Dispersion in Beliefs among Active Mutual Funds and the

Cross-Section of Stock Returns

Hao Jiang and Zheng Sun∗

This Draft: August 2012

Abstract

This paper establishes a strong link between the dispersion in beliefs among active

mutual funds, as revealed through their active holdings (i.e., deviations from benchmarks),

and future stock returns. We find that after standard risk adjustments, stocks in the top

decile portfolio with large increases in dispersion outperform those in the bottom decile by

more than 1% per month. This effect of dispersion on returns is particularly pronounced

among stocks with high information asymmetry; moreover, the lower returns on stocks with

decreases in dispersion concentrate on those with binding short-sale constraints. These

results are consistent with a subgroup of informed managers driving up the dispersion

in active holdings when they place large bets after receiving positive information signals

unobserved by their peers; conversely, binding short-sale constraints prevent them from

fully using their negative private information, leading to low dispersion in active holdings.

JEL classification: G10, G11, G12, G14

Keywords: Mutual Funds; Private Information; Dispersion in Beliefs; Short-Sale Con-

straints; Asymmetric Information

∗Hao Jiang is from the Rotterdam School of Management, Erasmus University, The Netherlands. Phone: 31-10-4088810. E-mail: hjiang@rsm.nl. Zheng Sun is from Paul Merage School of Business, University of California,Irvine. Phone: 1-949-824-6907. Email: zsun@merage.uci.edu. The authors thank Joe Chen, Nai-fu Chen, YongChen, Will Goetzmann, Larry Harris, David Hirshleifer, Harrison Hong, Philippe Jorion, Jun Liu, Buhui Qiu,Chris Schwarz, David Solomon, Avanidhar Subrahmanyam, Ivo Welch, Wei Xiong, Moto Yogo, Jialin Yu, LuZheng, and participants at UC-Irvine, 7th Early Career Women in Finance Conference, J.P. Morgan QuantConference, Napa Conference on Financial Markets, and USC-UCLA-UCI Southern Cal Finance Day conferencefor their helpful comments and suggestions. We thank Kenneth French and Lubos Pastor for making data onfactor returns available through their Web sites, and are grateful to the Frank Russell Company for their datasupport. All remaining errors are ours.

Dispersion in Beliefs among Active Mutual Funds and the

Cross-Section of Stock Returns

This Draft: August 2012

Abstract

This paper establishes a strong link between the dispersion in beliefs among active

mutual funds, as revealed through their active holdings (i.e., deviations from benchmarks),

and future stock returns. We find that after standard risk adjustments, stocks in the top

decile portfolio with large increases in dispersion outperform those in the bottom decile by

more than 1% per month. This effect of dispersion on returns is particularly pronounced

among stocks with high information asymmetry; moreover, the lower returns on stocks with

decreases in dispersion concentrate on those with binding short-sale constraints. These

results are consistent with a subgroup of informed managers driving up the dispersion

in active holdings when they place large bets after receiving positive information signals

unobserved by their peers; conversely, binding short-sale constraints prevent them from

fully using their negative private information, leading to low dispersion in active holdings.

JEL classification: G10, G11, G12, G14

Keywords: Mutual Funds; Private Information; Dispersion in Beliefs; Short-Sale Con-

straints; Asymmetric Information

1 Introduction

The enormous expansion of institutional investors has led to a profound change in the capital

market: an institutional investor is more likely to interact with another institution rather than

individual investors (French, 2008; Stein, 2009). In this context, studying the heterogeneity

among institutional investors appears important. Although a large literature analyzes how

institutional investors as a group affect asset prices, relatively little empirical work has focused

on how the heterogeneity among institutional investors influences capital market outcomes.

In this paper, we empirically examine how heterogeneous beliefs among actively managed

mutual funds relate to stock prices and returns. We focus on active mutual funds for several

reasons. First, the dramatic expansion of the mutual fund industry in the stock market has led

to its increasing importance as a group of U.S. corporate shareholders.1 Second, the majority

of mutual fund assets are actively managed, which makes the industry an essential information

processor. A growing number of studies have shown that informed trading by active fund

managers can play an important role in determining stock prices.2 Given the importance of

the mutual fund sector, it is of interest to investigate how dispersion in beliefs among active

managers might influence stock prices and returns. Finally, actively managed mutual funds

have well-specified performance benchmarks, which allow us to use portfolio theory to infer

their beliefs about future stock returns.

To capture the beliefs held by active fund managers, we use a new instrument, namely,

mutual funds’active holdings or the deviations in their holdings from benchmarks. An active

manager, according to her prospectus, attempts to maximize the benchmark-adjusted return

while minimizing the tracking error variance. In this context, she would overweight a stock

when she believes the stock will outperform and underweight it otherwise.3 Motivated by these

1According to the U.S. Census Bureau, the fraction of corporate equities owned by mutual funds grew from2.84% in 1980 to 20.61% in 2010.

2See, e.g., Coval and Moskowitz (2001), Cohen, Frazzini, and Malloy (2008), and Massa and Rehman (2008).3A mean-variance analysis of tracking errors in the spirit of Roll (1992) indicates that the deviation in portfolio

weights of a stock in the fund portfolio from its benchmark index, under certain assumptions, is linearly relatedto the expected return to that stock, conditional on the fund manager’s information set. Recent empirical worksupports the notion that active holdings help to reveal fund managers’expectation of future returns. Cremersand Petajisto (2009) shows that the deviation from benchmarks aggregated at the fund level or a fund’s ActiveShare predicts future fund performance. Jiang, Verbeek, and Wang (2010) show that a stock-level measure ofdeviations from benchmarks aggregated across active managers predicts returns on individual stocks.

1

observations, we create a new measure of dispersion in beliefs using the standard deviation of

active holdings across all active fund managers whose investment universe includes the stock.

We find intuitively that stocks with high dispersion tend to be small and growth stocks.

Our results establish a strong and robust relation between dispersion in beliefs among active

mutual funds and future stock returns. We find that stocks in the top decile portfolio with large

increases in dispersion outperform those in the bottom decile with large decreases by 1.38%

per month. After adjusting for the differences in their exposures to the market, size, value,

momentum, and liquidity factors, the return spread between stocks in the top and bottom

deciles remains more than 1% per month. Moreover, the return forecasting power of dispersion

in active fund holdings is pervasive across small and large stocks, persistent up to one year, and

robust to controlling for a variety of stock characteristics.4

The notion that stocks with higher dispersion in beliefs among active mutual funds earn

higher average returns may seem puzzling at first, given that several studies have documented

a negative association between proxies for dispersion in beliefs and future stock returns.5 These

studies typically invoke the idea put forth by Miller (1977) that in situations with heterogeneous

beliefs, binding short-sale constraints can wipe the negative opinions of pessimistic investors

from the market, thereby leading to overpricing and lower future returns. We argue that our

results are in fact consistent with a model of asset markets populated by investors holding

divergent beliefs in the presence of short-sale constraints. The key new ingredient that leads to

a different result is the source of divergent beliefs: differential information.

To understand the mechanism, assume that active fund managers are differentially informed

about individual stocks. For a given stock, some managers have an information advantage and

receive accurate information signals, whereas others receive noisy information signals or appear

to be uninformed investors.6 When informed managers receive positive signals about the stock

4The high returns on stocks with high dispersion do not necessarily imply large mutual fund alphas. Berkand Green (2004) present an equilibrium model to explain the coexistence of substantial mutual fund skill instock picking and zero abnormal returns to mutual fund investors.

5See Section I for a review of the literature.6The information advantage of certain fund managers could arise from their special connection (e.g., shared

educational network with firm managers, or proximity to the location of the firms in which fund managers invest)or specialized expertise (e.g., special knowledge about a particular industry as emphasized by Kacperczyk, Sialmand Zheng (2005)).

2

unobserved by other managers, they tend to place large bets relative to their peers, which

drive up the observed dispersion in beliefs among fund managers. When they obtain negative

information signals, however, binding short-sale constraints prevent them from fully using their

negative private information, leading to low dispersion in beliefs among managers.7 In other

words, when bad news occurs, market frictions of shorting force active mutual fund managers to

appear homogeneous. Therefore, observed dispersion in beliefs can vary with the private signals

informed managers receive. In line with the arguments by Grossman and Stiglitz (1980), as long

as the cost of information acquisition is nonzero, the equilibrium stock prices do not fully reveal

agents’private information, which generates the return forecasting power of the dispersion in

beliefs. We refer to this mechanism as the "differentially informed managers" hypothesis.

Results from several tests lend further support to this hypothesis. First, we study the

price reactions to earnings announcements for stocks with large increases and decreases in

dispersion during the quarter after portfolio formation. We find that the earnings announcement

returns are substantially higher for stocks with large increases in dispersion than for those with

large decreases in dispersion. On average, stocks with large increases in dispersion experience

positive surprises, earning a cumulative abnormal return (CAR) of 0.51% during the three days

surrounding earnings announcements. In contrast, stocks with large decreases in dispersion

deliver low performance, generating a CAR of —0.22%. The difference of 0.73%, realized over

only three trading days, represents approximately 20% of the 3.72% total difference during the

quarter. These results suggest that earnings-related information drives the return forecasting

power of dispersion in beliefs among active mutual funds.

Second, we find that the return forecasting power of the change in dispersion is particularly

strong for stocks with high information asymmetry, which is captured by the adverse selection

component of bid-ask spreads. We also conduct subsample analyses for different industries

and find that the dispersion effect is stronger for industries that are associated with greater

information asymmetry, such as information technology and health care.

Third, we examine how short-sale constraints affect the return forecasting power of disper-

7A majority of mutual funds are prohibited from shorting by their charter. For example, Almazan et al.(2004) report that only approximately 30% of mutual funds are allowed by their charters to sell short, and only3% of funds do sell short.

3

sion in active fund holdings. If a low level of dispersion reflects negative private information

obtained by fund managers, such information should be incorporated into stock price less ef-

ficiently when the short-sale constraints are bound more tightly. We measure the degree of

short-sale constraints by jointly considering the level of short interest and institutional own-

ership. The idea is that the level of short interest could reflect the demand for shorting and

institutional ownership could capture the supply for shares loanable for shorting. Thus, a stock

is more likely to be short-sale constrained if it has a higher level of short interest but a lower

level of institutional ownership. Combining our dispersion variable with the extent of short-

sale constraint provides a strong result. For stocks not likely to be short-sale constrained, the

abnormal return subsequent to large declines in dispersion is only —0.05% per month, with

a t-statistic of —0.28. On the other hand, for stocks likely to be short-sale constrained, the

abnormal return subsequent to large declines in dispersion reaches —1.25% per month, with a

t-statistic of —4.23. Among stocks with large increases in dispersion, we do not find significant

differences in returns between stocks with binding and nonbinding short-sale constraints. These

results strongly support the differentially informed manager hypothesis.

Our study contributes to the literature on how heterogeneous beliefs combined with mar-

ket frictions affect asset prices. It illustrates the need to understand the economic forces that

drive the divergent beliefs among investors. In Miller (1977) and Chen, Hong, and Stein’s

(2002) formalization, investors hold different beliefs for exogenous reasons. In their world, with

pessimistic investors sitting on the sidelines, optimistic investors push stock prices above the

consensus view of all investors, which is assumed to be an unbiased estimator of the funda-

mental value. These optimists hold overvalued equities and generate negative risk-adjusted

returns. A plausible interpretation of that result is that optimistic investors may be overcon-

fident, either in their ability to pick stocks or in the precision of the information signals they

observe (see, e.g., Daniel, Hirshleifer, and Subramanyam (1998)). Our results indicate that if

we replace behaviorally biased investors with rational informed investors endowed with superior

information, optimists could push prices toward the fundamental level, thus generating superior

risk-adjusted returns. Therefore, instilling information asymmetry into models with divergent

beliefs and short-sale constraints could yield noteworthy insights.

4

The rest of the paper is organized as follows: Section 2 summarizes the relevant literature

and discusses our contribution in relation to existing studies. Section 3 details the construction

of the dispersion variable and presents the data used. Section 4 presents the empirical findings

on how dispersion in active fund holdings relates to future stock returns, and Section 5 provides

possible interpretations to the findings. Section 6 presents several empirical tests that further

support our main findings. Section 7 concludes.

2 Related Literature

Our work extends the growing literature that studies how differences of opinion affect stock

prices.8 The empirical studies in this literature have used several proxies for differences of

opinion to examine its relationship with future returns, e.g., dispersion in analyst earnings

forecast (Diether, Malloy, and Scherbina (2002)), idiosyncratic volatility (Ang et al. (2006))

, trading volume (Brennan, Chordia, and Subrahmanyam (1998)), heterogeneous behavior of

retail investors (Goetzmann and Massa, (2005)), and the breadth of ownership by mutual

funds (Chen, Hong, and Stein, (2002)). The general finding of these papers is that proxies for

difference of opinion and future stock returns are negatively correlated. These empirical results

can be viewed as support for the idea put forth by Miller (1977), which Chen, Hong, and Stein

(2002) subsequently formalize. In their model economy, each investor holds dogmatic beliefs

that are either upwardly or downwardly biased, yet the average opinion among all investors

is unbiased. Thus, when short-sales constraints suppress the view of the pessimistic investors,

stocks are overpriced relative to the level when both types of investors are present, and optimistic

investors earn negative risk-adjusted returns.

Our study examining dispersion in beliefs among active mutual funds fleshes out a different

relation between dispersion and future stock returns. The story we favor shares a feature with

the above mentioned papers in that divergent beliefs in combination with short sale constraints

may be important for stock prices. However, rather than assuming that dispersion in beliefs

8Theoretical works pertaining to this subject include Miller (1977), Harrison and Kreps (1978), Diamond andVerrecchia (1987), and Chen, Hong, and Stein (2002). There is also a considerable literature that empiricallylooks at the impact of difference of opinion and short-sale restrictions on asset prices. See, e.g., Chen, Hong andStein (2002), Diether, Malloy, and Scherbina (2002), Goetzmann and Massa (2005).

5

arises for exogenous reasons, we emphasize the importance of private information as a driving

force of dispersion. For active mutual fund managers who specialize in ferreting out private

information, difference in their information set can be an important source for divergence of

beliefs. If the observed dispersion in beliefs reflects the large bets from superiorly informed man-

agers, these investors could earn positive expected returns, and a positive association between

dispersion in beliefs and future returns could emerge.

This paper is also related to the literature on how investor heterogeneity affects the ad-

justment of security prices to private information. Hong and Stein (1999) show that when

private information diffuses gradually across investors, prices adjust slowly to the information.

Diamond and Verrecchia (1987) model the effects of short-sale constraints on the speed of

adjustment to private information of security prices and show that prohibiting traders from

shorting reduces the adjustment speed of prices to private information, especially to bad news.

Empirical test of these models may be challenging, because it is diffi cult to observe the ar-

rival of private information.9 In this paper, we present evidence that suggests that changes in

dispersion of active mutual fund holdings can be driven by the arrival of private information.

We show that the return forecasting power of the change in dispersion persists for up to four

quarters, which is consistent with information gradually flowing into stock prices.

Finally, our paper also contributes to the growing literature that investigates the value of

active management. Although much evidence shows that on average active mutual funds do

not outperform passive benchmarks net of fees and expenses,10 several studies have identified a

subset of mutual fund investments in which superior information emerges. They have examined

the information content of the portion of fund holdings that is likely to be ex ante informed11 and

whether the stock holdings by a group of potentially skilled fund managers contain information

9Existing studies use indirect tests such as the autocorrelation of security returns (e.g., Hong, Lim, and Stein(2000)).10See, for example, Jensen (1968), Gruber (1996), Carhart (1997), and Fama and French (2008).11For example, Coval and Moskowitz (2001) investigate mutual fund holdings of stocks of firms located in the

same area; Cohen, Frazzini, and Malloy (2008) examine holdings of the shares of firms managed by the alumniof fund managers; Massa and Rehman (2008) examine holdings of the stocks held by bank-affi liated mutualfunds; and Tang (2009) examines holdings of the stocks by fund managers who previously covered those stocksas sell-side financial analysts. Moreover, Chen, Jegadeesh, and Wermers (2000) examine the recent portfolioadjustments by mutual funds; Cohen, Polk, and Silli (2010) examine the top holdings by mutual funds; andJiang, Verbeek, and Wang (2010) examine the deviation of active funds from their performance benchmarks.These studies conclude that holdings by active mutual funds contain information about future stock returns.

6

about future stock returns.12 There is, however, little analysis on the implications of the

dispersion in active mutual fund holdings for stock returns. In fact, our paper is one of the

first to examine the question. We provide new evidence that dispersion in active fund holdings

contains value-relevant information, which indicates the value of active management.

3 Construction of the Dispersion Variable

This section first explains the construction of our main variable, the dispersion in active mutual

fund holdings. Then, it provides a description of the sample and summary statistics.

3.1 Constructing the Dispersion in Active Mutual Fund Hold-

ings

Our key innovation is to create a novel measure of dispersion in beliefs among actively managed

mutual funds. We construct this dispersion measure as the standard deviation of the funds’

active holdings of a particular stock, i.e., the standard deviation of the difference between the

weight of the stock in each fund manager’s portfolio and that in the manager’s benchmark

index:

Dispersioni,t = { 1

Ni − 1

Ni∑j=1

[(wji,t − wbji,t)− (wji,t − w

bji,t)]

2}1/2, (1)

where wji,t is the weight of stock i in fund j’s portfolio at the end of quarter t, wbji,t is the weight

of stock i in fund j’s benchmark portfolio at the end of quarter t, and Ni is the number of funds

whose investment universe includes the stock i. A stock enters a mutual fund’s investment12For example, Cohen, Coval, and Pastor (2005) argue that a fund manager’s skill can be predicted by com-

paring his or her investment decisions with those of star fund managers. Kacperczyk, Sialm, and Zheng (2005)show that mutual fund managers sometimes deviate from a well-diversified portfolio and concentrate their hold-ings in industries in which they have informational advantages. Cremers and Petajisto (2009) find that fundswith the highest ActiveShare values significantly outperform their benchmarks both before and after expenses.Kacperczyk and Seru (2007) find that mutual funds that rely less on public information perform better. Wer-mers, Yao, and Zhao (2010) argue that the stock holdings by fund managers with superior past performancecontain information relevant for future stock returns. Finally, Shumway, Szefler, and Yuan (2011) contend thatthe revealed beliefs of a group of fund managers whose beliefs correlate positively with subsequent stock returnstend to be persistently correct.

7

universe if it (1) is held by the mutual fund or (2) is a member of the fund’s benchmark index.

3.2 Sample and Summary Statistics

To construct our dispersion variable, we collect portfolio holdings for actively managed eq-

uity mutual funds from Thomson Financial’s CDA/Spectrum Mutual Fund Holdings Database.

We obtain information on individual mutual funds from the Center for Research in Security

Prices (CRSP) Survivor-Bias-Free U.S. Mutual Fund Database.13 We eliminate balanced, bond,

money market, international, index funds, and sector funds, as well as funds not invested pri-

marily in equity securities, from our sample. After the filter, our sample consists of 2,667 active

equity funds, which range from the first quarter of 1984 to the third quarter of 2008.

Our selection of the benchmark index for fund managers follows Cremers and Petajisto

(2009). The universe of benchmark indexes includes 19 benchmark indexes widely used by

practitioners: the S&P 500, S&P 400, S&P 600, S&P 500/Barra Value, S&P 500/Barra Growth,

Russell 1000, Russell 2000, Russell 3000, Russell Midcap, the value and growth variants of the

four Russell indexes, Wilshire 5000, and Wilshire 4500. For each fund in each quarter, we select

from the 19 indexes the one that minimizes the average distance between the fund portfolio

weights and the benchmark index weights. Data on the index holdings of the 12 Russell indexes

since their inception come from the Frank Russell Company, and data on S&P 500, S&P 400,

and S&P 600 index holdings since December 1994 come from COMPUSTAT. For the remaining

indexes and periods, we use the holdings of index funds to approximate the index holdings.

The information on the monthly returns, prices, and market values of equity for common

stocks traded on the NYSE, AMEX, and NASDAQ comes from the CRSP. In line with previous

research, we exclude closed-ended funds, real estate investment trusts, American Depository

Receipts, foreign companies, primes, and scores (we keep only shares with codes of 10 or 11).

To mitigate the concern that our stock return tests might be influenced by return outliers, we

eliminate stocks with prices below $5 as of the portfolio formation date (typically the end of the

previous quarter). To mitigate the potential influence of mutual funds’preferential access to

13We merge these two databases using the MFLINKS data set maintained by Russ Wermers and the WhartonResearch Data Services.

8

initial public offerings on our results (Gaspar , Massa, and Matos (2005), and Reuter (2006)),

we exclude all stocks whose return history in CRSP falls below six months from our sample.

Finally, we require that at least five funds have active holdings information in the computation

of the dispersion variable. Panel A in Appendix A summarizes the size of our sample. In terms

of the number of stocks, our sample covers from 40% to 56% of the total number of CRSP

stocks in the period from 1984 to 2008.14 Yet the total market equity constitutes more than

95% of the entire CRSP sample. This is consistent with the notion that mutual funds tend

to hold large stocks. Overtime, the percentage of the number of stocks held by mutual funds

increases much faster than the percentage of the market value covered by mutual funds, which

suggests that mutual funds gradually include more small stocks in their portfolios.

Table 1 shows the descriptive statistics.15 First, Panel A shows that the dispersion in active

fund holdings is on average 0.387%, whereas the consensus (average) of active fund holdings

is on average 0.055%, which suggests that the dispersion in active fund holdings is large. The

standard deviation of dispersion in active fund holdings is 0.36%. Approximately 55% of it

comes from within-firm variation over time,16 which indicates that variation in the dispersion

variable is driven by both cross-sectional and time-series variation. Second, Panel B presents

the Fama-MacBeth (1973) cross-sectional regressions of dispersion on stock characteristics.

The results indicate that dispersion is correlated with stock characteristics in an intuitive way.

For example, small and growth stocks tend to have higher dispersion in beliefs among active

mutual funds. We also find a positive relation between dispersion in active fund holdings and

the breadth of mutual fund ownership. In other words, stocks with low dispersion in active fund

holdings tend to have low breadth in mutual fund ownership. If we interpret low dispersion

in active fund holdings as arising mainly from the presence of negative private information

combined with short-sale constraints, the positive correlation between dispersion and breadth

is consistent with the argument of Chen, Hong, and Stein (2002) that those stocks should also

have low breadth of mutual fund ownership.

<Insert Table 1 here>14The corresponding number is 69% in 2007.15Appendix B provides definitions of the major variables used in this paper.16The average within-firm standard deviation is 0.0020, which is 55% of the total standard deviation.

9

Interestingly, our dispersion variable exhibits a negative correlation with idiosyncratic volatil-

ity and dispersion in analyst earnings forecasts, which suggests that the information captured

by dispersion in active fund holdings could be distinct from that captured by idiosyncratic

volatility and dispersion in analyst earnings forecasts. Is this result particularly surprising?

Garfinkel (2009) uses proprietary limit order and market order data to construct a proxy for

divergence of investors’opinions. He finds a negative correlation between his proxy and disper-

sion in analyst earnings forecasts and stock return volatility, and interprets it as evidence that

the order data contain information on investors’private valuations, not captured by publicly

available data such as the analyst earnings forecasts or stock returns. In our case, mutual funds

do not instantly disclose their portfolio holdings. Thus, our dispersion variable measured in real

time could reflect information on fund managers’private valuations. In this sense, the negative

correlation between our dispersion variable and dispersion in analyst forecasts and idiosyncratic

volatility is consistent with that of Garfinkel (2009).

Finally, Panel C of Table 1 calculates a 10-by-10 transition matrix of dispersion from quarter

to quarter. Consistent with the variance decomposition of the dispersion variable, the transition

matrix shows that dispersion in active fund holdings tends to be relatively persistent over

time. Due to this persistence, we use the fresh component of the dispersion, the change in the

dispersion, to examine the return forecasting power of dispersion in active fund holdings.17

4 Dispersion and Future Stock Returns

In this section, we study the main question of the paper: Does dispersion in active mutual fund

holdings have significant forecasting power for future returns? We probe this question using

both a portfolio sorting and a multivariate predictive regression approach.

4.1 Portfolio Sorting17Using the level of dispersion, we obtain quantitatively weaker but qualitatively similar results.

10

To understand how divergence in active fund holdings is related to future stock returns, at

the end of each quarter we sort stocks into decile portfolios on the basis of the change in the

dispersion. We then compute the average monthly portfolio returns in the subsequent quarter.

To adjust for risk, we consider various factor models, including the CAPM, the Fama and French

(1993) three-factor model, the Carhart (1997) four-factor model, and a five-factor model that

augments the Carhart model with Pastor and Stambaugh’s (2003) liquidity risk factor. To

account for the possible nonlinear relation between characteristics and returns, we also use the

characteristic-based benchmarks proposed by Daniel et al. (DGTW, 1997).

Panel A of Table 2 presents the results for equal-weighted portfolios. We find that average

portfolio returns increase with changes in dispersion in active fund holdings in the past quarter.

For stocks in the top decile with the largest increase in dispersion, the average return is 1.90%

per month, whereas the average return for stocks in the bottom decile with the largest decrease

in dispersion is only 0.52% per month. Such a high return spread of 1.38% per month is

highly statistically significant with a t-statistic of 8.18 and cannot simply be explained by the

stocks’differential factor loadings. For example, according to the Carhart four-factor model,

stocks in the bottom decile portfolio with large decreases in dispersion in active holdings realize

an average abnormal return of —0.33% per month, while stocks in the top decile with large

increases earn an average abnormal return of 0.82% per month. Both the abnormal returns are

statistically significant, with t-statistics of —3.21 and 8.40, respectively. A long-short strategy

that buys stocks in the top decile and shorts stocks in the bottom decile generates an average

monthly abnormal return of 1.15% in the subsequent quarter. This return spread is statistically

significant (t-statistic = 7.40) and economically large.

<Insert Table 2 here>

Panel B of Table 2 shows the results for value-weighted portfolios. Again, the results

indicate a close to monotonic increasing relationship between changes in the dispersion in active

fund holdings and the subsequent stock returns. Moreover, the difference in returns between

portfolios with large increases and decreases in dispersion remains statistically significant and

economically large. For example, according to the Carhart four-factor model, an average dollar

11

invested in the portfolio with large increases in dispersion earns an abnormal return 0.54%

per month higher than that invested in the portfolio with large decreases in dispersion. The

abnormal return is significantly different from 0, with a t-statistic of 3.15.

How pervasive is the dispersion effect in stock returns? Following Fama and French (2008),

we examine the dispersion effect across size groups. Specifically, we perform two-way indepen-

dent sorts on the market capitalization and the change in dispersion in active holdings. We

then compute the return differences between the high and low dispersion portfolios for each size

group. The results in Table 3 indicate that the dispersion variable significantly predicts future

stock returns across all size quintiles. A careful look at the patterns indicates that the return

forecasting power of dispersion in active fund holdings is especially strong among mid-cap stocks

but relatively weak among large-cap stocks.

<Insert Table 3 here>

4.2 Multivariate Predictive Regression

In this section, we extend our analysis by using the Fama and MacBeth (1973) cross-sectional

regression approach. Specifically, at the end of each quarter from 1984Q1 to 2008Q3, we

perform cross-sectional regressions of quarterly returns in quarter t + k on the change in the

dispersion of active fund holdings measured in quarter t, ∆Dispersiont, and control variables,

with k ranging from 1 to 12. The control variables consist of the natural log of market cap; the

natural log of book-to-market ratio; the stock return in the past year, skipping the most recent

month (Jegadeesh and Titman (1993)); the stock return in the past month (Jegadeesh (1990));

idiosyncratic volatility (Ang, Hodrick, Xing, and Zhang (2006)); turnover (Brennan, Chordia,

and Subrahmanyam (1998); and Lee and Swaminathan (2000)); the breadth of mutual fund

ownership (Chen, Hong, and Stein (2002)); the consensus view of active mutual funds (i.e.,

the mean of the active fund holdings as in Jiang, Verbeek, and Wang (2010)); and dispersion

in analyst earnings forecasts (Diether, Malloy, and Scherbina (2002)). As the inclusion of the

12

dispersion in analyst earnings forecasts leads to a significant reduction (approximately 40%) in

our sample size, we present the results that includes this variable in a separate column.

Table 4 presents the regression results. In the forecasting regression for returns in quar-

ter t+1, the slope coeffi cient for ∆Dispersiont is significantly positive, with a t-statistic of

6.79. The magnitude is also economically meaningful. A one standard deviation increase in

∆Dispersiont (0.216) is associated with an increase in returns of approximately 1.20% over the

subsequent quarter (= 0.216 × 5.546), after we control for other stock characteristics. The re-

gression coeffi cients for the control variables are largely consistent with the findings in previous

research. For example, small stocks, value stocks, stocks with low idiosyncratic volatility, stocks

with low turnover, and stocks with high breadth of mutual fund ownership tend to earn higher

future returns. Moreover, stock returns tend to exhibit short-term reversal and intermediate-

term momentum. Consistent with Diether, Malloy, and Scherbina (2002), the dispersion in

analyst earnings forecasts shows a negative correlation with future stock returns.18

<Insert Table 4 here>

The inclusion of dispersion in analyst earnings forecasts appears to have little influence on

the return forecasting power of the dispersion in active fund holdings. This result suggests that

the information content of dispersion in active mutual fund holdings may be distinct from that

contained by dispersion in analyst earnings forecasts. Why do these two proxies for dispersion

in beliefs among different players in the stock market capture distinct information about future

stock returns? One interpretation could be that the dispersion in active fund holdings cap-

tures the dispersion in beliefs among sophisticated institutions, while the dispersion in analyst

earnings forecasts may be driven by differences of opinion among individual investors.19 As

institutional and retail investors tend to have opposing investment performance (e.g., Barber

18 In our sample period, the ownership breadth variable used in this paper is more strongly related to stockreturns than the original measure used in Chen, Hong, and Stein (2002). Using their measure of ownershipbreadth, however, we obtain both qualitatively and quantitatively similar results.19Goetzmann and Massa (2005) use data from individual investor accounts and construct a measure of disper-

sion of opinion among retail investors. They argue that differences of opinion among retail investors Granger-causedispersion of opinion among financial analysts. Another literature shows that the behavior of sophisticated andinformed investors tends to correlate less with analysts’opinions (e.g., Kacperczyk and Seru, 2007), while thebehavior of retail investors is more likely to be influenced by analysts (e.g., Mikhail, Walther, and Willis, 2007).

13

and Odean, 2000), it is likely that dispersion in active fund holdings and dispersion in analyst

earnings forecasts have different implications for future stock returns.

When we extend the return forecasting horizon, we find that the forecasting power of the

change in dispersion for future returns persists up to the next four quarters; and there is no

return reversal up to the next three years. This result suggests that the dispersion variable

contains information about the fundamental value of the firms, rather than simply reflects the

short-term price pressure effect. Also notably, the magnitude of the regression coeffi cients for the

dispersion variable declines substantially after the first quarter. Since mutual funds are required

by the Securities and Exchange Commission to disclose their portfolio composition within 60

days after the portfolios’effective date,20 the significant drop in the return forecasting power of

the dispersion variable after the first quarter is consistent with the stock market impounding a

large fraction of the information contained by the dispersion variable when information about

fund holdings becomes publicly available.

5 Differentially Informed Fund Managers or Differential Un-

certainties?

In this section, we consider two competing explanations of our finding. First, given that the

association between dispersion and future stock returns tends to be permanent and that the

strength of the association concentrates during the most proximate quarter when the holdings

information becomes public, a natural interpretation of our finding is that dispersion in active

fund holdings contains information about firms’fundamentals. Thus, we propose a hypothesis of

differentially informed managers to explain the positive association between dispersion in active

mutual fund holdings and future stock returns. Second, we consider a competing explanation:

the higher dispersion in the holdings of active funds reflects greater uncertainty, which leads to

higher expected returns on those stocks.

To understand the mechanism of the differentially informed managers hypothesis, assume

20http://www.sec.gov/rules/final/33-8393.htm#IIB.

14

that active fund managers are differentially informed about individual stocks. For a given

stock, some managers have an information advantage and receive accurate information signals,

whereas others receive noisy information signals or appear to be uninformed investors. When

informed managers receive positive signals about the stock unobserved by other managers, they

tend to place large bets relative to their peers, which drive up the observed dispersion in beliefs

among fund managers. When they obtain negative information signals, however, binding short-

sale constraints prevent them from fully using their negative private information, leading to low

dispersion in beliefs among managers. In other words, when bad news occurs, market frictions

of shorting force active mutual fund managers to appear homogeneous. Therefore, observed

dispersion in beliefs can vary with the private information signal informed managers receive. In

line with Grossman and Stiglitz (1980), as long as the cost of information acquisition is nonzero,

the equilibrium stock prices do not fully reveal agents’private information, which generates the

return forecasting power of dispersion in beliefs.

Why does the dispersion in active holdings have incremental return predictive power relative

to the average active holdings? We conjecture that the main reason is because it better captures

the distribution of differentially informed managers. Consider two stocks that are otherwise

identical. For the first stock, information about its future payoff is evenly distributed across a

large number of managers. For the second, only a small group of managers receive information

signals about its payoff whereas other managers receive either very noisy signals or are largely

uninformed. In the first case, stock price is more informative, as the competition among a large

number of informed investors diminishes the return to each informed investor; in the second

case, the price can be less informative so that a higher return can be earned by each informed

investor.

Alternatively, the positive association between dispersion in active fund holdings and subse-

quent stock returns may be consistent with a hypothesis of differential uncertainty. In particular,

a higher dispersion in mutual fund holdings may reflect a higher level of uncertainty about the

stock. The uncertainty can be due to either a high volatility in fundamentals or poor infor-

mation, both of which may lead to a high dispersion in beliefs among fund managers (Kraus

and Smith (1989), Harris and Raviv (1993)). Because a high level of uncertainty implies a high

15

required rate of return, a positive association between dispersion and future returns thus could

emerge.21 We refer to this explanation as the information uncertainty hypothesis.

To distinguish between the two explanations, we examine the relationship between changes

in dispersion and the contemporaneous changes in stock prices. According to our differentially

informed manager hypothesis, dispersion in active fund holdings captures the private informa-

tion obtained by more informed managers, with positive information driving up the dispersion

and negative information driving down the dispersion. In stylized models with asymmetric

information among investors, such as that of Grossman and Stiglitz (1980), positive (negative)

private information triggers buy (sell) orders from the informed investors, which partially push

up (down) the stock price as they trade. In such a scenario, stock prices partially reveal the

private information obtained by informed investors. Hence, this hypothesis predicts that large

increases in dispersion should be associated with contemporaneous increases in stock prices

whereas large decreases in dispersion should be associated with contemporaneous decreases in

stock prices.

The information uncertainty hypothesis, however, predicts a negative association between

changes in dispersion and the contemporaneous changes in stock prices. The idea is that if

dispersion in active fund holdings is driven by the degree of information uncertainty about the

stock, an increase in dispersion (i.e., an increase in the level of uncertainty) should be associated

with an increase in investors’required rates of return, which leads to a contemporaneous decline

in stock prices.

In Table 5, we form decile portfolios on the basis of changes in dispersion and compute

the average contemporaneous portfolio returns. The results are striking. We observe a strict

monotonic increasing relationship between change in dispersion and contemporaneous quarter

returns, throughout all specifications. The strong positive association between changes in the

dispersion and contemporaneous returns lends support to our differentially informed manager

21According to Merton (1987), investors would demand compensation for holding stocks with high idiosyncraticrisk if they hold under-diversified portfolios. In addition, uncertainty increases investors’estimation risk aboutthe true distributions of assets’ payoff. If estimation risk is non-diversifiable, investors require compensationfor this risk (Coles and Loewenstein (1988), and Lambert, Leuz, and Verrecchia (2007)). Empirically, Botosan(1997) finds that when the amount of publicly available information about a firm is low or imprecise, the firm’scost of capital is higher.

16

hypothesis but contradicts the information uncertainty hypothesis.

<Insert Table 5 here>

6 Further Empirical Tests

In this section, we perform several tests that lend further support to the hypothesis of differ-

entially informed fund managers. First, we examine the information content of the dispersion

variable by looking at the relation between dispersion in active fund holdings and subsequent

earnings announcement returns. Second, we study how the dispersion effect varies across stocks

with different degrees of information asymmetry. Third, we examine how short-sale constraints

affect the return forecasting power of dispersion in active fund holdings. Fourth, we consider

how the return forecasting power of dispersion varies across time period. Finally, we conduct

further robustness checks by controlling several other variables in the return predictive regres-

sion.

6.1 Dispersion and Stock Returns during Earnings Announce-

ments

To understand the strong return forecasting power of dispersion in beliefs, we examine the

stock price reactions to earnings announcements during the quarter after portfolio formation.

If dispersion in active fund holdings contains value-relevant information that becomes available

to the public during subsequent earnings announcements, we would expect to observe a positive

correlation between dispersion and subsequent earnings announcement returns. In particular,

we expect stocks with large increases in dispersion to enjoy positive performance during earnings

announcements and stocks with large decreases in dispersion to experience negative performance

during earnings announcements. To examine this conjecture, for each quarter we sort stocks

into quintile portfolios on the basis of changes in dispersion in active fund holdings. For each

portfolio, we then calculate the three-day cumulative abnormal returns (CARs during the most

immediate earnings announcements). We measure abnormal returns by deducting the returns

17

on the benchmark portfolios that match the size and book-to-market characteristics of the

stocks from daily individual stock returns.

Panel A of Table 6 indicates that the earnings announcement returns are substantially higher

for stocks with large increases in dispersion than for those with large decreases in dispersion. On

average, the portfolio with large increases in dispersion experiences positive surprises, earning

a CAR of 0.51%. In contrast, the portfolio with large decreases in dispersion delivers rather

disappointing performance, earning a CAR of −0.22%. The difference of 0.73%, realized over

only three trading days, represents approximately 20% of the 3.72% total difference in returns

during the quarter.22 This results suggests that a significant portion of the return forecasting

power of dispersion comes from its ability to predict earnings surprises.

<Insert Table 6 here>

As La Porta et al. (1997) note, it is possible that the differences in event returns between

the high- and low-dispersion portfolios “just represent differences in ex ante risk premia realized

around a small number of important information events.”(p. 870) If a disproportionately high

percentage of risk is realized during earnings announcements, a disproportionate share of the

risk premium may show up as well. If high-dispersion stocks are also high-risk stocks, high

abnormal returns might also occur during earnings announcement. A powerful test of this risk

premium/uncertainty hypothesis, according to La Porta, Lakonishok, Shleifer, and Vishny, is

to examine its implication that for both high and low dispersion stocks, event returns are higher

than nonevent returns.

In Panel B of Table 6, we follow their approach. For each portfolio formed on the basis of

changes in dispersion in each quarter, we perform regressions of daily excess stock returns on the

excess market return and an indicator variable that equals one if the day is within one trading

day before and after earnings announcements and zero otherwise. The statistical inference is

based on the Fama and MacBeth procedure. Two results are noteworthy. First, we observe a

large decline in returns of 3.74 basis points (t-statistic = 1.95) for the portfolio with decreases

22The 3.72% difference in quarterly returns is obtained by sorting stocks into quintile portfolios based on theend of quarter changes in dispersion, and then compute the abnormal returns for the “high minus low”portfolioover the next quarter.

18

in dispersion in Quintile 1 during the earnings announcement days, which is inconsistent with

the prediction of the risk-based hypothesis. Second, Panel B provides clear evidence that the

dispersion effect in returns is more pronounced during the earnings announcement period. The

difference in average daily returns between stocks with increases and decreases in dispersion

is 19.26 basis points during the event days, approximately four times that of 4.49 basis points

during the non-event days.

6.2 Information Asymmetry and Return Predictability

The informed manager hypothesis ascribes the return forecasting power of dispersion in active

fund holdings to the private information obtained by informed fund managers. If informed

managers have greater information advantages for less transparent firms, our hypothesis implies

that the return forecasting power of dispersion in active fund holdings is stronger among stocks

with greater information asymmetry.

To examine this prediction, we adopt a widely used measure of information asymmetry in

the literature– namely, the adverse selection component of the bid-ask spread.23 This measure

is designed to capture the degree of informed trading perceived by the market makers. To

the extent that informed mutual fund managers constitute a subset of informed investors, this

measure can capture markets’perception of the information advantage gained by informed fund

managers. We follow the method George, Kaul, and Nimalendran (1991) develop to calculate

the adverse selection component. In particular, we calculate the measure as

AS = S − 2×√−COV (RDt, RDt−1), (2)

where S is the proportional quoted spread and RD is the difference between daily returns

computed using transaction prices and bid-ask midquotes.24

23For papers that use this empirical proxy, see, for example, Jones, Kaul, and Lipson (1994), Kumar, Sarin,and Shastri (1998), Flannery, Kwan, and Nimalendran (2004), and Bharath, Pasquariello, and Wu (2009).24We use CRSP end-of-day closing bid-ask quotes to calculate the quoted bid-ask spread. We drop all quotes

with negative bid-ask spreads and require the recorded ask and bid prices to be strictly positive. We also requirea minimum of 20 valid observations within a quarter to calculate the quarterly adverse selection measure. Finally,we exclude observations with negative adverse selection measures.

19

To examine our conjecture, we perform independent sorts. Along one dimension, we sort

stocks into quintile portfolios according to changes in dispersion, and along the other dimension

we sort stocks into terciles on the basis of the adverse selection component of bid-ask spread.

Fifteen portfolios thus emerge from this double sort. We compute equal- and value-weighted

returns on these portfolios and present the results in Table 7. Consistent with the differentially

informed managers hypothesis, we observe a monotonic increasing relationship between the

return forecasting power of dispersion in active fund holdings and the degree of information

asymmetry. For example, on the value-weighted basis, a spread portfolio that buys stocks with

high dispersion in active fund holdings and shorts stocks with low dispersion in active holdings

earns an abnormal return of 1.64% per month (t-statistic=5.78), for stocks with a high level of

information asymmetry. In contrast, a similar spread portfolio generates an abnormal return of

only 0.36% per month (t-statistic=1.75) for stocks with a low level of information asymmetry.

The difference in abnormal returns between the two spread portfolios is 1.28% per month (t-

statistic=3.91). These results indicate that the level of information asymmetry is important

in determining the return forecasting power of dispersion in active fund holdings, which lends

further support to our differentially informed manager hypothesis.

<Insert Table 7 here>

6.3 Dispersion Effect across Industries

Next, we subdivide our sample into different industries and reexamine the return forecasting

power of the dispersion variable within each industry. The test serves two purposes. First,

dispersion might be correlated with industry-wide fundamental shocks that are not captured

by the standard asset pricing factors (e.g., Hou (2007)). Therefore, performing a within-industry

analysis helps mitigate the sector effects. Second, given that firms in different industries differ

significantly in terms of informational opaqueness, the test provides another way to examine

the impact of information asymmetry on the dispersion effect.

Specifically, we use the Fama—French 10 industry classifications to group stocks and con-

struct portfolios according to changes in dispersion within each industry. Because the industries

20

of consumer durables, oil, and telephone contain only a small number of firms, we exclude them

from our industry analysis.25

Table 8 summarizes the portfolio sorting results for each of the seven industries. The

results indicate that for most of the industries, a spread portfolio that buys stocks with higher

dispersion in active fund holdings and shorts stocks with low dispersion in active holdings

earns significant alphas in both equal- and value-weighted returns. This result suggests that

the return forecasting power of dispersion in active fund holdings is not confined to just a few

industries. More importantly, we find that the superior performance of high dispersion stocks

is not uniform across various industries. The dispersion effect in stock returns is particularly

pronounced among stocks in the information technology industry, followed by stocks in the

health care and service industries. In contrast, the dispersion effect in stock returns is relatively

weak among stocks in the consumer staples and utilities industries. This pattern is consistent

with our expectation, as stocks in the technology-oriented industries are presumably more

diffi cult to value and more likely to be subject to asymmetric information.

<Insert Table 8 here>

6.4 Short-Sale Constraints and Return Predictability

In addition to information asymmetry, another building block for the differentially informed

managers hypothesis is short-sale constraint. Therefore, in this subsection, we examine how

short-sale constraints affect the return forecasting power of dispersion in active fund holdings.

According to our hypothesis, low dispersion in active fund holdings arises from binding short-sale

constraints preventing informed managers from fully using their negative private information.

Assuming that negative private information held by the informed mutual fund managers is also

observed by some short sellers (e.g., hedge funds), the shorting will help the negative information

be incorporated into the stock price, unless shorting is prohibitive. Therefore, the negative

return forecasting power of low dispersion in active holdings should be particularly strong among

stocks with binding short-sale constraints, whereas the positive return forecasting power of high

25Panel B of Appendix A summarizes the sample size across different industries.

21

dispersion in active holdings should be largely uninfluenced by short-sale constraints.

To capture short-sale constraints, we follow Asquith, Pathak, and Ritter (2005) and combine

the information on the level of institutional ownership and short interest. The idea is that the

level of institutional ownership could be proxy of the supply for loanable shares (e.g., Nagel

(2005)), whereas the level of short interest captures the loan capacity already utilized. A stock

is hit by binding short-sale constraints when the supply for loanable shares is limited and there

is already a large outstanding demand for shorting (D’Avolio (2002)).

In particular, we create a stock-level short-sale constraint index by performing double sorts

on institutional ownership (IO) and short interest ratios. A stock receives an index value of 3 if

it has low IO and a high short ratio, 1 if it has high IO and a low short ratio, and 2 if otherwise.

A higher value of the index indicates more binding short-sale constraints. Figure 2 illustrates

the construction of the measure.

Institutional investors exhibit preferences to hold large company stocks (Gompers and Met-

rick, 2001). To purge a mechanical size effect, we compute residuals from cross-sectional re-

gressions of log(IO/(1− IO)) on log(ME) and log(ME)2. We then use the residual IO in the

double sorts. Our short interest data for common stocks traded on the NYSE, AMEX and

NASDAQ between 1988 and 2008 come from Bloomberg. The short interest ratio is calculated

as the number of shares sold short divided by the number of shares outstanding.

The results in Table 9 provide supporting evidence for the differentially informed managers

hypothesis. On an equal-weighted basis, a strategy that buys stocks with large increases in

dispersion and shorts stocks with large decreases in dispersion generates a monthly four-factor

alpha of 1.63% for stocks with the most binding short-sale constraints. In contrast, a similar self-

financing strategy generates a monthly four-factor alpha of only 0.71% for stocks with the least

binding short-sale constraints. A further examination of the 0.92% return difference between

the two strategies indicates that it comes primarily from the abysmally low performance of

stocks with low dispersion and binding short-sale constraints, which is —1.20% lower than stocks

with low dispersion but nonbinding short-sale constraints. Among stocks with high dispersion

in active fund holdings, the difference in the monthly four-factor alpha between stocks with

22

binding and nonbinding short-sale constraints is only —0.27% and statistically insignificant.

The results on value-weighted returns indicate a qualitatively similar pattern. These results

provide further support to our differentially informed managers hypothesis.

<Insert Table 9 here>

6.5 Time Varying Return Forecasting Power of Dispersion in

Beliefs

In this subsection, we consider how the return forecasting power of dispersion in beliefs varies

across periods. Specifically, we examine the dispersion effect for the periods before and after

the Regulation Fair Disclosure (RegFD).

The SEC instated the RegFD in October 2000 to eliminate selective disclosures by firms

to a subset of market participants. Research on the effects of RegFD finds a decline in the

value of financial analyst earnings forecasts and stock recommendations, consistent with ana-

lysts having less access to private information (Gintschel and Markov, 2004; Francis, Nanda

and Wang, 2006). Given that mutual fund managers constitute another important group of

information processors, it is interesting to explore how their informational role varies across

the two regulation regimes. We divide our sample period into two subperiods: the pre-RegFD

period from July 1984 to December 2000 and the post-RegFD period from January 2001 to

December 2008. During the pre-RegFD period, a long-short portfolio that buys stocks with

large increases in dispersion in Decile 10 and shorts stocks with large decreases in dispersion

in Decile 1 generates an equal-weight four-factor alpha of 0.79% per month (t = 5.22) and a

value-weight four-factor alpha of 0.48% per month (t = 2.36). During the post-RegFD period,

the long-short portfolio yields an equal-weight four-factor alpha of 1.88% per month (t = 6.21)

and a value-weight four-factor alpha of 0.59% per month (t = 1.68). Therefore, the dispersion

effect in the returns remains strong in the period after the implementation of RegFD. The

evidence suggests that the RegFD does not weaken the role of mutual fund managers as infor-

mation processors as it does for financial analysts. However, the gap in the abnormal returns

23

between the equal and value weighted portfolios widens after the RegFD. This result points to

the increasing informational role played by mutual funds toward smaller companies, which is

consistent with our earlier observation of the secular trend that mutual funds tend to invest

more in smaller stocks.

6.6 Robustness Tests with Further Controls

Finally, we examine the robustness of our results by adding further control variables into the

return predictive regression. The additional variables include (1) the three-day abnormal return

surrounding earnings announcements in the past quarter to control for earnings momentum;

(2) the "Best Ideas" stocks in each fund manager’s portfolio (Cohen, Polk and Silli, 2010);

(3) the short ratio; (4) an indicator variable for the index membership; (5) analyst earnings

forecast revisions; and (6) the stock return in the past three months. The results, presented in

Table 10, show that among the additional control variables, the Short Ratio, Best Ideas, and

analyst earnings forecast revisions stand out significant in predicting future returns. However,

the return forecasting power of dispersion in active fund holdings remains strong even after

controlling for these variables.

<Insert Table 10 here>

7 Conclusion

We have empirically established that higher dispersion in beliefs among active mutual fund

managers, as revealed through their active holdings, is associated with higher future stock

returns. After standard risk adjustments, stocks in the top decile portfolio with large increases

in dispersion outperform their peers in the bottom decile by more than 1% per month. This

effect of dispersion on returns is particularly pronounced among stocks with high information

asymmetry; moreover, the lower returns on stocks with decreases in dispersion concentrate

on those with binding short-sale constraints. These results are consistent with a subgroup of

informed managers driving up the dispersion in active holdings when they place large bets after

24

receiving positive information signals unobserved by their peers; conversely, binding short-sale

constraints prevent them from fully using their negative private information, leading to low

dispersion in active holdings.

Our results shed new light on the relation between investor disagreement and stock returns.

A large part of the empirical literature looks at dispersion in analyst earnings forecasts as a

proxy for investor disagreement, and documents a negative association between analyst dis-

agreement and stock returns. Moreover, this literature has interpreted this negative association

as supporting Miller’s (1977) argument that differences in opinion in combination with short-

sale constraints can lead optimistic investors to become price-setting marginal investors, who

hold overvalued equities and suffer from losses of negative expected returns. We provide fresh

evidence, which suggests that if the seemingly optimistic behavior of investors arises from their

superior information, these investors could earn positive expected returns, generating a posi-

tive association between dispersion in beliefs and future returns. Considering the increasingly

dominant role of sophisticated professional investors in the stock market, our analysis suggests

that it is important to deepen the investigation of the impact of investor disagreement on stock

returns.

More broadly, the large literature on institutional investors has started to emphasize the

heterogeneity and interaction among institutional investors (e.g., French, 2008; Stein, 2009).

Our study joins this literature by providing an interesting case for the influence of asymmetric

information among active mutual funds on asset prices and returns. We plan to examine this

issue more broadly in future research.

25

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30  

Appendix A

Sample Size

This table summarizes the sample used in the paper. Panel A presents the number and total market equity of the common stocks in our sample at the end of each year, as well as the fractions of all the CRSP common stocks. Panel B presents the time-series average number of stocks and total market equity in our sample for each of the Fama–French 10 industries.

Panel A: Sample Size by Year

Year # of stocks Total Market Value ($bn)

Fraction of CRSP (N)

Fraction of CRSP ($)

1984 2,725 1,611.49 0.46 0.96 1985 2,766 2,001.38 0.47 0.96 1986 2,732 2,239.90 0.44 0.95 1987 2,608 2,211.95 0.40 0.96 1988 2,716 2,422.89 0.44 0.97 1989 2,650 2,962.67 0.44 0.97 1990 2,349 2,672.80 0.40 0.97 1991 2,695 3,608.05 0.46 0.97 1992 2,960 4,006.50 0.49 0.97 1993 3,162 4,495.85 0.48 0.96 1994 3,174 4,485.93 0.46 0.97 1995 3,292 6,032.91 0.46 0.95 1996 3,821 7,433.73 0.51 0.96 1997 3,572 9,731.29 0.47 0.97 1998 3,680 12,067.03 0.51 0.98 1999 3,566 15,141.71 0.52 0.96 2000 3,270 14,053.33 0.50 0.98 2001 3,243 12,414.32 0.56 0.98 2002 2,881 9,594.14 0.53 0.97 2003 3,384 12,603.95 0.67 0.98 2004 3,419 13,952.69 0.69 0.98 2005 3,289 14,506.48 0.67 0.98 2006 3,328 16,116.44 0.69 0.98 2007 3,253 16,269.89 0.69 0.99 2008 2,458 9,727.72 0.56 0.97

31  

Panel B: Sample Size by Industry

Industry # of stocks

Total Market

Value ($bn) Fraction of

Industry (N) Fraction of Industry ($)

Other 892 1977.40 0.49 0.95

Computers, Software, and Electronic Equipment 507 1309.15 0.47 0.96

Manufacturing: Machinery, Trucks, Planes, Chemicals, Off Furn, Paper, Com Printing

461 938.54 0.64 0.99

Wholesale, Retail, and Some Services 349 663.21 0.56 0.97

Health Care, Medical Equipment, and Drugs 242 830.74 0.46 0.98

Consumer Nondurables: Food, Tobacco, Textiles, Apparel, Leather, Toys

192 531.73 0.59 0.99

Utilities 144 333.74 0.88 0.99

Oil, Gas, and Coal Extraction and Products 111 518.91 0.51 0.98

Consumer Durables: Cars, TV's, Furniture, Household Appliances

91 346.15 0.61 0.99

Telephone and Television Transmission 88 509.85 0.58 0.96

32  

Appendix B

Variable Description

In this appendix, we provide the detailed definitions of the variables used in our paper.

Variable Name Definition Dispersion The standard deviation of the difference between the weight of

the stock in each fund manager’s portfolio and that in the manager’s benchmark portfolio.

Consensus The arithmetic average of the difference between the weight of

the stock in each fund manager’s portfolio and that in the manager’s benchmark portfolio.

Size The natural log of market cap in millions. log(BM) The natural log of the book-to-market ratio. Mom1 The stock return in the past month. Mom12 The stock return in the past year skipping the most recent month. Earnings Mom The three-day abnormal return surrounding corporate earnings

announcements. IV Idiosyncratic volatility: the standard deviation of the residuals

from a regression of daily stock returns on the Fama and French (1993) three factors in a quarter.

Turnover The ratio of the trading volume divided by the number of shares

outstanding in a quarter. Following French (2008), we divide reported NASDAQ volume by 2.0 until 2001, by 1.5 in 2002 and 2003, and by 1.25 thereafter.

Breath The number of active mutual funds that hold the stock.

Log(Breadth) The natural log of one plus the number of active funds that hold

the stock. Dbreadth The change in the natural log of one plus the number of active

funds that hold the stock. Analyst Dispersion The standard deviation of the analyst annual earnings forecast

divided by the absolute value of the mean of the forecast. Best Idea A dummy variable that equals one if the stock has the highest

33  

overweight by a particular manager (Cohen et al., 2010). Bid-Ask Spread The average end-of-day bid-asks spread over bid-ask midpoint

during a quarter, computed using CRSP daily stock file. Adverse Selection Quarterly measure of the adverse selection component of bid-ask

spreads calculated according to George, Kaul, and Nimalendran (1991). The measure is computed using the end-of-day bid and ask quotes obtained from CRSP daily stock file.

Short-Sale Constraint

An index variable gauging the degree of short-sale constraint by performing double sorts on residual institutional ownership and short interest ratio. A stock receives a value of 3 (with binding short-sale constraints) if it has low residual institutional ownership and a high short interest ratio, a value of 1 (with nonbinding short-sale constraints) if it has high institutional ownership and low short interest ratio, and 2 if otherwise.

Index Membership An indicator variable that takes a value of 1 if a stock belongs to

one of the benchmark indexes used by mutual funds and 0 if otherwise.

Forecast Revision Quarterly change in the mean analyst annual earnings forecasts. MOM3 Stock return in the past three months.

  

Low Institutional Ownership

High Institutional Ownership

High Short Interest Most Constrained Medium Low Short Interest Medium Least Constrained

Figure 1. Short-Sale Constraints.

35  

Table 1

Descriptive Statistics

This table presents the descriptive statistics for our sample of 11,779 common stocks in the investment universe of 2,667 actively managed mutual funds from the period 1984Q1 to 2008Q3. A stock enters the investment universe of a fund if it is either held by the fund or in the benchmark index of the fund. For each stock–fund pair in each quarter, we compute the difference between the stock’s weight in the fund portfolio and its weight in the benchmark index. Then, for each quarter, we aggregate this difference in portfolio weights to individual stock level. Dispersion is the standard deviation of the difference in portfolio weights across all active funds whose investment universe includes the stock, and Consensus is the mean of the deviation from the benchmarks. Breadth is the number of funds that hold the stock. Size is the natural log of market cap, Log(BM) is the natural log of the book-to-market ratio, MOM1 is the stock return in the past month, MOM12 is the stock return in the past year skipping the past month (month t-12 to month t-1), and IV is the idiosyncratic volatility measured as the standard deviation of the residual from a time-series regression of a stock’s daily returns on the Fama and French (1993) factors in the past quarter. Turnover is the trading volume in the past quarter divided by the number of shares outstanding. Analyst Dispersion is the standard deviation of analyst annual earnings forecasts divided by the mean forecast (Diether, Malloy, and Scherbina (2002)). Analyst Dispersion is winsorized at the 99th percentile. We exclude stocks from the sample if their prices fall below $5 at the quarter end or in their first six months in the CRSP database. Panel A shows the distribution of these variables. Panel B shows the Fama-MacBeth (1973) cross-sectional regressions of the natural log of Dispersion on stock characteristics, with t-statistics based on Newey-West (1987) standard errors. *** Statistical significance at 1%. ** Statistical significance at 5%. * Statistical significance at 10% level. Panel C displays the 10-by-10 transition matrix of Dispersion from quarter to quarter. Each cell reports the percentage of stocks transitioning from a dispersion decile last quarter to a decile this quarter.

Panel A: Summary Statistics

N Mean Std Dev 25th Pctl Median 75th Pctl Dispersion(×100) 305020 0.387 0.360 0.136 0.323 0.538 ΔDispersion(×100) 282663 -0.004 0.216 -0.069 0.000 0.063 Consensus (×100) 305020 0.055 0.214 -0.022 0.009 0.073 Size (Log MM.$) 305020 6.087 1.662 4.879 5.910 7.119 Log(BM) 277962 -0.724 0.812 -1.160 -0.633 -0.199 MOM1 304984 0.006 0.136 -0.059 0.003 0.066 MOM12 295184 0.091 0.422 -0.124 0.098 0.310 IV 305018 0.024 0.014 0.015 0.021 0.030 Turnover 305020 0.276 0.380 0.081 0.169 0.340 Breadth 305020 25 38 5 11 30 Analyst Dispersion 171612 0.130 0.320 0.017 0.040 0.100

36  

Table 1 - Continued

Panel B: Determinants of Dispersion in Beliefs

Intercept Size Log(BM) Mom1 Mom12 IV Turnover Log(Breadth) Analyst

Dispersion Adj R2

2.071*** -0.080*** -0.061*** 0.346*** 0.297*** -7.501*** 0.036 0.753*** -0.011*** 0.516 (12.56) (-4.01) (-4.21) (15.06) (17.69) (-4.18) (0.80) (24.37) (-3.82)

Panel C: Transition Matrix (%)

Rank in Dispersion (t-1) Rank in Dispersion (t) 1 2 3 4 5 6 7 8 9 10

1 69.37 15.43 5.32 2.81 1.77 1.13 0.62 0.52 0.38 0.31 2 15.83 48.46 20.48 7.06 3.85 2.20 1.39 0.97 0.73 0.58 3 5.70 18.88 37.14 20.28 8.63 4.47 2.73 1.70 1.16 0.73 4 3.28 6.90 18.42 32.29 19.91 9.73 5.13 2.71 1.61 0.98 5 1.96 3.92 8.00 18.90 28.68 20.03 10.22 5.03 2.64 1.37 6 1.21 2.46 4.37 8.88 19.47 27.13 20.40 9.96 4.68 1.97 7 0.90 1.51 2.71 4.73 9.41 19.73 28.03 20.81 9.19 3.19 8 0.68 1.01 1.66 2.61 4.73 9.69 20.19 31.64 21.26 6.27 9 0.63 0.85 1.09 1.58 2.29 4.10 8.70 21.34 40.43 18.32

10 0.44 0.58 0.81 0.85 1.25 1.79 2.59 5.32 17.91 66.26 Sum 100 100 100 100 100 100 100 100 100 100

37  

Table 2

Changes in Dispersion and Future Stock Returns: Decile Portfolios

This table presents the returns on decile portfolios sorted on the basis of innovations in the dispersion of mutual fund holdings. At the end of each quarter from 1984Q1 to 2008Q3, we sort stocks into deciles in ascending order on the basis of innovations in the dispersion of mutual fund holdings and compute the average monthly equal-weight (Panel A) and value-weight (Panel B) portfolio returns in the subsequent quarter. We also present risk-adjusted performance of those portfolios, based on the CAPM, the Fama and French (1993) three-factor model, the Carhart (1997) four-factor model, and a five-factor model that augments the Carhart model with Pastor and Stambaugh’s (2003) liquidity. We also perform the Daniel et al. (DGTW 1997) characteristic-adjustment procedure. We exclude stocks with prices lower than $5 or those whose return history in CRSP falls below six months as of the portfolio formation date. *** Statistical significance at 1%. ** Statistical significance at 5%. * Statistical significance at 10% level.

Panel A: Equal-Weight Portfolio Returns (%) Low 2 3 4 5 6 7 8 9 High H-L

Average Returns 0.52 0.40 0.63 0.71 0.53 0.79 1.04 1.09 1.35 1.90 1.38*** (1.42) (1.18) (1.93) (2.34) (1.90) (2.86) (3.57) (3.67) (4.45) (5.68) (8.18)

CAPM -0.51 -0.58 -0.33 -0.20 -0.33 -0.06 0.15 0.19 0.43 0.96 1.46*** (-3.34) (-4.32) (-2.5) (-1.44) (-2.49) (-0.44) (1.12) (1.41) (3.35) (5.61) (8.52)

FF three-factor -0.54 -0.69 -0.46 -0.35 -0.48 -0.20 0.00 0.05 0.33 0.96 1.50*** (-4.54) (-6.3) (-4.32) (-3.46) (-5.22) (-2.41) (0.06) (0.63) (4.36) (9.33) (8.19)

Carhart four-factor -0.33 -0.45 -0.21 -0.13 -0.36 -0.11 0.11 0.11 0.32 0.82 1.15*** (-3.21) (-4.97) (-2.45) (-1.51) (-3.78) (-1.36) (1.32) (1.26) (3.99) (8.40) (7.40)

PS five-factor -0.31 -0.44 -0.20 -0.12 -0.35 -0.10 0.12 0.11 0.33 0.83 1.14*** (-2.95) (-4.82) (-2.34) (-1.45) (-3.75) (-1.27) (1.61) (1.31) (4.20) (8.37) (7.13)

DGTW -0.21 -0.24 -0.15 -0.12 -0.14 0.12 0.12 0.31 0.33 0.57 0.78*** (-2.22) (-2.75) (-1.75) (-1.37) (-1.53) (1.30) (1.58) (4.08) (4.03) (6.32) (5.67)

38  

Panel B: Value-Weight Portfolio Returns (%) Low 2 3 4 5 6 7 8 9 High H-L Average Returns 0.46 0.50 0.70 0.93 0.80 1.07 1.01 1.04 1.20 1.38 0.92***

(1.42) (1.62) (2.42) (3.43) (2.81) (3.84) (3.82) (4.05) (4.61) (4.61) (4.79) CAPM -0.50 -0.43 -0.20 0.06 -0.09 0.20 0.16 0.19 0.35 0.47 0.97***

(-3.61) (-3.45) (-1.86) (0.62) (-0.77) (1.65) (1.53) (2.17) (3.66) (3.95) (4.89) FF three-factor -0.35 -0.43 -0.28 0.00 -0.16 0.14 0.05 0.12 0.32 0.55 0.90***

(-2.99) (-3.55) (-2.56) (-0.03) (-1.3) (1.09) (0.57) (1.46) (3.48) (4.45) (4.64) Carhart four-factor -0.21 -0.23 -0.11 0.04 -0.01 0.23 0.10 0.08 0.21 0.34 0.54***

(-1.91) (-2.15) (-1.09) (0.45) (-0.08) (1.57) (1.00) (0.92) (2.40) (2.93) (3.15) PS five-factor -0.19 -0.21 -0.10 0.05 -0.03 0.22 0.11 0.07 0.23 0.35 0.54***

(-1.72) (-1.95) (-0.98) (0.50) (-0.17) (1.58) (1.18) (0.80) (2.61) (3.07) (3.10) DGTW -0.24 -0.28 -0.01 -0.01 0.01 0.12 0.18 0.13 0.27 0.30 0.54***

(-2.46) (-2.96) (-0.11) (-0.05) (0.11) (0.95) (2.02) (1.42) (2.58) (3.15) (3.68)

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Table 3

Two-Way Sorts on Changes in Dispersion and Market Cap

This table presents the average monthly returns on portfolios sorted on the basis of innovations in dispersion in mutual fund holdings and market cap. At the end of each quarter from 1984Q1 to 2008Q3, along one dimension, we sort stocks into quintiles in ascending order on the basis of the dispersion in mutual fund holdings; along another dimension, we sort stocks into quintiles on the basis of market cap. Twenty-five portfolios thus emerge from the intersection of the double sorts. We compute the average monthly equal- and value-weight portfolio returns in the subsequent quarter. We present risk-adjusted performance of those portfolios, based on the Carhart (1997) four-factor model. We exclude stocks with prices lower than $5 at the quarter end or those whose return history in CRSP falls below six months. *** Statistical significance at 1%. ** Statistical significance at 5%. * Statistical significance at 10% level.

Panel A: Equal-Weight Portfolio Returns (%)

ΔDispersion Market Cap Low 2 3 4 High High-Low

Small -0.33 -0.13 -0.21 0.14 0.61 0.97*** (-1.97) (-0.8) (-1.41) (0.95) (3.75) (6.31) 2 -0.23 -0.26 -0.31 0.26 0.77 1.00*** (-1.85) (-2.05) (-2.87) (2.12) (5.44) (6.14) 3 -0.52 -0.23 -0.17 0.08 0.71 1.23*** (-4.14) (-1.9) (-1.82) (0.78) (5.93) (7.09) 4 -0.59 -0.10 -0.11 0.11 0.49 1.08*** (-5.12) (-1.12) (-0.98) (1.09) (4.36) (6.42)

Large -0.33 -0.16 0.02 0.16 0.37 0.69*** (-3.17) (-2.13) (0.27) (2.24) (3.51) (4.29)

Panel B: Value-Weight Portfolio Returns (%)

ΔDispersion Market Cap Low 2 3 4 High High-Low

Small -0.25 -0.20 -0.18 0.14 0.66 0.95*** (-1.53) (-1.23) (-1.27) (1.01) (4.12) (5.90) 2 -0.28 -0.29 -0.30 0.22 0.81 1.09*** (-2.21) (-2.22) (-2.94) (1.89) (5.83) (6.52) 3 -0.54 -0.23 -0.14 0.09 0.74 1.27*** (-4.32) (-1.96) (-1.58) (0.86) (6.20) (7.13) 4 -0.53 -0.13 -0.07 0.15 0.50 1.03*** (-4.59) (-1.45) (-0.71) (1.59) (4.38) (5.80)

Large -0.17 0.00 0.18 0.10 0.24 0.41*** (-2.06) (-0.05) (1.15) (1.37) (2.86) (2.84)

40  

Table 4

Changes in Dispersion and Future Stock Returns:

Fama–MacBeth Cross-Sectional Regressions

This table presents the results of the Fama and MacBeth (1973) cross-sectional regressions of future stock returns on innovations in the dispersion of mutual fund holdings. Specifically, at the end of each quarter from 1984Q1 to 2008Q3, we perform cross-sectional regression of quarterly returns in the quarter t+k on the innovation of the dispersion of mutual fund holdings and control variables in quarter t, with k ranging from 1 to 12. The variables are defined in Table 1. We exclude stocks from the sample if their prices fall below $5 at the end of quarter t or in their first six months in the CRSP database. *** Statistical significance at 1%. ** Statistical significance at 5%. * Statistical significance at 10% level.

41  

Quarterly Returns: t+1

Quarterly Returns: t+2

Quarterly Returns: t+3

Quarterly Returns: t+4

Quarterly Returns: t+8

Quarterly Returns: t+12

ΔDispersion 5.546*** 7.011*** 0.927*** 0.659 0.645* 1.512*** 0.560** 0.997** -0.174 0.010 0.402 0.259 (6.79) (6.71) (2.65) (1.56) (1.75) (3.15) (2.11) (2.52) (-0.40) (0.02) (1.33) (0.69) Consensus 1.865*** 2.581*** 0.365 0.292 0.318 0.197 -0.007 -0.432 -0.026 -0.543 -0.174 -0.880** (5.57) (6.15) (1.24) (0.85) (1.08) (0.59) (-0.02) (-1.11) (-0.08) (-1.36) (-0.47) (-2.36) Size (0.002) (0.001) (0.001) 0.000 0.000 0.001 -0.001 0.000 0.000 0.001 0.000 0.001 (-1.45) (-0.57) (-0.78) (0.26) (-0.03) (0.29) (-0.48) (-0.16) (0.28) (0.63) (-0.04) (0.63) BM 0.003 0.001 0.004* 0.003 0.005** 0.004 0.004* 0.002 0.002 0.000 0.001 0.001 (1.21) (0.25) (1.87) (1.26) (2.18) (1.47) (1.80) (0.73) (0.86) (0.09) (0.22) (0.22) MOM1 -0.038*** -0.041** 0.024** 0.027** 0.015 0.022 0.023** 0.030** 0.016* 0.020 0.000 0.025* (-2.66) (-2.51) (2.12) (2.01) (1.08) (1.47) (2.13) (2.49) (1.76) (1.52) (-0.01) (1.84) MOM12 0.023*** 0.026*** 0.015*** 0.017*** 0.000 0.003 -0.001 0.000 -0.006** -0.004 -0.006 -0.002 (5.22) (5.01) (3.44) (3.47) (-0.01) (0.67) (-0.25) (-0.05) (-2.02) (-1.10) (-1.53) (-0.56) IV -0.752*** -0.894*** (0.297) (0.214) (0.032) (0.047) 0.072 0.111 0.244 0.310 0.341 0.522* (-3.31) (-3.34) (-1.29) (-0.84) (-0.14) (-0.18) (0.32) (0.42) (1.02) (1.11) (1.37) (1.80) Turnover -0.018** (0.010) -0.018** (0.007) -0.015* (0.005) -0.010 -0.010 -0.001 0.000 0.002 0.001 (-2.15) (-1.17) (-2.31) (-0.84) (-1.72) (-0.56) (-1.14) (-1.18) (-0.07) (-0.03) (0.22) (0.08) Log(Breadth) 0.004 0.001 0.004* 0.001 0.003 0.001 0.004* 0.001 0.000 -0.002 0.001 -0.001 (1.50) (0.62) (1.89) (0.21) (1.22) (0.58) (1.83) (0.51) (0.14) (-0.62) (0.36) (-0.41) Analyst Dispersion

-0.001** (0.001) 0.002 -0.001 0.000 0.003**

(-2.05) (-1.47) (1.47) (-1.13) (-0.48) (2.09) Intercept 0.051*** 0.045*** 0.034*** 0.028** 0.027** 0.024* 0.024** 0.028* 0.026* 0.020 0.025* 0.016 (4.60) (3.45) (3.06) (2.03) (2.43) (1.76) (2.11) (1.96) (1.86) (1.28) (1.81) (0.98) Adj R2 0.072 0.092 0.06 0.075 0.057 0.072 0.051 0.063 0.043 0.06 0.039 0.051

42  

Table 5

Changes in Dispersion and Contemporaneous Returns

This table presents the average monthly returns on decile portfolios sorted on the basis of change in dispersion in the contemporaneous quarter. At the end of each quarter from 1984Q1 to 2008Q3, we sort stocks into deciles in ascending order on the basis of the change in dispersion in mutual fund holdings and compute the average monthly equal-weight (Panel A) and value-weight (Panel B) portfolio returns in the contemporaneous quarter. We also present risk-adjusted performance of those portfolios, based on the CAPM, the Fama and French (1993) three-factor model, the Carhart (1997) four-factor model, and a five-factor model that augments the Carhart model with Pastor and Stambaugh’s (2003) liquidity. We exclude stocks with prices lower than $5 at the quarter end or those whose return history in CRSP falls below six months. *** Statistical significance at 1%. ** Statistical significance at 5%. * Statistical significance at 10% level.

Panel A: Equal-Weight Portfolio Returns (%) Low 2 3 4 5 6 7 8 9 High H-L Average Returns -1.27 -1.20 -0.59 -0.19 0.27 2.01 2.56 3.10 4.05 5.77 7.04***

(-3.51) (-3.59) (-1.89) (-0.66) (1.00) (7.21) (8.70) (10.09) (12.42) (15.57) (28.14) CAPM -2.25 -2.14 -1.51 -1.07 -0.55 1.19 1.69 2.21 3.14 4.83 7.08***

(-12.85) (-14.89) (-11.99) (-8.81) (-3.81) (7.79) (12.21) (15.05) (18.94) (21.39) (27.80) FF three-factor -2.25 -2.22 -1.62 -1.20 -0.69 1.06 1.56 2.12 3.08 4.85 7.10***

(-19.19) (-21.62) (-17.44) (-14.12) (-6.56) (10.94) (14.44) (19.86) (25.89) (27.27) (27.23) Carhart four-factor -2.25 -2.14 -1.51 -1.06 -0.51 1.19 1.71 2.27 3.19 4.84 7.09***

(-17.8) (-22.03) (-17.48) (-13.93) (-5.33) (11.33) (16.47) (20.19) (24.31) (25.93) (25.51) PS five-factor -2.26 -2.13 -1.50 -1.04 -0.49 1.19 1.75 2.29 3.21 4.86 7.12***

(-17.7) (-21.91) (-17.67) (-14.33) (-5.24) (11.30) (16.77) (20.00) (23.92) (25.54) (25.26) Panel B: Value-Weight Portfolio Returns (%)

Low 2 3 4 5 6 7 8 9 High H-L Average Returns -1.34 -0.67 0.00 0.71 1.04 1.64 2.14 2.77 3.68 5.38 6.72***

(-4.09) (-2.34) (-0.01) (2.76) (4.13) (6.59) (8.36) (10.75) (13.80) (16.48) (27.49) CAPM -2.29 -1.55 -0.88 -0.13 0.23 0.83 1.31 1.94 2.84 4.48 6.77***

(-17.83) (-13.93) (-9.07) (-1.53) (2.19) (8.24) (14.35) (19.56) (25.40) (25.18) (27.40) FF three-factor -2.17 -1.54 -0.95 -0.21 0.17 0.76 1.24 1.88 2.83 4.61 6.78***

(-17.18) (-13.1) (-9.74) (-2.81) (1.67) (8.05) (14.34) (19.64) (24.52) (24.86) (26.42) Carhart four-factor -2.28 -1.55 -0.96 -0.23 0.22 0.75 1.30 1.92 2.81 4.65 6.93***

(-18.34) (-13.64) (-10.03) (-2.62) (2.29) (7.86) (14.42) (18.80) (23.79) (20.26) (22.75) PS five-factor -2.27 -1.55 -0.96 -0.22 0.23 0.75 1.32 1.93 2.82 4.66 6.93***

(-18.1) (-13.23) (-10.07) (-2.59) (2.27) (7.66) (14.55) (18.50) (23.37) (20.61) (23.01)

43  

Table 6

Earnings Announcement Returns for Stocks with

Large Increases and Decreases in Dispersion

This table presents the performance of stocks with large increases and decreases in dispersion surrounding the most proximate earnings announcements. Panel A shows the average three-day abnormal returns for stocks sorted on the basis of dispersion in mutual fund holdings or their innovations. We measure abnormal returns by deducting the returns on the benchmark portfolio that match the size and book-to-market characteristics of the stock from daily individual stock returns. In Panel B, for each quarter from 1984Q1 to 2008Q3, we perform cross-sectional regressions of daily stock returns on the market return and a dummy variable that equals one if the day is within one trading day before and after earnings announcements and zero if otherwise. The regressions are conducted for each group of stocks with low or high innovations in dispersion in mutual fund holdings. The t-statistics are based on the time-series variation of the regression coefficients.

Panel A: Abnormal Earnings Announcement Returns (%)

ΔDispersion Low

Quintile 1 2

3

4

High Quintile 5

High-Low

CAR -0.22 -0.05 0.00 0.18 0.51 0.73*** -5.60 -1.57 0.07 5.80 14.99 14.06

Panel B: Cross-Sectional Regression Tests of Difference between Event and Nonevent Returns (bps)

Low ΔDispersion Quintile 1 High ΔDispersion Quintile 5

Intercept -0.45 4.04*** (-0.56) (5.82)

Event Day Dummy -3.74* 15.52*** (-1.95) (8.89)

Market Return 0.94*** 0.93*** (43.18) (49.40)

44  

Table 7

Two-Way Sorts on Changes in Dispersion and Information Asymmetry

This table presents the average monthly returns on portfolios sorted on the basis of innovations in dispersion in mutual fund holdings and information asymmetry. We use the adverse selection component of bid-ask spreads calculated according to George, Kaul, and Nimalendran (1991) as a proxy for information asymmetry. At the end of each quarter from 1984Q1 to 2008Q3, along one dimension, we sort stocks into quintiles in ascending order on the basis of the change in dispersion in mutual fund holdings; along another dimension, we sort stocks into terciles on the basis of the information asymmetry measure. Fifteen portfolios thus emerge from the intersection of the double sorts. We compute the average monthly equal- and value-weight portfolio returns in the subsequent quarter. We present risk-adjusted performance of those portfolios, based on the Carhart (1997) four-factor model. We exclude stocks with prices lower than $5 at the quarter end or those whose return history in CRSP falls below six months. *** Statistical significance at 1%. ** Statistical significance at 5%. * Statistical significance at 10% level.

Panel A: Equal-Weight Portfolio Returns (%)

Information Asymmetry ΔDispersion

Low 2 3 4 High High-Low Low -0.22 -0.06 0.04 0.21 0.53 0.76***

(-1.99) (-0.57) (0.33) (1.70) (3.99) (5.74) 2 -0.36 -0.22 -0.21 0.15 0.64 1.01*** (-2.84) (-1.71) (-1.82) (1.17) (4.84) (6.73)

High -0.71 -0.46 -0.55 -0.09 0.69 1.40*** (-4.57) (-3) (-4.1) (-0.78) (4.78) (7.32)

High-Low -0.49** -0.39** -0.60*** -0.30* 0.15 0.64*** (-2.59) (-2.08) (-2.96) (-1.86) (0.84) (3.47)

Panel B: Value-Weight Portfolio Returns (%)

ΔDispersion Information Asymmetry Low 2 3 4 High High-Low

Low -0.09 -0.07 0.28 0.05 0.27 0.36* (-0.49) (-0.48) (1.41) (0.36) (1.73) (1.75) 2 -0.42 -0.11 0.02 0.19 0.44 0.86*** (-2.66) (-0.71) (0.13) (1.30) (2.97) (4.44)

High -0.97 -0.56 -0.11 -0.34 0.67 1.64*** (-4.53) (-2.82) (-0.5) (-1.96) (3.04) (5.78)

High-Low -0.88*** -0.50** -0.39 -0.39* 0.40* 1.28*** (-3.18) (-2.14) (-1.55) (-1.89) (1.67) (3.91)

45  

Table 8

Changes in Dispersion and Future Stock Returns: Industry Comparison

This table presents the returns on quintile portfolios sorted on the basis of innovations in the dispersion of mutual fund holdings, conducted separately for seven of the Fama–French 10 industries. At the end of each quarter from 1984Q1 to 2008Q3, we sort stocks into quintiles in ascending order on the basis of innovations in the dispersion of mutual fund holdings and compute the average monthly equal-weight (Panel A) and value-weight (Panel B) portfolio returns in the subsequent quarter. We present risk-adjusted performance of those portfolios, based on the Carhart (1997) four-factor model. We exclude stocks with prices lower than $5 at the quarter end or those whose return history in CRSP falls below six months. *** Statistical significance at 1%. ** Statistical significance at 5%. * Statistical significance at 10% level.

Panel A: Equal-Weight Portfolio Returns (%)

Industry Low 2 3 4 High High-Low

Computers, Software, and Electronic Equipment -0.13 -0.09 -0.16 0.30 0.94 1.06***

(-0.66) (-0.57) (-1.03) (2.01) (5.30) (5.76)

Health Care, Medical Equipment, and Drugs -0.08 0.04 -0.05 0.28 0.87 0.95***

(-0.36) (0.17) (-0.23) (1.20) (3.96) (4.57)

Wholesale, Retail, and Some Services -0.37 -0.22 -0.32 0.03 0.52 0.89***

(-2.02) (-1.32) (-2.12) (0.18) (3.06) (5.70)

Other -0.46 -0.19 -0.18 0.10 0.38 0.84***

(-3.79) (-1.77) (-1.60) (0.92) (3.10) (6.69)

Manufacturing: Machinery, Trucks, Planes, -0.29 -0.15 -0.31 0.08 0.42 0.70***

Chemicals, Off Furn, Paper, Com Printing (-2.03) (-1.10) (-2.42) (0.62) (2.94) (5.60)

Consumer Nondurables: Food, Tobacco, -0.29 -0.36 -0.04 -0.07 0.22 0.51***

Textiles, Apparel, Leather, Toys (-1.69) (-2.40) (-0.32) (-0.52) (1.39) (2.78)

Utilities -0.03 -0.01 0.20 0.18 0.35 0.38**

(-0.17) (-0.09) (1.32) (1.09) (1.90) (2.21)

46  

Table 8 - Continued

Panel B: Value-Weight Portfolio Returns (%)

Industry Low 2 3 4 High High-Low

Computers, Software, and Electronic Equipment -0.22 0.08 0.58 0.17 0.78 0.99***

(-0.86) (0.33) (2.35) (0.79) (3.11) (3.37)

Wholesale, Retail, and Some Services -0.21 -0.04 0.06 -0.11 0.46 0.67***

(-0.93) (-0.19) (0.25) (-0.54) (2.23) (2.83)

Health Care, Medical Equipment, and Drugs 0.15 0.44 0.26 0.45 0.74 0.60**

(0.54) (1.76) (0.96) (1.84) (3.22) (2.06)

Other -0.47 -0.12 -0.08 -0.09 0.08 0.56***

(-3.05) (-0.82) (-0.59) (-0.68) (0.60) (3.19)

Manufacturing: Machinery, Trucks, Planes, -0.31 -0.12 -0.17 0.10 0.12 0.43*

Chemicals, Off Furn, Paper, Com Printing (-1.62) (-0.78) (-0.83) (0.66) (0.65) (1.72)

Utilities -0.09 -0.08 -0.04 0.01 0.23 0.32

(-0.33) (-0.37) (-0.16) (0.04) (0.98) (1.30)

Consumer Nondurables: Food, Tobacco, 0.00 -0.04 0.20 0.33 0.25 0.26

Textiles, Apparel, Leather, Toys (-0.01) (-0.20) (1.02) (1.71) (1.22) (0.84)

47  

Table 9

Two-Way Sorts on Changes in Dispersion and Short-Sale Constraint

This table presents the average monthly returns on portfolios sorted on the basis of innovations in dispersion in mutual fund holdings and short-sale constraint. The short-sale constraint is indexed by performing double sorts on residual institutional ownership and short interest ratio. A stock receives an index value of 3 if it has low residual institutional ownership and a high short interest ratio, 1 if it has high institutional ownership and low short interest ratio, and 2 if otherwise. At the end of each quarter from 1988Q1 to 2008Q3, along one dimension, we sort stocks into quintiles in ascending order on the basis of the change in dispersion in mutual fund holdings; along another dimension, we sort stocks into terciles on the basis of the short-sale index. Fifteen portfolios thus emerge from the intersection of the double sorts. We compute the average monthly equal- and value-weight portfolio returns in the subsequent quarter. We present risk-adjusted performance of those portfolios, based on the Carhart (1997) four-factor model. We exclude stocks with prices lower than $5 at the quarter end or those whose return history in CRSP falls below six months. *** Statistical significance at 1%. ** Statistical significance at 5%. * Statistical significance at 10% level.

Panel A: Equal-Weight Portfolio Returns (%)

Short-Sale Constraint ΔDispersion

Low 2 3 4 High High-Low Low -0.05 0.16 -0.06 0.27 0.66 0.71***

(-0.28) (0.95) (-0.36) (1.44) (3.73) (3.86) 2 -0.38 -0.15 -0.08 0.22 0.69 1.08*** (-3.77) (-1.65) (-1.08) (2.59) (7.20) (7.31)

High -1.25 -0.49 -1.04 -0.11 0.38 1.63*** (-4.23) (-1.97) (-4.18) (-0.47) (1.46) (4.47)

High-Low -1.20*** -0.66** -0.98*** -0.37 -0.27 0.93** (-3.39) (-1.99) (-2.95) (-1.16) (-0.79) (2.58)

Panel B: Value-Weight Portfolio Returns (%)

ΔDispersion Short-Sale Constraint Low 2 3 4 High High-Low

Low -0.39 0.26 0.19 0.29 0.26 0.64** (-1.87) (1.02) (0.70) (1.44) (1.11) (2.60)

2 -0.21 -0.03 0.25 0.16 0.30 0.51*** (-2.22) (-0.3) (1.53) (2.03) (3.13) (3.12)

High -1.03 -0.42 -0.54 0.06 0.46 1.49*** (-2.81) (-1.74) (-2.02) (0.28) (1.65) (3.75)

High-Low -0.65 -0.68* -0.73* -0.23 0.21 0.85* (-1.37) (-1.83) (-1.74) (-0.69) (0.50) (1.82)

48  

Table 10 Fama-MacBeth Return Predictive Regressions with More Control Variables

This table uses the Fama and MacBeth (1973) cross-sectional regressions to examine the relationship between dispersion in mutual fund holdings and future stock returns. Specifically, for each quarter from 1984Q2 to 2008Q4, we perform cross-sectional regression of stock returns on the dispersion in mutual fund holdings in the most proximate quarter end, with several control variables. Dispersion is the standard deviation of the difference in portfolio weights across all active funds whose investment universe includes the stock, and Consensus is the mean of the deviation from benchmarks. Breadth is the natural log of one plus the number of funds that hold the stock. Size is the natural log of market cap, Log(BM) is the natural log of the book-to-market ratio, MOM1 is the stock return in the past month, MOM12 is the stock return in the past year skipping the past month (month t-12 to month t-1), Earnings Mom is the three-day abnormal return surrounding earnings announcements in the past quarter, IV is the idiosyncratic volatility measured as the standard deviation of the residual from a time-series regression of a stock’s daily returns on the Fama and French (1993) factors in the past quarter, Turnover is the trading volume in the past quarter divided by the number of shares outstanding, Best Idea is a dummy variable that equals one if the stock has the highest overweight by a particular manager (Cohen et al., 2010), Analyst Dispersion is the standard deviation of analyst annual earnings forecasts divided by the mean forecast, Short Ratio is the ratio of short interest to the number of shares outstanding, and Index Membership is an indicator variable that takes a value of 1 if a stock belongs to one of the benchmark indexes used by mutual funds. Forecast Revision is the quarterly change of mean analyst forecast, and MOM3 is the stock return in the past three months.

49  

 (1) (2) (3) (4)

ΔDispersion 8.710*** 8.656*** 8.688*** 8.697***   (6.61) (6.60) (6.26) (6.29)

Consensus 2.941*** 2.930*** 3.427*** 3.447***   (6.39) (6.29) (6.59) (6.71)

Size -0.002 -0.002 -0.002 -0.001   (-0.95) (-0.94) (-0.77) (-0.70)

BM 0.001 0.001 -0.001 -0.001   (0.23) (0.35) (-0.49) (-0.38)

MOM1 -0.053*** -0.054*** -0.054*** -0.054***   (-2.82) (-2.89) (-3.12) (-3.17)

MOM12 0.019*** 0.019***   (3.57) (3.55)

Earnings Mom 0.007 0.004 0.022 0.02   (0.45) (0.25) (1.31) (1.22)

IV -0.846*** -0.819*** -0.919*** -0.896***   (-3.06) (-2.98) (-3.26) (-3.18)

Turnover 0.004 0.005 0.015 0.015   (0.46) (0.48) (1.54) (1.56)

Log(Breadth) 0.001 0.001 0.001 0.000   (0.37) (0.44) (0.32) (0.17)

Best Idea  0.025*** 0.026*** 0.027*** 0.027***   (4.69) (4.73) (4.80) (4.79)

Analyst Dispersion -0.002 -0.001 -0.002* -0.002

  (-1.59) (-1.46) (-1.75) (-1.66)

Short Ratio -0.162*** -0.160*** -0.182*** -0.182***

(-4.47) (-4.43) (-5.11) (-5.11)

Index Membership 0.016 0.018*

  (1.45) (1.69)

Forecast Revision 0.121** 0.153***   (2.24) (2.68)

MOM3 0.006 0.004   (0.50) (0.35)

Intercept 0.036** 0.050*** 0.051*** 0.033*   (1.99) (3.55) (3.47) (1.81)

Adj R2 0.096 0.097 0.09 0.092