship between breadth change and future return for the subsample of positive breadth

change, whereas a significantly positive coefficient of L.IBREADTH in Column (5) shows a positive

relationship between breadth change and future return for the subsample of negative breadth change.

These results are consistent with Section 3 which is based on total number of all investors. Overall,

the above analyses show that our conclusion still holds when we measure breadth change based on the

number of institutional investors.8

8 We do not add both contemporaneous and lagged breadth change in one model in the Section 3 is due to the

autocorrelation of breadth change based on the total number of all investors is weak. The Pearson correlation

coefficient between IBREADTH and L.IBREADTH is 0.129, which is similar to Lehavy and Sloan (2008), while

the Pearson correlation coefficient between BREADTH and L.BREADTH based on the total number of all investors

is 0.015. Both of the results indicate that the problem of autocorrelation mentioned in Lehavy and Sloan (2008)

does not affect the main results in this paper. When we add both of them in one model, the results remain similar.

21

******************************

Insert Table 10 here

******************************

5. Conclusions

The relationship between ownership breadth change and future stock return is puzzled both from

theory and empirical evidence. Merton (1987) proposed a positive breadth- return relationship based

on investor recognition theory, in which ownership breadth represents investor recognition. On the

other hand, a negative breadth- return relationship is assumed based on short-sale constraint theory of

Miller (1977). Both theories are supported by some empirical literature. For example, Lehavy and

Sloan (2008) provide empirical evidence on investor recognition theory of Merton (1987), whereas

Chen, Hong and Stein (2002) support Miller (1977)’s short-sale constraint theory. However, the

conflicting theories and empirical evidences do not reach a consensus.

In this paper, we find an invert-U shape relationship between breadth change and future stock

return. More specifically, when ownership breadth increases, higher breadth change predicts lower

future return, whereas when ownership breadth decreases, higher breadth change predicts higher

future return. The asymmetric effects of breadth change on contemporaneous return also exist, but

with a U-shape pattern. We argue that investor recognition theory holds when breadth increases,

whereas short-sale constraint theory holds for the decrease of breadth.

Further tests support our above argument. We find that corporate investing and financing

activities are positively associated with breadth change only when ownership breadth increases,

whereas short-sale constraint is negatively associated with breadth change only when breadth

decreases. In addition, we also show that our results are not driven by investor sentiment. Moreover,

our conclusion holds whether we measure ownership breadth whether based on the total number of all

investors or based on the number of institutional investors. Overall, our paper shows that ownership

breadth can represent investor recognition only when breadth increases, whereas breadth reflects

short-sale constraints only when breadth decreases.

This paper extends researches on the ownership breadth by providing an asymmetric

interpretation of the relationship between ownership breadth and stock returns, which is different from

22

the examined unidirectional relationship in the prior literature (Chen, Hong and Stein, 2002; Lehavy

and Sloan, 2002; Cen, Lu and Yang, 2013; Choi, Jin and Yan, 2013). We reconcile conflicting

empirical evidence on the relationship between ownership breadth and future stock return in the prior

literature. Moreover, the competing theories of Merton (1987) and Miller (1977) can also be reconciled

by our findings on an asymmetric meaning of positive and negative breadth change.

23

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26

Figure 1. The future return and ownership breadth change

Figure 1 illustrates the relationship between the future returns and ownership breadth change. We divide

our sample by annual ownership breadth change in each year, from bottom to top into 20 groups. We

then calculate the time-series average next year’s return of each group. In the middle of the plot, the red dash line indicates group including the zero breadth change.

27

Figure 2. The contemporaneous return and ownership breadth change

Figure 2 illustrates the relationship between the contemporaneous returns and ownership breadth

change. We divide our sample by annual ownership breadth change in each year, from bottom to top

into 20 groups. We then calculate the time-series average current year’s return of each group. In the middle of the plot, the red dash line indicates group including the zero breadth change.

28

Table 1. Summary Statistics

This table shows summary statistics of all annual variables of firms listed in NYSE, AMEX and NASDAQ from 1976 to 2017. Panel A reports summary

statistics of the full sample, whereas Panel B reports the mean and median value of subsamples with positive and negative breadth changes, respectively. The

stock return RET covers the period from the first trading day of July, year t to the end trading day of June, year t+1. Breadth change BREADTH is calculated as the difference of investor base between fiscal year t and t-1, scaled by investor base in fiscal year t-1. SIZE is log of market capitalization in June, year t. B/M

is log of book-to-market ratio. Book value is measured in June, year t and market capitalization is measured in December, year t-1. LEV is leverage, calculated

as the ratio of total liability to total asset. Dispersion of analysts’ forecast ANALYST is standard deviation of fiscal year one analysts’ forecast scaled by mean of analysts’ forecast. The corporate financing activities FIN is calculated as net cash from financing activities. The corporate investing activities INV is calculated

as capital expenditures plus acquisitions less depreciation and sales of property and equipment. Short-sales constraint SSI is calculated as percentage of shares

held short of the total shares outstanding. Earning news EARN is calculated as difference of earnings before extraordinary items between two fiscal years scaled

by average total assets. ERROR is calculated as the actual reported earnings minus the consensus earnings forecast outstanding prior to the earnings announcement divided by price at the beginning of the period. The revision in annual earnings forecast REVISION equals the change in the consensus annual

earnings forecast scaled by price at the beginning of the period.

Panel A: Summary Statistics of full sample

Variable Yearly

average N Data range

MEAN STD MIN P25 P50 P75 MAX

BREADTH 2795 1976-2017 0.0313 0.2213 -0.2500 -0.0721 -0.0240 0.0462 0.7600

RET 2795 1976-2017 0.1402 0.6006 -0.8339 -0.1762 0.0409 0.2923 3.6349

SIZE 2795 1976-2017 5.6869 2.0462 0.1959 4.1989 5.5394 7.0358 10.7317

B/M 2795 1976-2017 -0.6695 0.7951 -3.2802 -1.1132 -0.5856 -0.1472 1.4476

LEV 2795 1976-2017 0.5442 0.2569 0.0406 0.3512 0.5414 0.7220 1.3364

ANALYST 2049 1983-2017 0.1444 0.1527 0.0167 0.0441 0.0843 0.1789 0.6146

FIN 2559 1987-2017 0.0269 0.1665 -0.3910 -0.0449 -0.0013 0.0522 0.9512

INV 2559 1987-2017 0.0374 0.0824 -0.1656 -0.0043 0.0112 0.0560 0.4154

SSI 1711 2000-2017 4.3499 4.9385 0.0336 1.1271 2.6117 5.6931 25.5169

EARN 2433 1976-2017 0.0126 0.0913 -0.3926 -0.0126 0.0074 0.0362 0.4863

ERROR 1827 1983-2017 -0.0180 0.0978 -0.9595 -0.0079 -0.0004 0.0020 0.1380

REVISION 1827 1983-2017 -0.0002 0.0846 -0.5373 -0.0038 0.0031 0.0103 0.5360

29

Panel B: subsample of positive and negative breadth changes

Variable

Subsample of positive breadth change Subsample of negative breadth change Mean difference

(T-value) Median difference

(Z-value) Yearly average N

MEAN Median Yearly

average N MEAN Median

BREADTH 1098 0.2027 0.0848 1697 -0.0850 -0.0610 167.46 302.00

RET 1098 0.1061 0.0198 1697 0.1786 0.0711 -29.36 -39.84

SIZE 1098 5.5544 5.3725 1697 5.8438 5.7892 -28.26 -30.30

B/M 1098 -0.6742 -0.5919 1697 -0.6648 -0.5795 -7.93 -8.27

LEV 1098 0.5614 0.5549 1697 0.5273 0.5305 25.52 25.16

ANALYST 731 0.1410 0.0806 1318 0.1475 0.0872 -5.20 -12.72

FIN 949 0.0421 0.0045 1528 0.0129 -0.0083 27.37 37.75

INV 949 0.0417 0.0123 1528 0.0335 0.0105 15.57 14.30

SSI 572 3.9877 2.2875 1139 4.6585 2.8962 -13.69 -23.16

EARN 958 0.0138 0.0071 1475 0.0115 0.0077 4.51 8.71

ERROR 788 -0.0210 -0.0004 1039 -0.0155 -0.0003 -5.65 -4.86

REVISION 788 -0.0007 0.0033 1039 0.0002 0.0028 -1.10 6.07

30

Table 2. Correlation Matrix Among Main Variables

This table shows time-series average of cross-sectional Pearson-correlation coefficients among main variables. The stock return RET covers the period from the

first trading day of July, year t to the end trading day of June, year t+1. Breadth change BREADTH is calculated as the difference of investor base between fiscal

year t and t-1, scaled by investor base in fiscal year t-1. SIZE is log of market capitalization in June, year t. B/M is log of book-to-market ratio. Book value is measured in June, year t and market capitalization is measured in December, year t-1. LEV is leverage, calculated as the ratio of total liability to total asset.

Dispersion of analysts’ forecast ANALYST is standard deviation of fiscal year one analysts’ forecast scaled by mean of analysts’ forecast. The corporate financing

activities FIN is calculated as net cash from financing activities. The corporate investing activities INV is calculated as capital expenditures plus acquisitions less depreciation and sales of property and equipment. Short-sales constraint SSI is calculated as percentage of shares held short of the total shares outstanding.

Earning news EARN is calculated as difference of earnings before extraordinary items between two fiscal years scaled by average total assets. ERROR is

calculated as the actual reported earnings minus the consensus earnings forecast outstanding prior to the earnings announcement divided by price at the beginning

of the period. The revision in annual earnings forecast REVISION equals the change in the consensus annual earnings forecast scaled by price at the beginning of the period. ***, **, and * indicate p-values of 1%, 5%, and 10% or less, respectively.

Variable RET BREADTH SIZE B/M LEV ANALYST FIN INV SSI EARN ERROR REVISION

RET 1

BREADTH -0.051*** 1

SIZE -0.138*** -0.010*** 1

B/M 0.177*** -0.117*** -0.357*** 1

LEV 0.042*** -0.023*** 0.038*** 0.066*** 1

ANALYST -0.010** -0.020*** -0.204*** 0.078*** -0.070*** 1

FIN 0.041*** 0.115*** -0.136*** -0.180*** -0.027*** 0.136*** 1

INV -0.023*** 0.096*** 0.091*** -0.137*** -0.065*** -0.066*** 0.244*** 1

SSI -0.098*** 0.005 -0.041*** -0.109*** -0.046*** 0.083*** 0.084*** 0.026*** 1

EARN 0.267*** 0.049*** -0.049*** -0.054*** 0.019*** -0.006 -0.066*** 0.028*** -0.028*** 1

ERROR 0.254*** -0.013** 0.119*** -0.094*** -0.021*** -0.134*** -0.031*** 0.050*** -0.091*** 0.187*** 1

REVISION 0.148*** 0.008 -0.010** -0.098*** 0.016*** -0.036*** 0.058*** 0.023*** -0.060*** 0.284*** 0.244*** 1

31

Table 3. Regression of future returns on breadth change

This table reports mean coefficient estimates and standard errors from annual Fama and MacBeth (1973) regressions of stock return on breadth change,

dispersion of analysts, size, book-to-market ratio, leverage and lagged return, using samples with positive and negative breadth change. All variables are

measured over a year. The dependent variable is annual stock return RET, holding from the first trading day of July, year t to the end trading day of June, year t+1. Breadth change L.BREADTH is calculated as the difference of investor base between fiscal year t-1 and t-2, scaled by investor base in fiscal year t-2.

L.SIZE is lagged log of market capitalization. L.B/M is lagged log of book-to-market ratio. L.LEV is lagged leverage, calculated as the ratio of total liability to

total asset. L.RET is lagged annual return. Dispersion of analysts’ forecast L.ANALYST is standard deviation of fiscal year one analysts’ forecast scaled by mean of analysts’ forecast. Standard errors are in parentheses, which is adjusted using the Newey and West (1987) correction with two lags. ***, **, and * indicate p-

values of 1%, 5%, and 10% or less, respectively.

Full

sample

Full

sample

Positive

group

Negative

group

Full

sample

Full

sample

Positive

group

Negative

group

(1) (2) (3) (4) (5) (6) (7) (8)

L.BREADTH -0.0754*** -0.0352 -0.0887*** 0.153*** -0.0746*** -0.0239 -0.0935*** 0.140***

(0.0137) (0.0230) (0.0136) (0.0406) (0.0159) (0.0218) (0.0175) (0.0491)

L.BREADTH2 -0.0765** -0.102**

(0.0378) (0.0407)

L.SIZE -0.0295*** -0.0297*** -0.0337*** -0.0274*** -0.0256*** -0.0260*** -0.0287*** -0.0256***

(0.0042) (0.0042) (0.0047) (0.0038) (0.0064) (0.0065) (0.0070) (0.0060)

L.B/M 0.0434*** 0.0433*** 0.0405*** 0.0429*** 0.0341** 0.0336** 0.0364** 0.0293*

(0.0101) (0.0101) (0.0105) (0.0099) (0.0150) (0.0149) (0.0160) (0.0143)

L.LEV 0.0923*** 0.0913*** 0.0754** 0.0936*** 0.123** 0.121** 0.101* 0.122**

(0.0302) (0.0300) (0.0318) (0.0287) (0.0530) (0.0526) (0.0501) (0.0562)

L.RET -0.0954*** -0.0945*** -0.0989*** -0.0908*** -0.0929*** -0.0917*** -0.0770*** -0.0979***

(0.0131) (0.0130) (0.0132) (0.0143) (0.0210) (0.0211) (0.0260) (0.0203)

L.ANALYST -0.201*** -0.200*** -0.223*** -0.186***

(0.0540) (0.0540) (0.0635) (0.0497)

Ave yearly N 2795 2795 1098 1697 2049 2049 731 1318

Ave R2 0.080 0.081 0.087 0.077 0.087 0.088 0.095 0.089

32

Table 4. Regression of contemporaneous returns on breadth change

This table reports mean coefficient estimates and standard errors from annual Fama and MacBeth (1973) regressions of stock return on breadth change, size,

book-to-market ratio, leverage, dispersion of analysts, and lagged return, using samples with positive and negative breadth change. All variables are measured

over a year. The dependent variable is annual stock return RET, holding from the first trading day of July, year t to the end trading day of June, year t+1. Breadth change BREADTH is calculated as the difference of investor base between fiscal year t and t-1, scaled by investor base in fiscal year t-1. L.SIZE is lagged log

of market capitalization. L.B/M is lagged log of book-to-market ratio. L.LEV is lagged leverage, calculated as the ratio of total liability to total asset. L.RET is

lagged annual return. Dispersion of analysts’ forecast ANALYST is standard deviation of fiscal year one analysts’ forecast scaled by mean of analysts’ forecast. Standard errors are in parentheses, which is adjusted using the Newey and West (1987) correction with two lags. ***, **, and * indicate p-values of 1%, 5%, and

10% or less, respectively.

Full

sample

Full

sample

Positive

group

Negative

group

Full

sample

Full

sample

Positive

group

Negative

group

(1) (2) (3) (4) (5) (6) (7) (8)

BREADTH -0.104*** -0.396*** 0.0827*** -0.707*** -0.0112 -0.195*** 0.123*** -0.288**

(0.0347) (0.0677) (0.0209) (0.135) (0.0148) (0.0541) (0.0235) (0.110)

BREADTH2 0.635*** 0.380***

(0.0906) (0.0847)

L.SIZE -0.0292*** -0.0274*** -0.0397*** -0.0194*** -0.0170** -0.0155** -0.0242*** -0.0112*

(0.0041) (0.0039) (0.0048) (0.0036) (0.0060) (0.0059) (0.0064) (0.0058)

L.B/M 0.0438*** 0.0413*** 0.0483*** 0.0377*** 0.0376** 0.0377** 0.0423** 0.0332**

(0.0098) (0.0095) (0.0116) (0.0085) (0.0159) (0.0158) (0.0185) (0.0145)

L.LEV 0.0957*** 0.0999*** 0.0774** 0.111*** 0.119** 0.122** 0.0856* 0.138**

(0.0296) (0.0295) (0.0301) (0.0291) (0.0548) (0.0548) (0.0493) (0.0589)

L.RET -0.0900*** -0.0945*** -0.108*** -0.0850*** -0.0980*** -0.0995*** -0.0894*** -0.105***

(0.0130) (0.0128) (0.0144) (0.0134) (0.0211) (0.0214) (0.0254) (0.0215)

ANALYST 0.00224 -0.00182 -0.0626 0.0258

(0.0505) (0.0501) (0.0597) (0.0442)

Ave yearly N 2795 2795 1098 1697 2049 2049 731 1318

Ave R2 0.085 0.094 0.101 0.081 0.081 0.086 0.094 0.086

33

Table 5. Regression of corporate financing and investing activities on breadth change

This table reports coefficient estimates and standard errors from annual Fama and MacBeth (1973) regressions of corporate financing activities on breadth

change, size, book-to-market ratio, leverage, lagged return, and dispersion of analysts of firms with positive and negative breadth change. All variables are

measured over a year. The dependent variable is corporate financing activities FIN, which is calculated as net cash from financing activities, and corporate investing activities INV, which is calculated as capital expenditures plus acquisitions less depreciation and sales of property and equipment. Breadth change

BREADTH is calculated as the difference of investor base between fiscal year t and t-1, scaled by investor base in fiscal year t-1. L.SIZE is lagged log of market

capitalization. L.B/M is lagged log of book-to-market ratio. L.LEV is lagged leverage, calculated as the ratio of total liability to total asset. L.RET is lagged annual return. Dispersion of analysts’ forecast ANALYST is standard deviation of fiscal year one analysts’ forecast scaled by mean of analysts’ forecast. Standard

errors are in parentheses, which is adjusted using the Newey and West (1987) correction with two lags. ***, **, and * indicate p-values of 1%, 5%, and 10% or

less, respectively.

Corporate financing activities Corporate investing activities

Full

sample

Full

sample

Positive

group

Negative

group

Full

sample

Full

sample

Positive

group

Negative

group

(1) (2) (3) (4) (5) (6) (7) (8)

BREADTH 0.0336*** 0.0256*** 0.0363*** -0.0170 0.0138*** 0.0136*** 0.00949** -0.00878

(0.0055) (0.0084) (0.012) (0.018) (0.0027) (0.0043) (0.0044) (0.0087)

BREADTH2 0.0166 0.0003

(0.0139) (0.0079)

L.SIZE -0.0367*** -0.0366*** -0.0121 -0.0446*** -0.0037*** -0.0037*** -0.0091*** -0.0016

(0.0113) (0.0113) (0.0411) (0.0036) (0.0014) (0.0014) (0.0028) (0.0015)

L.B/M -0.0448* -0.0448* 0.0123 -0.0613*** -0.0288*** -0.0288*** -0.0340*** -0.0276***

(0.0250) (0.0250) (0.0897) (0.0044) (0.0017) (0.0017) (0.0036) (0.0020)

L.LEV -0.163*** -0.163*** -0.0563 -0.213*** -0.134*** -0.134*** -0.146*** -0.131***

(0.0503) (0.0503) (0.162) (0.0187) (0.0071) (0.0071) (0.0134) (0.0081)

L.RET 0.0154** 0.0154** 0.0301 0.0101*** 0.0064*** 0.0064*** 0.0077*** 0.0042***

(0.0069) (0.0068) (0.0234) (0.0027) (0.0013) (0.0013) (0.0027) (0.0014)

ANALYST -0.0551*** -0.0551*** -0.0767* -0.0493*** -0.0265*** -0.0265*** -0.0297*** -0.0215***

(0.0131) (0.0131) (0.0415) (0.0118) (0.0045) (0.0045) (0.0099) (0.0051)

34

Ave yearly N 1178 1178 420 759 1178 1178 420 759

Ave R2 0.093 0.093 0.109 0.063 0.089 0.089 0.092 0.083

35

Table 6. Regression of short-sales constraint on breadth change

This table reports mean coefficient estimates and standard errors from annual Fama and MacBeth (1973)

regressions of short-sales constraint on breadth change, size, book-to-market ratio, leverage, and lagged

return. All variables are measured over a year. The dependent variable is SSI, calculated as percentage of shares hold short of the total shares outstanding, as a proxy for the constraints of short-sale constraints.

Breadth change BREADTH is calculated as the difference of investor base between fiscal year t and t-

1, scaled by investor base in fiscal year t-1. L.SIZE is lagged log of market capitalization. L.B/M is lagged log of book-to-market ratio. L.LEV is lagged leverage, calculated as the ratio of total liability to

total asset. L.RET is lagged annual return. Standard errors are in parentheses, which is adjusted using

the Newey and West (1987) correction with two lags. ***, **, and * indicate p-values of 1%, 5%, and 10%

or less, respectively.

Full

sample

Full

sample

Positive

group

Negative

group

(1) (2) (3) (4)

BREADTH 0.126 -0.0615 0.249 -1.202**

(0.132) (0.233) (0.197) (0.519)

BREADTH2 0.401

(0.408)

L.SIZE 0.431*** 0.434*** 0.565*** 0.333**

(0.121) (0.121) (0.177) (0.141)

L.B/M -0.165 -0.165 -0.254 -0.148

(0.106) (0.106) (0.178) (0.121)

L.LEV 1.393*** 1.392*** 0.446 1.985***

(0.489) (0.489) (0.696) (0.574)

L.RET -0.430*** -0.431*** -0.430*** -0.367***

(0.0684) (0.0684) (0.112) (0.0857)

Ave yearly N 1711 1711 572 1139

Ave R2 0.085 0.085 0.096 0.084

36

Table 7. Regression of returns on breadth change with earnings news

This table reports mean coefficient estimates and standard errors from annual Fama and MacBeth (1973) regressions of stock return on breadth change, size,

book-to-market ratio, leverage, lagged return, and earning news,. All variables are measured over a year. The dependent variable is annual stock return RET,

holding from the first trading day of July, year t to the end trading day of June, year t+1. Breadth change BREADTH is calculated as the difference of investor base between fiscal year t and t-1, scaled by investor base in fiscal year t-1. L.BREADTH lagged breadth change. L.SIZE is lagged log of market capitalization.

L.B/M is lagged log of book-to-market ratio. L.LEV is lagged leverage, calculated as the ratio of total liability to total asset. L.RET is lagged annual return.

Earning news EARN is calculated as difference of earnings before extraordinary items between two fiscal years scaled by average total assets. L.EARN is lagged EARN. Forecast errors ERROR is calculated as the actual reported earnings minus the consensus earnings forecast outstanding prior to the earnings

announcement divided by price at the beginning of the period. The revision in annual earnings forecast REVISION equals the change in the consensus annual

earnings forecast scaled by price at the beginning of the period. L.REVISION is lagged REVISION. Standard errors are in parentheses, which is adjusted using

the Newey and West (1987) correction with two lags. ***, **, and * indicate p-values of 1%, 5%, and 10% or less, respectively.

Contemporaneous return

Future stock return

Positive

group

Negative

group

Positive

group

Negative

group

Positive

group

Negative

group

Positive

group

Negative

group

(1) (2) (3) (4) (5) (6) (7) (8)

BREADTH 0.0132*** -0.705*** 0.0586** -0.379**

(0.0039) (0.122) (0.0224) (0.167)

L.BREADTH -0.0897*** 0.143*** -0.0725*** 0.1495***

(0.0165) (0.0401) (0.0169) (0.0497)

L.SIZE -0.0347*** -0.0125*** -0.0212*** -0.0161*** -0.0279*** -0.0209*** -0.0193*** -0.0218***

(0.0043) (0.0032) (0.0054) (0.0049) (0.0041) (0.0033) (0.0050) (0.0054)

L.B/M 0.0722*** 0.0571*** 0.0407** 0.0410*** 0.0679*** 0.0641*** 0.0509*** 0.0427***

(0.0134) (0.0096) (0.0148) (0.0088) (0.0125) (0.0111) (0.0134) (0.0094)

L.LEV 0.0620** 0.0732** 0.0958** 0.130*** 0.0507* 0.0790*** 0.0779* 0.134***

(0.0265) (0.0276) (0.0378) (0.0322) (0.0277) (0.0270) (0.0404) (0.0316)

L.RET -0.136*** -0.120*** -0.154*** -0.128*** -0.121*** -0.131*** -0.142*** -0.135***

(0.0166) (0.0134) (0.0214) (0.0231) (0.0140) (0.0157) (0.0243) (0.0197)

37

EARN 1.565*** 1.721*** 1.552*** 1.695***

(0.0851) (0.103) (0.0818) (0.0990)

L.EARN 0.287*** 0.529*** 0.266*** 0.490***

(0.0602) (0.0582) (0.0581) (0.0522)

ERROR 1.073*** 1.086*** 1.293*** 1.084***

(0.112) (0.0888) (0.154) (0.126)

REVISION 0.694*** 0.824*** 0.803*** 0.768***

(0.146) (0.104) (0.126) (0.105)

L.REVISION 0.107 0.0386 0.124 0.0607

(0.114) (0.103) (0.128) (0.102)

Ave yearly N 958 1475 788 1039 958 1475 788 1039

Ave R2 0.201 0.196 0.208 0.187 0.188 0.182 0.213 0.180

38

Table 8. Investor sentiments and breadth change

This table presents mean of breadth change of firms in positive and negative breadth change groups in each quintile of change of sentiment indices

∆𝑆𝐸𝑁𝑇𝐼𝑀𝐸𝑁𝑇⊥ within each year. ∆𝑆𝐸𝑁𝑇𝐼𝑀𝐸𝑁𝑇⊥ is obtained from Baker and Wurgler (2006) from 1981 to 2015. Panel A reports the percentage of number

of firms with positive and negative breadth changes, whereas Panel B reports the mean of breadth change of positive and negative groups in each quintile of sentiment indices.

Panel A: Percentage of firms with positive and negative breadth change

Positive group Negative group

Year High 2 3 4 Low High 2 3 4 Low

1 0.4007 0.5239 0.4213 0.4039 0.4987 0.5993 0.4761 0.5787 0.5961 0.5013

2 0.4420 0.4779 0.4499 0.4353 0.4281 0.5580 0.5221 0.5501 0.5647 0.5719

3 0.4279 0.3977 0.4768 0.4802 0.4463 0.5721 0.6023 0.5232 0.5198 0.5537

4 0.4732 0.3674 0.4400 0.4728 0.4877 0.5268 0.6326 0.5600 0.5272 0.5123

5 0.4097 0.3738 0.3598 0.3535 0.4857 0.5903 0.6262 0.6402 0.6465 0.5143

6 0.4230 0.3348 0.3517 0.3015 0.3091 0.5770 0.6652 0.6483 0.6985 0.6909

7 0.4077 0.3046 0.3064 0.3021 0.3218 0.5923 0.6954 0.6936 0.6979 0.6782

Total 0.4263 0.3972 0.4009 0.3928 0.4253 0.5737 0.6028 0.5991 0.6072 0.5747

Panel B: Mean of breadth change of firms with positive and negative breadth change

Positive group Negative group

Year High 2 3 4 Low High 2 3 4 Low

1 0.1481 0.2107 0.1915 0.1394 0.2073 -0.0692 -0.0722 -0.0835 -0.0735 -0.0808

2 0.1618 0.2459 0.2445 0.2079 0.1557 -0.0709 -0.0975 -0.0932 -0.0913 -0.0770

3 0.1777 0.2063 0.2614 0.1419 0.1756 -0.0813 -0.0874 -0.0928 -0.0655 -0.0692

4 0.1609 0.2136 0.2468 0.2778 0.2151 -0.0726 -0.0873 -0.0961 -0.0974 -0.0796

5 0.2597 0.2108 0.2543 0.2341 0.2252 -0.0988 -0.0897 -0.0888 -0.0951 -0.0784

6 0.2289 0.1885 0.2317 0.2121 0.1992 -0.0912 -0.0848 -0.0959 -0.0840 -0.0886

7 0.1824 0.1945 0.1915 0.2141 0.1906 -0.0882 -0.0816 -0.0893 -0.0948 -0.0945

Total 0.1885 0.2100 0.2317 0.2039 0.1955 -0.0817 -0.0858 -0.0914 -0.0860 -0.0812

39

Table 9. Regression of returns on breadth change of groups separated by sentiment indices This table reports mean coefficient estimates and standard errors from annual Fama and MacBeth (1973) regressions of stock return on breadth change, size,

book-to-market ratio, leverage and lagged return, first separated by change of sentiment indices ∆𝑆𝐸𝑁𝑇𝐼𝑀𝐸𝑁𝑇⊥, then by breadth change. All variables are

measured over a year. ∆𝑆𝐸𝑁𝑇𝐼𝑀𝐸𝑁𝑇⊥ is obtained from Baker and Wurgler (2006). The high sentiment group consist of years within the highest first quintile

of ∆𝑆𝐸𝑁𝑇𝐼𝑀𝐸𝑁𝑇⊥ in each year from 1981 to 2015. The low sentiment group consist of years not in the high sentiment group. The dependent variable is

annual stock return RET, holding from the first trading day of July, year t to the end trading day of June, year t+1. Breadth change BREADTH is calculated as

the difference of investor base between fiscal year t and t-1, scaled by investor base in fiscal year t-1. L.BREADTH is lagged breadth change. L.SIZE is lagged

log of market capitalization. L.B/M is lagged log of book-to-market ratio. L.LEV is lagged leverage, calculated as the ratio of total liability to total asset. L.RET is lagged annual return. Standard errors are in parentheses. ***, **, and * indicate p-values of 1%, 5%, and 10% or less, respectively.

High Sentiment Low Sentiment

Positive

group

Negative

group

Positive

group

Negative

group

Positive

group

Negative

group

Positive

group

Negative

group

(1) (2) (3) (4) (5) (6) (7) (8)

BREADTH 0.0704** -0.533** 0.0852*** -0.742***

(0.0306) (0.189) (0.0207) (0.104)

L.BREADTH -0.122*** 0.320*** -0.0818*** 0.119***

(0.0254) (0.0780) (0.0146) (0.0417)

L.SIZE -0.0441*** -0.0175 -0.0339** -0.0254** -0.0388*** -0.0197*** -0.0336*** -0.0278***

(0.0103) (0.0096) (0.0114) (0.0072) (0.0040) (0.0032) (0.0038) (0.0034)

L.B/M 0.123*** 0.0866*** 0.123*** 0.0953*** 0.0334*** 0.0279*** 0.0235** 0.0321***

(0.0176) (0.0133) (0.0166) (0.0171) (0.0102) (0.0082) (0.0087) (0.0082)

L.LEV 0.203** 0.221** 0.213** 0.179** 0.0523* 0.0892*** 0.0470 0.0761**

(0.0777) (0.0701) (0.0652) (0.0705) (0.0278) (0.0273) (0.0297) (0.0292)

L.RET -0.147** -0.0752** -0.108** -0.108** -0.100*** -0.0870*** -0.0971*** -0.0872***

(0.0426) (0.0267) (0.0319) (0.0364) (0.0159) (0.0171) (0.0178) (0.0173)

Ave yearly N 1101 1596 1101 1596 1097 1718 1097 1718

Ave R2 0.159 0.093 0.147 0.107 0.089 0.079 0.075 0.070

40

Table 10. Regression of returns on institutional breadth change

This table reports mean coefficient estimates and standard errors from quarterly Fama and MacBeth

(1973) regressions of size-adjusted stock return on institutional investors-based breadth change. All

variables are measured over a quarter. Following Lehavy and Sloan (2008), the dependent variable is

quarterly size-adjusted stock return. Breadth change IBREADTH is calculated as the difference of the

number of institutional investors between quarter t and t-1, scaled by the total number of institutional

investors in the market in quarter t-1, with newcomer funds and liquidated funds in each quarter

adjusted. L.IBREADTH is lagged breadth change. L.B/M is lagged log of book-to-market ratio. L.LEV

is lagged leverage, calculated as the ratio of total liability to total asset. L.RET is lagged yearly return.

Standard errors are in parentheses, which is adjusted using the Newey and West (1987) correction with

four lags. ***, **, and * indicate p-values of 1%, 5%, and 10% or less, respectively.

Full sample Full sample Full sample Positive

group

Negative

group

(1) (2) (3) (4) (5)

L.IBREADTH 0.371** -0.467** -1.580*** 0.674**

(0.185) (0.193) (0.311) (0.317)

IBREADTH 10.156*** 10.36*** 11.47*** 9.984***

(0.683) (0.702) (0.743) (0.649)

L.B/M 0.00249 0.00732** 0.00715** 0.00504* 0.00882***

(0.00315) (0.00290) (0.00296) (0.00292) (0.00295)

L.LEV 0.00334 -0.00254 -0.00114 -0.00132 -0.000938

(0.0101) (0.00854) (0.00887) (0.00865) (0.00896)

L.RET -0.0158** -0.0450*** -0.0483*** -0.0416*** -0.0644***

(0.00655) (0.00820) (0.00698) (0.00750) (0.00824)

Ave yearly N 2745 2745 2745 1548 1197

Ave R2 0.033 0.104 0.106 0.142 0.102