Mutual Fund Disproportionate Portfolio Adjustment

Claire Yurong Hong∗

This Draft: Feburary, 2016

Abstract

This paper looks into the disproportionate portfolio adjustments behaviors of mu-

tual funds. Instead of proportionally scaling up (down) existing holdings when having

inflows (outflows), mutual funds disproportionally adjust holdings in their portfolio.

The dispersion of funds’ cross sectional holdings adjustments is highly persistent and

proxies for both stock picking and timing abilities. Funds with high dispersion of hold-

ings adjustment persistently outperform those with low dispersion by over 2% annually,

both before and after expenses. At the cross sectional stock level, stocks over-weighted

by high dispersion funds outperform stocks under-weighted by them, while such pattern

does not exist for stocks held by low dispersion funds.

∗Hong Kong University of Science and Technology, Department of Finance (E-mail: Claire.hong@ust.hk)

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1 Introduction

With the rise of delegated portfolio management in the past 30 years, mutual funds nowadays

are attracting more and more attention from both practitioners and academics. By end of

2014, 43.3% of U.S. households invest in mutual funds, and over 80% of equity funds’ total

net assets are managed actively1. From academia’s perspective, one of the central questions

is always whether mutual funds possess superior skills that they could generate alpha for

investors. Previous research shows that mutual funds in aggregate fail to outperform the

benchmark especially after taking into consideration fees and other expenses (Fama and

French, 2010; French, 2008). On the other hand, a large group of literature tries hard to

separate the alpha-generating funds from the bad-performing ones (Kacperczyk, Sialm, and

Zheng, 2005, 2007; Cremers and Petajisto, 2009; Amihud and Goyenko, 2013; etc.). Given a

large proportion of society’s wealth is managed by mutual funds, it is important to identify

mutual funds with superior skills that could generate alpha for investors.

In this paper, I construct a new measure of mutual fund skill, based on their dispro-

portionate portfolio adjustment. The measure is intuitively straightforward. Considering a

fund manager who does not possess any skill but passively follow a benchmark index, then

he would proportionately expand or liquidate the existing holdings when there are capital

inflows or outflows2. On the other hand, if he possesses superior information about stocks’

future performance either because of selectivity or timing abilities, he would dynamically

adjust the existing holdings, overweight or underweight certain stocks. Hence, the cross

sectional dispersion of holdings adjustment may convey information about a fund’s skills.

Indeed, I find that U.S. actively managed equity mutual funds on average has a holdings

adjustment dispersion of 29.4%, where the dispersion is calculated as the standard deviation

of fund’s cross sectional stock trading (Dispi,t = stdi,t(sharesi,j,t/sharessplitadj

i,j,t−1 − 1). This

dispersion is large given that the median stock trading (sharesi,j,t/sharessplitadj

i,j,t−1 − 1) in the1Data from 2015 investment company fact book published by investment company institute (ICI).2Liquidity and other constraints may hinder funds from adjusting at exactly the optimal level, but they

would have similar or universal impact on all the existing holdings.

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sample is 0% and that the null under passive holding implies a zero Disp. Huge cross

sectional variation in terms of how funds adjust their portfolio exists at fund level, varying

from the very passive style of zero dispersion to the very active style of dispersion over 100%.

When I calculate the weighted average dispersion of holdings adjustments Dispw, with the

weights given by the last quarter end portfolio weights, the average Dispw is at 3.53% with

standard deviation 2.31%, which also indicates a large cross sectional variation across funds.

High Dispw funds are those with higher turnover, smaller age, higher expenses, and fewer

holdings. Consistent with previous known measures of mutual fund skills, high Dispw funds

are also correlated with higher fund flow, higher alpha estimated using previous 24 months,

lower R2, and higher Activeshare3

In addition, Dispw or Disp is a highly persistent fund characteristic with an autocorre-

lation of around 0.52. When sorting funds into deciles each quarter based on Dispw, funds

in the top decile (decile=10) this quarter on average has a decile rank of 7.14 in twelve

quarters. The high persistency of holdings adjustment dispersion at fund level gives us much

confidence that Dispw or Disp captures some time-invariant fund level characteristics that

likely proxies for skills.

Taken Dispw as a measure of fund skills, I find that high Dispw funds outperform low

Dispw funds for a prolonged period of time. The calendar time portfolio longing the top

decile funds and shorting the bottom decile funds generates a benchmark adjusted annualized

alpha of at least 2.35% (t=3.26). The predictability of Dispw is robust when I do a double

sorting on alpha and Dispw, or when I use regression based analysis to control for fund

characteristics and existing measures that are shown to predict fund skills. Since high Dispw

funds are also those with slightly higher expenses, hence from an investor’s perspective, it

is crucial to see if higher Dispw funds still earn higher abnormal return after expenses and

fees. Table 9 shows that after expenses, top decile funds outperform bottom decile funds by

an annualized four factor alpha of 2.03% (t=2.81).3Dispw is different from change in activeshare 4Activeshare, in fact the two has a correlation close to

zero.

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Given that Dispw measure captures funds’ activities of strategically adjusting the ex-

isting portfolio weights, one would expect the measure predict managers’ skills in selecting

stocks that outperform the benchmark or timing the portfolio weights on stocks’ character-

istics or market. Following Daniel et al. (1997), I decompose the return earned by mutual

fund into “characteristic selectivity” and “characteristic timing”, and find evidence that high

Dispw funds are both successful in stock selectivity and timing, namely they increase expo-

sure to the stock when the stock outperforms the corresponding characteristic benchmark

portfolio, or when the corresponding size, momentum or book-to-market strategy is prof-

itable. Alternatively, one could define market timing ability of the funds by benchmarking

to the market index. Consistent with the characteristics based method, funds overweight

high beta stocks when the forthcoming market realized return is high.

Building on the results that fund’s disproportionate portfolio adjustment contains infor-

mation about fund skills, I then extend the hypothesis into the cross sectional stocks. If

high Dispw funds are indeed making the right decisions, then the stocks they overweight

should outperform the stocks they underweight. For low dispersion funds, there should be

no such prediction or even opposite prediction. Indeed, I find stocks over-weighted or newly

initiated by high Dispw funds outperform those they under-weight by a monthly alpha of

0.18% (t=2.68), and no effect on low Dispw funds. Meantime, I also find some suggestive

evidence that high Dispw funds outperform low Dispw funds partially through their better

private information access, reflected in the worse information environment of stocks held by

high Dispw funds but not by low Dispw funds.

This paper thus contributes to the mutual fund literature mainly in two ways. First, no

existing literatures have looked into the information content of mutual funds disproportion-

ate portfolio adjustments. A large literature on mutual fund flow and cross sectional stock

returns are based on the assumption that mutual funds proportionately adjust their existing

holdings when having inflows or outflows (Lou, 2012; Coval and Stafford, 2007; Hau and

Lai, 2012; etc.). However, in this paper, I show that mutual funds instead of proportionately

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expand or liquidate existing holdings, a large percentage of them strategically underweight

or overweight existing holdings. Such large scale strategic adjustment would imply that the

flows pumping into (out of) stocks as driven by the flows at fund level are not purely uninfor-

mative. The disproportionate holdings adjustment if expected by investors may invalidate

the widely used predicted flow induced trading as a measure of cross sectional stock price

pressure. In fact, the results indicate that investors are learning from funds disproportionate

portfolio adjustment, and a two standard deviation increase in Dispw predicts that there

being around 2% increase in capital flows next quarter.

Second, as funds’ disproportionate holdings adjustment may convey information about

their skills, I construct a new measure of fund skill Dispw, which is simply the standard

deviation of their quarterly holdings change. Many previous literatures have constructed fund

level skill measures from different angels. For example, Kacperczyk, Sialm, and Zheng (2005,

2007) find that mutual fund industry concentration and unobserved fund performance predict

future fund performance. From the aspect of funds’ activeness, Amihud and Goyenko (2013)

use funds’ R2 estimated by regressing fund return on multifactor benchmark model, and

Cremers and Petajisto (2009) use the fraction of portfolio that differs from the benchmark

index holdings to define how active a fund is. Dispw comparing with the previous measures,

has the benefit that it does not depend on the benchmark index or the underlying factor

models that one uses, and is more clear-cut what theDispw is looking into. More specifically,

the Dispw measure is constructed based on the dynamic stock trading of mutual funds,

instead of their stock holdings at a snapshot. Hence, Dispw, by its nature, conveys also

more information about their timing ability, apart from stock selectivity. One caveat is that

I am not arguing that the Dispw measure subsumes all the existing known measure of firm

skill, but Dispw measures fund’s skill from a different angel4.

The remainder of the paper is organized as follows. Section II of the paper discusses

the data and methodology. Section III then shows the characteristic of the Dispw measure,4I discuss in detail how the Dispw measure differs with respect to other known measures at the method-

ology section.

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including its determinants and persistency. Section IV provides our evidence on Dispw as a

measure of fund skill. And section V extends our implications of disproportionate portfolio

adjustment to the cross sectional stocks. Finally, Section VI concludes.

2 Data and Methodology

Quarterly mutual fund holdings data are obtained from the CDA/Spectrum database for

period 1984-2012, and mutual fund monthly returns are obtained from the Center for Re-

search in Security Prices (CRSP) Survivor-Bias-Free Mutual Fund Database. I then merge

the holdings and return using MFLINKS. The sample period starts from 1984, because there

is selection bias in the period prior to 1983 due to the voluntary monthly return reporting in

CRSP MFDB as discussed in Fama and French (2010). Since the date on which the holdings

are valid (report date) is often different from the filing date, to calculate the number of

shares held by each mutual fund at the end of the quarter, I assume that the manager does

not trade between the report date and the quarter-end (adjusting for stock splits). Mutual

funds’ total net assets, net monthly returns, expense ratios, and other fund characteristics

are obtained from the CRSP MFDB, and the TNA-weighted average of the variable is com-

puted if the fund has multiple share classes. CRSP MFDB reports the monthly return net

expenses for mutual funds, and monthly fund returns are backed out as net returns plus 1/12

of annual fees and expenses. I focus the main analysis on the gross returns because I want

to see if the managers who disproportionally adjust holdings possess superior skills in stock

selectivity or timing. I also include a version of net returns in the robustness check, which is

useful from investor’s perspective in selecting good mutual funds versus bad mutual funds,

or making decisions on investing in active mutual funds or a passive portfolio. The results

do not depend on which returns to use.

The sample includes U.S. actively managed equity funds, whose ratio of the equity hold-

ings to total net assets is between 0.75 and 1.25. Besides, following the previous literature, I5The upper bound is used to eliminate apparent data errors.

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require a minimum fund size of $1 million and that the TNAs reported by CDA/Spectrum

and CRSP do not differ by more than a factor of two (i.e., 0.5 < TNACDA/TNACRSP < 2)6.

In order to reduce the noise in calculating the dispersion of stock holdings change, I require

funds to have at least 15 stocks in its portfolio. Following Amihud and Goyenko (2013), I

use nine style categories: (1) aggressive growth, (2) equity income, (3) growth, (4) long-term

growth, (5) growth and income, (6) mid-cap, (7) micro-cap funds, (8) small cap, and (9)

maximum capital gains to define mutual fund styles. Index funds are deleted by excluding

those whose name includes the word “index” or the abbreviation “ind”, “S&P”, “DOW”,

“Wilshire”, and/or “Russell”. Balanced funds, international funds, and sector funds are also

excluded. At the stock level, I exclude the very small stocks with price less than 5 or falls

into the NYSE lowest decile.

The cross sectional stocks’ information comes from CRSP. Following previous literature

to make sure that the results are not driven by small stocks, I restrict the sample to stocks

with price larger than 5 dollar, and exclude those small stocks that fall into the bottom

NYSE size decile.

I then calculate the cross sectional holdings adjustment dispersion for each fund each

quarter, where the dispersion is taken as standard deviation of stock trading7 as follow.

Dispi,t = stdi,t(sharesi,j,t/sharessplitadj

i,j,t−1 − 1)

The dispersion measure is constructed based on shares adjustment, instead of portfolio weight

(shares ∗ PRC), hence it captures only the active fund trading and excludes the passive

changes in portfolio weights that occur because of stock price changes during a quarter.

I also calculate the portfolio weighted standard deviation of holdings adjustment Dispwi,t,

where the weight is given by beginning of quarter portfolio weights (sharessplitadj

i,j,t−1 ·PRCsplitadj

i,j,t−1 ).6There is a severe missing data issue of TNA in the CDA database for the recent years, hence I do not

impose this criteria for period after 2008.7I delete the top and bottom 2% stock trading, which leads to a more conservative measure of Dispw

and Disp.

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To some extent, the weighted standard deviation captures more of the essence. For example,

consider a fund with 99% positions in stock A and 1% position in stock B, the fund increase

its holdings in stock A by 40% and 0% for stock B in response to a capital inflow. Then

the Disp will be 20%, while the Dispw will only be 3.98%. Disp captures more of the

cross sectional variations of fund holdings change, but is less appropriate when there is large

differences among portfolio weights. I focus the analysis on Dispw, but all results remain if

using Disp.

Requiring all the fund characteristic variables and Disp variables available then leave me

with 96,854 quarterly observations and 2,859 unique funds for the sample period 1984-2012.

The number of mutual funds in my sample increases from 175 at year 1984 to 2,034 at year

2008, and then decline slightly to 1600 in year 2012. The aggregate value of active open-

ended equity mutual funds increases from $34.94 billion in end of 1984 to $1.86 trillion in

2012. By 2012, these active mutual funds in our sample had a stockholdings of 9.13% of the

aggregate market capitalization in CRSP.

Table 1 shows the summary statistics of all the relevant variables. The summary statistics

matches well with the previous literature. On average, the fund in my sample has a total

net asset of $1,253 million, an age of 14.4 years, around 80 number of stock holdings, an

annual expense ratio of 1.23%, and 0.84% annual turnover. I also construct the known

measures that predict fund return including fund flow following Lou (2012), fund alpha and

R2 estimated using previous 24 months following Amihud and Goyenko (2013), and RetGap

following Kacperczyk et al. (2007). The Activeshare defined as active share of the fund

relative to the index that produced the lowest Active Share for a fund as of each report date

comes from Prof. Petajisto’s website for the sample period 1984-2009.

The fund on average has a positive flow of 2.39%, indicating that there are more capital

inflows into the active managed mutual fund than outflows in my sample period. The return

gap is on average of zero basis point and R2 is around 91.1% using the four factor model

to estimate. Finally, the summary statistics for Dispw and Disp indicates that there exists

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much cross sectional variations among funds in terms of how they adjust portfolios. Fund on

average has a Disp of 29.4%. This dispersion is large given that the median stock trading in

my sample is around 0%8 and that the null of passive holding indicates a Disp of zero. Huge

cross sectional variation in terms of how funds adjust their portfolio exists at fund level,

varying from the very passive style of zero dispersion to the very active style of dispersion

over 100%. Disp is concentrated in the range of 10% to 60% as shown in the Disp histogram

in figure 1. Disp is positively skewed, with some very extreme values on the right tail. When

I turn to the weighted dispersion of holdings adjustment Dispw, the average Dispw is at

3.53% with standard deviation 2.31%, which also indicates a large cross sectional variation

across funds. Consistent with the hypothesis that high dispersion in holdings adjustment

indicates higher skills of funds, Dispw and Disp is positively related with fund flow, alpha,

and Activeshare, negatively related with R2 as shown in Panel B of Table1.

Comparing with existing known measures of mutual fund skill, Dispw has the benefit that

it does not depend on the benchmark index or the underlying factor models that one uses, and

is more clear-cut what theDispw is looking into. For example, Kacperczyk, Sialm, and Zheng

(2007) find that the unobserved fund performance as measured by the difference between the

reported fund return and the return on a portfolio that invests in the previously disclosed

fund holdings predicts fund return. However, it is unclear what causes the return difference

or Retgap, and the predictability of Retgap is weak for recent years. Amihud and Goyenko

(2013) introduce funds’ R2 estimated by regressing fund return on multifactor benchmark

model as a measure of fund skill, where low R2 indicates less explanatory power of the factor

model, and higher fund skill. On one hand, there is some concern that the predictability of

R2 might be spurious or mechanical. On the other hand, the Dispw measure, comparing

with R2, has the benefit that it does not depend on certain factor model. Finally, Cremers

and Petajisto (2009) use the fraction of portfolio that differs from the benchmark index

holdings to define how active a fund is. However, Activeshare has been criticized that the8The mean of stock trade is smaller than the mean of flow in my sample, indicating that funds on average

adjust on a scale smaller than the capital flow, which is consistent with Lou (2012).

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predictability are mainly driven by the abnormal return from benchmark (Frazzini, Friedman

and Pomorski, 2015). Hence, comparing with Activeshare, Dispw is less of a concern as it

does not depend on fund’s benchmark index. Besides, Dispw is constructed based on the

dynamic stock trading of mutual funds as driven by flows, instead of their stock holdings at

a snapshot. If a fund first replicates a benchmark with a slight difference and it keep such

difference passively, then Activeshare will capture such difference permanently, while Dispw

will not. There is some concern that my Dispw measure, to some extent, may be captured

by the change of Activeshare – the difference between current quarter end and last quarter

end active share. However, Panel B of Table 1 shows that ∆Activeshare and Dispw has a

correlation close to zero, indicating that the disproportionate portfolio adjustment measure

is capturing much more than the simple change in Activeshare. Besides, the change of

Activeshare is on average -0.16%, ignorable comparing with the mean of 77.62%.

3 Characteristics of Dispw and Persistency

As there exists much cross sectional variation among funds’ disproportionate portfolio ad-

justment, a natural question would be what type of funds tends to adjust their holdings

disproportionately. Intuitively, funds will only under- or over-weight stocks if they have

private information that incentivize them to deviate from current holdings. Since private

information is unlikely to be acquired on large scale, one would expect funds with smaller

size and holdings to disproportionately adjust holdings more often. On the other hand, funds

with better skills may also trade more comparing to the null of passive investment.

I thus examine the determinants ofDispw by regressing next quarterDispwi,t+1 on lagged

Dispwi,t, fund characteristics Log(TNA), Log(Age), Turnover, Expense, Log(nholds), and

variables that have been shown to predict fund performance Flow, Alpha, R2, Retgap and

style dummies. Table 2 shows that the coefficient on lagged Dispwi,t is significantly positive

under all circumstances, indicating that funds that disproportionately adjust portfolio last

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quarter also has a high probability to do it next quarter. Dispw is a decreasing and convex

function of Log(TNA), which is consistent with Berk and Green’s (2002) suggestion that

performance-chasing investors make successful funds grow in size, which in turn erodes their

performance. This is also evidenced by the comparison of Fama-Macbeth regression vs.

Pooled regression results. The relation of Log(TNA) and Dispw is not there under Fama-

Macbeth regression, but is quite strong under Pooled regression, indicating the relation

mostly comes from fund’s time-series evolution instead of their cross sectional variations.

Fund Turnover has a positive coefficient, suggesting that high Dispw funds are accom-

panied with more frequent trading. This is consistent with the intuition that funds will

trade more when they want to exploit possessed superior information comparing to the null

of passive investment. One caveat is that the disproportionate portfolio adjustment alone

will not drive high turnover. This is because when a fund has inflows or outflows, it will

trade even under the passive style to universally level up or down its existing holdings. My

disproportionate adjustment story only argues that it will adjust differentially across them.

High Dispw funds also have higher expense fees. This could be due to the reason that

investors are willing to pay more for funds with superior information, or because fund needs

higher fees to account for its information acquisition cost. Funds with higher Dispw also

are younger funds with small number of holdings. This is because intuitively it is unlikely

for funds to possess private information for a large scale of stocks.

Next, I add existing known mutual fund skill measures to see whether high Dispw funds

are more likely to be those with high skills documented. We can see that high Dispw funds

have positive past capital inflows, with a marginal significance though. It is positively related

with fund’s four factor alpha and R2 estimated using past 24 months. The positive relation

with Retgap retains in the Pooled regression analysis but is not there under Fama-Macbeth

regression. Finally, in column (3) and (6), I also add the nine style dummies as defined

following Amihud and Goyenko (2013). The results are similar.

So far, the determinants regression indicates that Dispw is related to many of fund’s

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characteristics, has a high autocorrelation, and is positively related with funds’ skill measures

that documented by the literature. This gives us much confidence that Dispw might be

capturing some fund level characteristic that is quite persistent over time. Hence, I conduct

more tests try to understand Dispw and its persistence. Table 3 shows the transition matrix

of fund’s Dispw estimated using funds’ quarterly Dispw for the whole sample period. Each

quarter end I sort all mutual funds into deciles based on their current quarter end Dispw,

and then estimate the average transition vectors for Dispw from current quarter end to next

quarter end, where the transition vector for the fund is the probability of the fund in current

decile rank to fall into each of the decile ranks next quarter. We can see that for funds in

the top decile current quarter, 45.63% of them stay in the top decile next quarter, and only

0.95% of them migrate to the bottom decile. Figure 2 shows the average mutual fund Dispw

decile rank when we trace it from current formation quarter to 12 quarters in the future.

For each quarter, I form ten decile portfolios by ranking mutual funds based on their current

quarter end disproportionate portfolio adjustment Dispw. Holding the portfolios fixed for

the next 12 quarters, I compute the average Dispw rank for each portfolio. Funds in the top

decile have an average decile rank of 7.14 three years from now, and funds in the bottom

decile have an average rank of only 3.06 three years from now. Hence, the figure shows that

the persistence of Dispw not only remains at the neighboring two quarter, but also extends

far into the distant future. In brief, funds’ disproportionate portfolio adjustment behavior

is quite stable and persistent over a prolonged period of time.

4 Dispw and Fund Performance

4.1 Predicting fund performance by Dispw

Having shown that Dispw is a highly persistent variable that likely proxies for some fund

level characteristics, next I would like to see how this variable predicts fund level perfor-

mance. I use both portfolio sorting methodology and Fama-Macbeth regression to show the

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information content of fund disproportionate holdings adjustment, where the latter allows

controlling for the documented skill measures.

In Table 4, every quarter end I sort all mutual funds into deciles based on the Dispw

variable, form equal weighted hedging portfolio by longing the highDispw funds and shorting

the low Dispw funds, and hold for varying horizons from 3 months to 12 months. To

deal with overlapping months when holding horizon is 6 or 12 months, I follow Jegadeesh

and Titman (1993) to take the equal-weighted average return across portfolios formed in

different quarters. The “Formation Qtr.” category in Panel A of Table 4 shows the portfolio

abnormal return for the formation quarter, which is not tradable (in-sample). There exists

significant positive annualized alpha of at least 3.09% for top decile Dispw funds comparing

with bottom decile Dispw funds in the formation quarter. This indicates that funds who

disproportionately adjust their portfolios contemporaneously exhibit higher abnormal return.

The “m1-3”, “m1-6”, and “m1-12” column results are consistent with the hypothesis that

high Dispw funds disproportionately adjust portfolios for informative reasons, and hence

subsequently outperform low Dispw funds. Specifically, the four factor annualized alpha

is 2.35% (t stat=3.26) when we hold the high Dispw decile stocks for 6 months, and is

3.17% (t stat=4.18) under Fama-French three factor model. The Carhart alpha is smaller

in magnitude than the abnormal return defined under other models (ranging from 2.98% to

4.4%), consistent with Carhart (1997) that momentum explains a large proportion of funds’

persistence. The Carhart alpha shrinks to 1.5% (t stat=2.45) when we hold the stocks for

12 months, which kind of suggests that the predictability of Dispw is mostly strong at the

six month holding horizon.

Figure 3 plots the cumulative excess return of the hedge portfolio for the 24 months after

the formation time. We see that the cumulative excess return is a concave function of time,

where it first increase linearly from month 1 to 6, with a lower speed from month 6 to 12,

and finally flat out for period 12 to 24 months. Apparently, the disproportionate holdings

adjustment predicatability is not driven by the price pressure based hypothesis that would

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eventually reverse back in the horizon of two to three years.

Many of previous literatures have looked into the persistence of mutual fund performance.

For example, Grinblatt and Titman (1992), Goetzmann and Ibbotson (1994), and Brown and

Goetzmann (1995) find considerable persistence in mutual fund rankings based on abnormal

performance. Hendricks, Patel, and Zeckhauser (1993) show that mutual funds in the top

return octile outperform those in the bottom octile by about 8%. Carhart (1997) cuts that

return spread by half after including stock price momentum as an additional source of risk in

both the ranking and holding periods. More recently, Bollen and Busse (2005) find stronger

performance persistence using daily mutual fund data. Since the Dispw variable is quite

persistent, it would be interesting to see if it provides additional information than just the

pure performance persistence in mutual fund. Panel B of Table 4 indicates that when I

independently double sort funds into quintiles on four factor alpha estimated using previous

24 months, and disproportionate portfolio adjustment Dispw, the predictability of Dispw

still remains. Specifically, the three factor alpha ranges from 0.91% to 2.19% when I separate

the effect of alpha and Dispw, and is significant in four out of five alpha quintiles.

Next, I use regression based analysis to examine the predictability of Dispw, which

allows us to control for fund characteristics as well as known skill variables that have been

documented before. Specifically, I conduct the following Fama-MacBeth return predictive

regression:

Reti,t+k,t+j = β0 + β1Dispwi,t + β2Charateristicsi,t + β3Controlsi,t + εi,t,

Where the characteristics variables include Log(TNA), Log(TNA)2, Turnover, Expenses,

Log(nholds), Log(age), and the control variables include the known skill measures Flow,

alpha, R2, Retgap. In Table 10, I also include the version controlling for Activeshare. Con-

trolling for Activeshare shrinks my sample as Activeshare data comes from Prof. Petajisto’s

website and is only available till 2009. Table 5 Column (1) to (4) shows that the results un-

14

der Fama-Macbeth regression, and column (5) to (8) for pooled OLS regression. Specifically,

we can see that Log(TNA) is negatively significant, and Turnover, Log(nholds), Log(age)

have positive coefficients under different specifications, consistent with the existing known

literatures. This implies that elder funds with smaller size, higher turnover, more number of

holdings tend to outperform. Regarding the skill measures, alpha estimated using previous

24 months is positively significant under all specifications. Retgap and R2 has the right

sign as predicted by the literature, but is only statistically significant under the pooled OLS

version when controlling for all the fund characteristics and other fund skill measures. Our

variable in interest Dispw is positively significant under varying horizons from next quarter

to four quarters from now. A two standard deviation increase in Dispw leads to an addi-

tional 1% increase in the future 12 months returns, controlling for all the fund characteristics

and known fund skill predicative variables. Hence, the regression based analysis lend further

support to the argument that high Dispw funds outperform low Dispw funds, and funds

disproportionately adjust portfolio for informative reasons. In Table 10, when I control for

Activeshare in the regression analysis, we could see that the significance of Dispw remains

with a similar economic magnitude.

So far I have been focusing on the analysis of raw fund return. However, in Panel B

of Table 1 we see that high Dispw funds are more likely to be those with slightly higher

expenses. The raw return based analysis enables us to see if the managers who dispro-

portionally adjust holdings possess superior skills. However, from investor’s perspective in

selecting good mutual funds versus bad mutual funds, or making decisions on investing in

active mutual funds or a passive index fund, it is crucial to see if higher Dispw funds still

earn higher abnormal return after expenses and fees. In Table 9, I repeat Table 4 and Table

5 using funds’ return net expenses. We can see that the long short portfolio’s alpha now

shrinks slightly as high Dispw funds tend to have higher expenses than low Dispw funds.

Still, the hedging portfolio generates a four factor alpha of 2.03% (t stat=2.81) when holding

for six months, and 1.85% (t stat =2.13) when holding for three months. When excluding

15

expenses, low Dispw funds now earns a negative alpha, consistent French (2008). Panel B

of Table 9 shows the regression results using funds’ return net expenses. Again, the results

are similar to the version using raw return, and this time, even in slightly larger magnitude.

A two standard deviation in Dispw leads to over 1.13% increase in return net expenses for

the following twelve months.

4.2 Dispw and fund’s timing and selectivity ability

Having shown that the disproportionate portfolio adjustment of funds predicts fund future

performance, the next step would be to see what specific skills Dispw is reflecting, whether

it is mangers’ timing ability or selectivity? Intuitively, Dispw captures funds’ active under-

weighting and overweighting portfolio adjustment behaviors, and the stocks being under- or

over-weighted already exist in the portfolio by construction. Hence, one might expect the

Dispw measure captures not only the stock picking ability that has been widely documented

in the literature, but also their timing ability.

I adopt two ways in constructing fund’s selectivity and timing ability. Daniel et al.

(1997) propose two measures of fund skill: (1) “Characteristic Selectivity” (CS), and (2)

“Characteristic Timing” (CT). The former measures how good a fund selects stocks, and is

captured by the difference between the weighted average return of the previously disclosed

fund stock holdings and the matching benchmark of the 125 passive benchmark portfolios.

The latter measures funds’ timing ability, calculated as the difference between the weighted

return on the 125 characteristics portfolios in month t where the weights are those of the

stocks with similar characteristics in the fund in month t−1, and the weighted return on

the 125 characteristics portfolios in month t where the weights are those of the stocks with

similar characteristics in the fund in month t−13. Specifically, CT and CS are calculated as

follows:

CSt =N∑

j=1wj,t−1(Rj,t −R

bj,t−1t )

16

CTt =N∑

j=1(wj,t−1R

bj,t−1t − wj,t−13R

bj,t−13t )

Where wj,t−1 , and wj,t−13 is the portfolio weight of stock j at the end of month t − 1 and

t − 13 respectively, Rj,t is the month t return for stock j, and Rbj,t−1t is the month t return

of the characteristic-based passive portfolio that is matched to stock j during month t–1,

similarly for Rbj,t−13t .

The construction of timing and picking ability depends on the stocks’ benchmarking

portfolio. The Daniel et al. (1997)’s methodology compares stocks’ with its peers in the

similar characteristic category. Funds with positive CS has better skills in picking stocks

that outperform its peers. However, the charateristic timing ability is less straght forward

when constructed based on current and last year same month benchmarking portfolio. Alter-

natively, instead of defining “Timing” based on the 125 characteristics portfolios, one could

use the market portfolio as a benchmark. Following Kacperczyk et al. (2014), I create the

“Market Timing” (MT) that measures how a fund’s holdings of each asset, relative to the

market, comove with the systematic component of the stock return as follow:

Timingt =N∑

i=1(wi,t − wm

i,t)βi,tRmt+1

where wi,t is the weight of stock i in the fund, and wmi,t is the weight of the stock in the

market portfolio, both are constructed based on the information before time t. βi,t measures

the systematic risk of the stock i under market model using mothly return from t − 12 to

t − 1. Hence, if a fund has good market timing ability, it overweights the stocks that are

more exposed to the market portfolio in periods when the realized market return is high and

underweight them when the realized market return is low.

Table 6 shows the OLS regression results for “Characteristic Selectivity” (CS), “Charac-

teristic Timing” (CT), and “Market Timing” (MT). The dependent variable is the next 6 to

12 months monthly average CS, CT and MT. The main independent variable of interest is

Dispw, our disproportionate holdings adjustment, and I include controls and fund charac-

17

teristics as in Table 5. The results indicate that funds increase their exposure to the stock

when the stock outperforms the corresponding characteristic benchmark portfolio, which is

an evidence for their stock characteristic picking ability. The coefficient of Dispw is positive

no matter how long the window I use to define Characteristic Selectivity. Meantime, I also

find evidence that funds strategically overweight the stocks when the corresponding size,

momentum or book-to-market strategy is profitable, an evidence for their timing ability.

Similar results are found in column (7) to (9) when I define the benchmarking portfolio as

the value weighted market portfolio, indicating that funds overweight high beta stocks when

the forthcoming market realized return is high. Specifically, if a fund has a Dispw of 10%,

its characteristic selectivity, characteristic timing and market timing ability are expected

to be 0.71%, 0.87% and 1% annually. This is because Dsipw, by its construction, looks

at how fund managers dynamically adjusting their portfolio weights, hence, may also con-

vey information about their timing ability. I also conduct the regression analysis under the

Fama-Macbeth regression procedures. The regression results are qualitatively similar and

significant, though slightly weaker for the characteristic timing category.

4.3 Do investors know about high Dispw funds?

So far, I have shown that mutual fund managers disproportionately adjust their holdings,

and such behavior reflects fund managers’ superior skills in both picking stocks and timing

the market. Specifically, top decile Dispw funds outperform bottom decile Dispw funds by

around 2% annually after expenses. Since a large proportion of retail investors’ wealth is

being delegated by mutual funds (around 43.3% of household’s wealth in U.S.), a natural

follow-up question would be “Do retail investors know about this? Whether they transfer

their capitals from low Dispw funds to high Dispw funds?”

The argument here is close to the “smart money” hypothesis. If performance is pre-

dictable and at least some investors are aware of this, then cash flows into and out of funds

should be predictable by the very same metrics that predict performance (Gruber, 1996).

18

Applying to our Dispw measure, it implies that if investors are able to distinguish good

managers from bad ones based on Dispw, then capital flows should be also predicted by

Dispw.

Following the pervious literature, I define capital flow flowi,t as the change in total net

asset value minus the appreciation in the funds assets, scaled by beginning of quarter total

net assets. Appreciation is calculated as the total net asset value at the beginning of the

period times the rate of return the fund earned during the period. I also exclude MGNi,t,

which is the increase in TNA due to fund mergers in quarter t.

flowi,t = TNAi,t − TNAi,t−1 × (1 +Reti,t)−MGNi,t

TNAi,t−1

In Table 7, I present the regression results of running forward quarter capital flows against

laggedDispw, flows, fund characteristics, and other measures that predict fund performance.

Column (1) to (4) show the Fama-Macbeth regression results, and column (5) to (8) show

the pooled OLS regression with fund fixed effect and time fixed effect. Standard errors are

clustered at fund level. The Fama-Macbeth regression captures more of the capital flows into

different funds at the cross sectional level, while the OLS regression to some extent captures

more of the time series variation for each fund as fund fixed effect is included.

For all specifications, we see that younger funds with smaller size and lower expenses

attract more capital flows. Past capital flows also predict future capital flows, which is

consistent with the finding that mutual fund flows are quite persistent. Dispw, Alpha,

R2, Retgap are measures of fund skills, and all of them predicts funds’ future capital flows

to some extent. Specifically, for our measure of interest Dispw, a two standard deviation

increase in Dispw predicts that there being around 2% increase in capital flows next quarter.

The predictability of Dispw for the more distant flows gradually decreases from first quarter

to the fourth quarter, and this is especially the case for the OLS regression with fund fixed

effect. Hence, the regression results seem to imply that investors do learn and infer from

19

funds’ disproportionate portfolio adjustment behaviors about their skills. They allocate

more capitals into funds that disproportionately adjustment portfolios, especially for the

funds that recently do so. However, the increase in flows to high Dispw funds are not

enough to crowd out their superior performance, and meantime the skills of high Dispw

funds are also not fully compensated by the higher expense ratios as I show Section 4.1.

5 Dispw and Cross Sectional Stocks

Having established the relation between Dispw, fund performance, and fund skills, next I

would like to examine the information content of funds’ disproportionate portfolio adjustment

and cross sectional stock returns and characteristics. There are mainly two cross sectional

stock implications stemming from funds’ disproportionate portfolio adjustment. First, if

funds indeed disproportionately adjust portfolios for information based reasons, one should

expect there being a difference between the performance of stocks that they over-weight and

those they under-weight. Second, depending on whether funds have better public information

analytical abilities or superior access to the private information, the information environment

of the stocks held by high Dispw funds versus low Dispw funds, might be different.

5.1 Over-weighted stocks vs. Under-weighted stocks

My first hypothesis is that stocks over-weighted by high Dispw funds should outperform

those they under-weight, and this is not necessarily the case for stocks held by low Dispw

funds. The rationale is that if high Dispw funds disproportionately adjust their portfolios

for good reasons, then their information advantage would be reflected at the cross sectional

stocks they hold. Otherwise if over-weighted stocks underperform under-weighted stocks, or

ex-post realized outcome is different from ex-ante expectations, mangers would not contin-

uously involving in such disproportionate portfolio adjustment activities.

To test this hypothesis, I first rank all funds into deciles each quarter end based on their

20

disproportionate portfolio adjustment Dispw, and high (low) Dispw funds are those funds

in the top (bottom) decile of Dispw. I then sort the cross sectional of stocks into terciles for

each fund each quarter end based on the current quarter trade (sharesi,j,t/sharessplitadj

i,j,t−1 −1).

Underweight (overweight) stocks are those stocks in the bottom (top) tercile9. Table 8 shows

that over-weighted stocks outperform under-weighted stocks by a monthly alpha of 0.18% (t

stat=2.68) for stocks held by high Dispw funds. For low Dispw funds, over-weighted stocks

actually underperform under-weighted stocks (though not statistically significant), and the

difference between the “over-under” gap for high and low Dispw funds is 0.25% (t stat=2.7).

One caveat is that 0.25% monthly alpha at the cross sectional stock level might seem

a bit small in magnitude. However, remember that we are comparing stocks over-weighted

versus under-weighted by mutual funds instead of stocks held versus not held by mutual

funds. In other words, the 0.25% magnitude is conditional on stocks already being held

by mutual funds. The fact that funds still hold the under-weighted stocks (if they are not

entirely sold out) indicates that they expect the under-weighted stocks to outperform those

stocks not in their portfolio. Second, I am not claiming any trading strategy based on the

test. In fact, each stock is given the same weight in the test and I am not taking into the

portfolio weight of each stock held by high or low Dispw funds, which potentially could add

more information to the predictability of cross sectional stock returns.

I also include “New Initiate” category in the analysis, where it is consisted of stocks newly

initiated by the funds. Newly initiated stocks account for 29.64% for highDispw funds, while

only 11.38% for low Dispw funds. This is consistent with the hypothesis that high Dispw

funds enjoy positive contemporaneous return (Table 4), attracts more capital flows (Table

7), hence be able to invest more in new stocks. Stocks newly initiated by the high Dispw

funds slightly outperform those they underweight, though statistically insignificant.

I also look into the comparisons of over- vs. under-weighted stocks’ earnings announce-

ment abnormal return (unreported) to see what specific information type the funds managers9In an unreported version, I exclude stocks that are simultaneously over (under) weighted by high and

low Dispw funds, the results are even slightly stronger.

21

are trading on. There is some evidence that certain proportion of funds’ information comes

from their superior knowledge on predicting earnings announcement. The over-weighted

stocks’ three day earnings announcement abnormal return [-1, 1] is larger than the under-

weighted stocks for high Dispw funds, but is not for low Dispw funds. Since the results is

only marginally significant (0.11%, t stat=1.67 for high Dispw funds), I do not include it as

the main results.

5.2 Information environment for stocks held by high Dispw funds

My second hypothesis is that since high Dispw funds have better skills in selecting stocks

and timing the markets, their skills must stem from either their better analytical abilities in

digesting public information or superior access to private information. If the former channel

dominates, then there may or may not be any difference between the information environment

of the stocks held by high and low Dispw funds. It could be that high Dispw funds hold

stocks with good information environment and they better utilize the public information in

the market, or the information environments are the same (or even worse) for stocks held

by high Dispw funds versus low Dispw funds, but high Dispw funds have better analytical

skills in understanding and digesting the public information and then make a wiser decision.

On the other hand, if the latter channel dominates, and the information advantage of

high Dispw funds comes from their private channel, then it is more likely that stocks held

by high Dispw funds have worse information environment. The rationale is that given

everything else the same, the private information acquisition cost should be lower for stocks

with poorer information environment. Firms with rich and transparent public information

environment pre-empts managers’ ability to excavate private information, leading to higher

private information acquisition cost (Healy and Palepu, 2001; Barth et al. 2001). There

is no clean way to test exactly it is through which channel that high Dispw funds obtain

their information advantage. Looking into the information environment of the cross sectional

stocks held by high and low Dispw funds would only offer us some suggestive evidence, and

22

is by no means conclusive.

I employ two variables that are commonly used in the literature to proxy for firms’

information environment: institutional ownership (Kelley and Boehmer, 2009) and analyst

coverage (Hong, Lim and Stein, 2000). I include both the institutional ownership and the

residual institutional ownership after being orthogonalized with respect to firm size (Nagel,

2005). Analyst coverage is the number of analysts following the firm during the previous

fiscal year. I also include other firm characteristics like idiosyncratic volatility, firm size

and turnover, etc. Firms with higher idiosyncratic volatility are expected to have more firm

specific news and are thus more likely for private information to lease out.

Table 11 shows that for the stocks held solely by high Dispw funds, they on average has

35.01% institutional ownership, significantly lower than the 40.17% institutional ownership

for stocks held solely by low Dispw funds. Beside, stocks held by low Dispw funds have on

average 9.38 analysts following them, while only 7.73 analysts for low Dispw funds’ case.

High Dispw funds’ stocks also have higher turnover and idiosyncratic volatility, evidences

for their worse information environment. However, there is no significant difference between

the price level and average NYSE size decile rank for stocks held by high versus low Dispw

funds.

The empirical results seem to be more in support of the hypothesis that high Dispw

funds have better skills because of their private information advantage. However, one caveat

is that the results are based on the stocks held by high Dispw funds only or low Dispw

funds only, and stocks held simultaneously by both type of funds are excluded. Hence, we

could only say that for stocks held by high Dispw funds but not by low Dispw funds, their

information environment is poorer. In fact, unconditionally, high Dispw funds hold stocks

with more analyst coverage, higher IOR, and smaller idiosyncratic volatility than low Dispw

funds on average. This is because for the stocks that are simultaneously held by both type

funds, they have better information environment and it accounts for a larger percentage in

high Dispw funds. Thus, I do not offer conclusive evidence of which channel of information

23

do high Dispw funds get, though there seems to be some suggestive evidence that high

Dispw funds have better access to private information.

6 Conclusion

In this paper, I look into the strategic disproportionate portfolio adjustment activities of

mutual funds. Mutual fund instead of proportionally scaling up (down) existing holdings

when having inflows (outflows), they disproportionally adjust their existing positions. There

exists much cross sectional variations among firm’s portfolio adjustment behavior. On aver-

age, an actively managed equity mutual funds in U.S. has a holdings adjustment dispersion

of 29.4%, which is large comparing to the null of zero dispersion under passive investment.

The dispersion of funds’ cross sectional holdings adjustments is highly persistent and proxies

for both characteristic selectivity and timing abilities. A hedging portfolio that longs the

top decile Dispw funds and shorts the bottom decile Dispw funds generates an annualized

alpha of 2.35% - 4.40%. Investors do seem to infer from funds’ disproportionate portfolio

adjustment activities about their skills, but the capital inflows from low Dispw funds to high

Dispw funds are not enough to crowd out their superior performance.

Cross sectionally, stocks over-weighted by high dispersion funds outperform stocks under-

weighted by them, while such pattern does not exist for stocks held by low Dispw funds. The

difference between over- and under-weighted stocks also extends to the earnings announce-

ments, though statistical significance is weak. Cross sectionally, there is also evidence that

the information environment for stocks held solely by high Dispw funds is worse than the

stocks held solely by low Dispw funds, lending some suggestive support that high Dispw

funds might have better access to private information.

The results are quite robust whether using funds’ raw returns or return after expense

fees, whether the holding horizon is 3 months or 12 months, and whether I controlling for

other known fund skill measures or not.

24

Hence, the paper contributes to the mutual fund literature mainly in two ways. First,

I examine the information content of mutual funds disproportionate portfolio adjustments.

A large literature on mutual fund flow and cross sectional stock returns are based on the

assumption that mutual funds proportionately adjust their existing holdings when having

inflows or outflows (Lou, 2012; Coval and Stafford, 2007; Hau and Lai, 2011; etc.). However,

in this paper, I show that mutual funds instead of proportionately expand or liquidate

existing holdings, a large percentage of them strategically underweight or overweight existing

holdings.

Second, as funds’ disproportionate holdings adjustment may convey information about

their skills, I construct a new measure of fund skill Dispw, which is simply the standard

deviation of their quarterly cross sectional stocks’ holdings change. Dispw comparing with

the previous measures, has the benefit that it does not depend on the benchmark index or the

underlying factor models that one uses, and is more clear-cut what the Dispw is looking into.

More specifically, the Dispw measure is constructed based on the dynamic stock trading of

mutual funds, instead of their stock holdings at a snapshot. Hence, Dispw, by its nature,

conveys also more information about their timing ability, apart from stock selectivity.

25

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29

Table 1. Summary statistics on actively managed equity mutual funds

Panel A. Fund characteristics

Variable Nobs Mean Median Min Q1 Q3 Max Std

𝑇𝑁𝐴 96854 1253.2 236.2 1.0 66.2 834.2 195806.9 4829.4

𝐴𝑔𝑒 96854 14.4 10.1 0.2 5.5 17.8 88.4 13.9

#ℎ𝑜𝑙𝑑𝑠 96854 80.8 51.0 15.0 34.0 79.0 2391.0 129.2

𝐸𝑥𝑝𝑒𝑛𝑠𝑒 96854 1.23 1.19 0.00 0.96 1.48 9.72 0.46

𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟 96854 0.84 0.64 0.00 0.35 1.09 45.50 0.83

𝐹𝑙𝑜𝑤 96854 0.02 -0.01 -0.86 -0.05 0.05 7.19 0.20

𝑅𝑒𝑡𝑔𝑎𝑝 96854 -0.01% 0.00% -39.45% -0.35% 0.34% 21.38% 1.11%

𝑅2 96854 91.09% 93.51% 7.81% 88.75% 96.48% 100.00% 8.57%

𝐴𝑙𝑝ℎ𝑎 96854 0.06% 0.03% -10.25% -0.19% 0.28% 27.96% 0.52%

𝐴𝑐𝑡𝑖𝑣𝑒𝑠ℎ𝑎𝑟𝑒 60538 77.62% 80.70% 0.00% 67.62% 90.62% 99.71% 15.85%

∆𝐴𝑐𝑡𝑖𝑣𝑒𝑠ℎ𝑎𝑟𝑒 60023 -0.16% -0.08% -60.90% -1.21% 0.94% 81.16% 3.24%

𝐷𝑖𝑠𝑝 96854 29.37% 27.68% 0.00% 18.66% 38.31% 128.17% 15.00%

𝐷𝑖𝑠𝑝𝑤 96854 3.53% 3.04% 0.00% 1.99% 4.50% 27.27% 2.31%

30

Panel B. Cross-sectional correlations

𝐿𝑜𝑔(𝑇𝑁𝐴) 𝐿𝑜𝑔(𝐴𝑔𝑒) Log(#holds) 𝐸𝑥𝑝𝑒𝑛𝑠𝑒 𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟 𝐹𝑙𝑜𝑤 𝑅𝑒𝑡𝐺𝑎𝑝 𝑅2 𝐴𝑙𝑝ℎ𝑎 𝐴𝑐𝑡𝑖𝑣𝑒𝑠ℎ𝑎𝑟𝑒 ∆𝐴𝑐𝑡𝑖𝑣𝑒𝑠ℎ𝑎𝑟𝑒 𝐷𝑖𝑠𝑝𝑤 𝐷𝑖𝑠𝑝

𝐿𝑜𝑔(𝑇𝑁𝐴) 1

𝐿𝑜𝑔(𝐴𝑔𝑒) 0.467 1

Log(#holds) 0.289 0.040 1

𝐸𝑥𝑝𝑒𝑛𝑠𝑒 -0.345 -0.209 -0.276 1

𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟 -0.131 -0.087 -0.091 0.185 1

𝐹𝑙𝑜𝑤 -0.025 -0.209 -0.027 0.024 0.024 1

𝑅𝑒𝑡𝐺𝑎𝑝 -0.013 -0.011 -0.002 0.013 0.018 -0.024 1

𝑅2 0.089 0.057 0.353 -0.189 -0.065 -0.084 -0.011 1

𝐴𝑙𝑝ℎ𝑎 0.053 -0.053 -0.030 0.024 -0.038 0.229 0.014 -0.140 1

𝐴𝑐𝑡𝑖𝑣𝑒𝑠ℎ𝑎𝑟𝑒 -0.191 -0.068 -0.461 0.263 0.038 0.053 0.013 -0.379 0.109 1

∆𝐴𝑐𝑡𝑖𝑣𝑒𝑠ℎ𝑎𝑟𝑒 -0.013 0.003 0.001 0.018 -0.003 -0.033 0.029 0.013 0.011 0.094 1

𝐷𝑖𝑠𝑝𝑤 -0.128 -0.145 -0.495 0.197 0.324 0.285 0.017 -0.249 0.097 0.206 0.006 1

𝐷𝑖𝑠𝑝 0.064 -0.102 -0.012 0.063 0.306 0.243 0.021 -0.076 0.078 -0.048 -0.003 0.770 1

Table 1 shows the summary statistics for the US actively managed equity mutual fund for the sample period 1984-2012. Panel A displays the fund

characteristics and Panel B shows the contemporaneous correlations. 𝑇𝑁𝐴 is the total net asset in millions at the end of each quarter. 𝐴𝑔𝑒 is the number

of years since the fund first offered. #holds is the number of stocks held in the fund. Expense is the annual expense ratio. Turnover is the minimum of

aggregated sales or aggregated purchases of securities divided by the average twelve-month TNA of the fund. Both expense and turnover are in

percentage and aggregated by share classes. Flow is the investment flow to the fund in the quarter, constructed based on Lou (2012). Retgap measures the

unobserved actions of mutual fund and is constructed following Kacperczyk et al. (2008). Following Amihud and Goyenko (2013), 𝑅2 and Alpha are

estimated based on Carhart (1997) factor model over the twenty-four months before the quarter end. Active share is available on Petajisto website, and is

defined as active share of the fund relative to the index that produced the lowest Active Share for a fund as of each report date. And ∆𝐴𝑐𝑡𝑖𝑣𝑒𝑠ℎ𝑎𝑟𝑒 is the

current quarter end active share minus last quarter end active share. Dispw is our main variable of interest, which measures fund disproportionate

holdings adjustment. Dispw is calculated as the cross sectional weighted average standard deviation of funds’ existing holdings change (𝑆ℎ𝑎𝑟𝑒𝑠𝑡

𝑆ℎ𝑎𝑟𝑒𝑠𝑡−1 − 1) at

each quarter end, with the weights being the quarter beginning portfolio weights. Disp is the non-weighted standard deviation of existing holdings change.

The mutual fund return data is from CRSP survivorship-bias-free mutual fund database and fund holdings data is from Thompson Financials

CDA/Spectrum database. We require all the variables in Table 1 Panel A to be available for the fund quarter to remain in our sample. Thus, our sample

consists of 96,854 fund quarterly observations with 2,859 unique funds.

31

Table 2. Determinants of Dispw

Dep. Var.: Next Quarter Dispw

Fama-Macbeth Regression Pooled OLS

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

𝐷𝑖𝑠𝑝𝑤 0.401 0.394 0.393 0.415 0.407 0.405

(42.67)*** (38.50)*** (38.26)*** (37.78)*** (32.96)*** (33.14)***

𝐿𝑜𝑔(𝑇𝑁𝐴) -0.000 -0.000 -0.000 -0.001 -0.001 -0.001

(0.95) (0.68) (0.96) (3.31)*** (3.18)*** (3.08)***

[𝐿𝑜𝑔(𝑇𝑁𝐴)]2 0.000 0.000 0.000 0.000 0.000 0.000

(1.83)* (1.50) (1.80)* (3.51)*** (3.22)*** (3.12)***

Turnover 0.007 0.007 0.007 0.005 0.005 0.005

(18.72)*** (18.55)*** (18.18)*** (8.09)*** (7.89)*** (7.80)***

Expense 0.002 0.002 0.002 0.002 0.001 0.001

(6.99)*** (6.53)*** (6.32)*** (5.01)*** (4.13)*** (3.93)***

Log(nholds) -0.008 -0.007 -0.007 -0.006 -0.006 -0.006

(32.21)*** (28.70)*** (27.79)*** (33.11)*** (29.37)*** (29.43)***

𝐿𝑜𝑔(𝑎𝑔𝑒) -0.001 -0.001 -0.001 -0.001 -0.001 -0.001

(8.13)*** (7.74)*** (7.29)*** (5.96)*** (5.52)*** (5.05)***

𝐹𝑙𝑜𝑤 0.002 0.002 0.001 0.002

(1.77)* (1.66)* (1.73)* (1.80)*

Alpha 0.044 0.045 0.053 0.051

(1.19) (1.26) (2.51)** (2.42)**

𝑅2 -0.010 -0.010 -0.014 -0.014

(4.58)*** (4.31)*** (7.07)*** (6.89)***

Retgap 0.010 0.008 0.031 0.031

(0.69) (0.58) (2.47)** (2.44)**

Intercept 0.047 0.055 0.056 0.045 0.057 0.062

(24.95)*** (20.37)*** (17.72)*** (34.62)*** (26.30)*** (8.51)***

Style dummies NO NO YES NO NO YES

R2_A 0.38 0.39 0.40 0.33 0.33 0.33

N 93,169 93,169 93,169 93,169 93,169 93,169

This table shows the determinants regression of fund disproportionate holdings adjustment (𝐷𝑖𝑠𝑝𝑡+1) on

lagged 𝐷𝑖𝑠𝑝𝑡, fund characteristics variables 𝐿𝑜𝑔(𝑇𝑁𝐴), 𝐿𝑜𝑔(𝐴𝑔𝑒), 𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟, 𝐸𝑥𝑝𝑒𝑛𝑠𝑒, 𝐿𝑜𝑔(𝑛ℎ𝑜𝑙𝑑𝑠), and

variables that have been shown to predict fund performance 𝐹𝑙𝑜𝑤, 𝐴𝑙𝑝ℎ𝑎, 𝑅2, 𝑅𝑒𝑡𝑔𝑎𝑝. We also include the

fund style dummies in column (3) and (6), where style dummies are defined following Amihud and Goyenko

(2013). The sample period is from 1984-2012. Column (1) to (3) show the results under Fama-Macbeth

regressions, while column (4) to (6) display the results under pooled OLS regression with time fixed effect and

standard errors are clustered at fund level. All explanatory variables are defined at the end of quarter 𝑡. 1%, 5%,

and 10% statistical significance is indicated with ∗∗∗,∗∗, and ∗, respectively.

32

Table 3. The migration of Dispw – Average Transition Vectors for Dispw

Ranks 1 2 3 4 5 6 7 8 9 10

1 45.63% 23.85% 5.72% 5.26% 10.33% 2.25% 2.91% 1.62% 1.48% 0.95%

2 13.71% 38.21% 10.93% 6.68% 19.73% 2.89% 4.15% 1.99% 1.03% 0.68%

3 6.46% 22.64% 18.17% 11.37% 24.41% 4.48% 6.94% 2.90% 1.86% 0.76%

4 4.15% 13.39% 19.79% 15.40% 21.19% 7.05% 11.09% 4.61% 2.33% 1.01%

5 3.35% 8.79% 17.55% 18.02% 14.22% 10.48% 15.55% 6.96% 3.63% 1.46%

6 2.03% 6.22% 14.82% 16.57% 10.06% 14.62% 17.44% 10.57% 5.44% 2.24%

7 1.72% 4.13% 10.82% 13.81% 6.56% 18.02% 16.40% 15.61% 9.51% 3.41%

8 1.59% 2.99% 6.97% 9.94% 4.89% 17.98% 15.21% 19.08% 15.99% 5.34%

9 1.01% 1.99% 4.91% 6.52% 3.18% 14.24% 9.76% 20.77% 24.26% 13.34%

10 1.02% 1.12% 3.62% 3.84% 2.61% 10.07% 6.24% 18.13% 27.80% 25.54%

This table shows the transition matrix of Dispw estimated using funds’ quarterly Dispw for the sample period

1984-2012. Each quarter end I sort all mutual funds into deciles based on their quarter end Dispw, and then

estimate the average transition vectors for Dispw from current quarter end to next quarter end, where the

transition vector for the fund is the probability of the fund in current decile rank to fall into each of the decile

ranks next quarter. The probability in row rank 𝑥 and column rank 𝑦 represents the transition probability of the

fund that currently has a Dispw in decile 𝑥 that ends in decile 𝑦 next quarter.

33

Table 4. Predicting future fund performance using Dispw – Portfolio Sort

Panel A. Sorting on Dispw

Mutual funds ranked by Dispw

Decile Excess

return

3-factor

alpha

4-factor

alpha

5-factor

alpha Excess

return

3-factor

alpha

4-factor

alpha

5-factor

alpha

Excess

return

3-factor

alpha

4-factor

alpha

5-factor

alpha

Excess

return

3-factor

alpha

4-factor

alpha

5-factor

alpha

Formation Qtr.

m1-3

m1-6

m1-12

1 7.41% 0.00% 0.34% -0.36%

7.44% 0.26% 0.68% 0.04%

7.04% 0.06% 0.43% -0.27%

7.54% 0.24% 0.55% -0.18%

10 11.41% 3.86% 3.41% 4.80%

10.65% 3.30% 2.86% 3.98%

10.02% 3.23% 2.78% 4.13%

9.78% 2.49% 2.05% 3.28%

10-1 4.00% 3.86% 3.07% 5.15%

3.22% 3.04% 2.17% 3.93%

2.98% 3.17% 2.35% 4.40%

2.24% 2.25% 1.50% 3.46%

(3.83) (5.32) (4.44) (7.08)

(2.54) (3.37) (2.51) (4.27)

(2.60) (4.18) (3.26) (5.88)

(2.09) (3.49) (2.45) (5.45)

Panel B. Double sorting on fund Alpha and Dispw

Dispw (Holding for 6 months, 3-Factor alpha)

Dispw (Holding for 6 months, 4-Factor alpha)

Alpha Low 2 3 4 High High - Low

Low 2 3 4 High High - Low

Low -0.27 -0.27 -0.55 0.26 0.64 0.92

0.06 -0.21 -0.63 0.00 0.58 0.52

(0.38) (0.45) (0.87) (0.45) (0.85) (1.33)

(0.08) (0.33) (0.94) (0.00) (0.72) (0.75)

2 -0.40 -0.16 0.35 0.17 1.21 1.60**

-0.14 0.03 0.32 0.13 0.88 1.02*

(0.87) (0.34) (0.81) (0.36) (1.88) (2.50)

(0.30) (0.06) (0.70) (0.27) (1.32) (1.69)

3 -0.41 0.24 0.45 0.08 1.61 2.03***

0.01 0.32 0.49 -0.03 1.45 1.44**

(0.92) (0.57) (1.04) (0.18) (2.26) (2.72)

(0.02) (0.73) (1.06) (0.05) (1.94) (2.10)

4 0.36 0.17 0.79 1.15 1.96 1.60***

0.70 0.48 0.78 1.12 1.63 0.92

(0.72) (0.32) (1.52) (2.07) (3.29) (2.6)

(1.45) (0.90) (1.46) (1.83) (2.55) (1.57)

High 0.95 1.05 1.35 1.61 3.13 2.19***

1.16 1.22 1.27 1.36 2.68 1.52*

(1.25) (1.50) (1.99) (2.12) (3.86) (2.60)

(1.53) (1.73) (1.81) (1.75) (3.09) (1.89)

High - Low 1.22 1.32 1.90** 1.35* 2.49***

1.10 1.43* 1.89** 1.37* 2.10**

(1.17) (1.57) (2.18) (1.70) (2.92) (1.04) (1.68) (2.12) (1.71) (2.43)

34

Panel A reports the association between our disproportionate holdings adjustment variable Dispw and mutual fund future annualized alpha (12 ∗ 𝛼 ). At

the end of each quarter, we form calendar time portfolios by sorting all mutual funds into deciles based on 𝐷𝑖𝑠𝑝𝑖,𝑡 , the disproportionate holdings

adjustment of the mutual fund in the quarter. The portfolios are rebalanced every quarter and are held for corresponding time periods. To deal with

overlapping portfolios in each holding month, we follow Jegadeesh and Titman (1993) to take the equal-weighted average return across portfolios formed

in different quarters. Monthly returns with different risk adjustments are reported: the return in excess of the risk-free rate, the Fama-French three-factor

alpha, the Carhart four-factor alpha, and the Fama-French five-factor alpha. Panel B displays the case when we independently sort on fund’s four factor

alpha and funds current quarter end Dispw. T -statistics, shown in parentheses, are computed based on standard errors with Newey-West corrections of

corresponding lags. 1%, 5%, and 10% statistical significance is indicated with ∗∗∗,∗∗, and ∗, respectively.

35

Table 5. Predicting future fund return using Dispw – Regression based approach

Dep.Var: Forward Cumulative Fund Quarterly Return (in %)

Fama-Macbeth Regression Pooled OLS

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

(Qtr.1) (Qtr.2) (Qtr.3) (Qtr.4) (Qtr.1) (Qtr.2) (Qtr.3) (Qtr.4)

𝐷𝑖𝑠𝑝𝑤 4.446 8.607 11.590 15.508 8.275 11.344 16.586 19.766

(0.91) (2.00)** (2.06)** (2.62)** (4.71)*** (4.28)*** (4.62)*** (4.52)***

𝐿𝑜𝑔(𝑇𝑁𝐴) -0.226 -0.567 -0.770 -0.988 -0.184 -0.359 -0.593 -0.754

(1.87)* (3.44)*** (3.64)*** (4.13)*** (3.04)*** (3.44)*** (3.83)*** (3.81)***

[𝐿𝑜𝑔(𝑇𝑁𝐴)]2 0.014 0.035 0.045 0.058 0.008 0.012 0.024 0.031

(1.25) (2.35)** (2.44)** (2.74)*** (1.42) (1.32) (1.75)* (1.76)*

Turnover 0.161 0.256 0.290 0.314 0.013 -0.014 -0.065 -0.105

(1.61) (1.87)* (1.68)* (1.58) (0.33) (0.22) (0.73) (0.94)

Expense 0.071 0.073 0.044 0.082 0.020 0.020 -0.059 -0.105

(0.57) (0.41) (0.20) (0.32) (0.29) (0.17) (0.34) (0.47)

Log(nholds) 0.148 0.279 0.451 0.543 0.348 0.583 0.819 0.971

(1.31) (2.37)** (2.76)*** (3.04)*** (7.97)*** (7.80)*** (7.53)*** (7.09)***

𝐿𝑜𝑔(𝑎𝑔𝑒) 0.047 0.141 0.159 0.146 0.044 0.121 0.148 0.154

(0.89) (2.37)** (2.06)** (1.59) (1.33) (2.08)** (1.70)* (1.38)

𝐹𝑙𝑜𝑤 0.316 -0.292 -0.465 -1.330 -0.392 -0.909 -1.342 -2.163

(0.53) (0.39) (0.50) (1.43) (2.42)** (3.73)*** (4.04)*** (5.31)***

Alpha 34.420 59.445 67.564 62.142 18.529 25.471 1.491 -25.989

(2.17)** (2.94)*** (3.06)*** (2.55)** (2.45)** (1.97)** (0.08) (1.17)

𝑅2 0.304 0.273 -0.575 -1.005 -2.989 -6.072 -8.870 -11.001

(0.31) (0.19) (0.33) (0.50) (7.40)*** (8.41)*** (8.38)*** (8.15)***

Retgap 6.795 4.353 0.640 11.292 2.959 9.993 22.468 35.285

(1.21) (0.55) (0.07) (1.05) (1.03) (2.21)** (3.87)*** (4.97)***

Intercept 2.434 5.414 10.461 14.489 3.550 8.441 13.618 18.670

(2.01)** (3.02)*** (4.48)*** (5.82)*** (5.06)*** (8.38)*** (7.82)*** (8.10)***

Style dummies YES YES YES YES YES YES YES YES

R2_A 0.15 0.15 0.15 0.14 0.59 0.63 0.61 0.60

N 95,683 94,450 93,227 92,011 95,683 94,450 93,227 92,011

This table reports Fama-MacBeth and Pooled OLS forecasting regressions of future fund returns. The

dependent variable is the next quarter return for column (1) and (5), next two quarter cumulative return for

column (2) and (6), next three quarter cumulative return for column (3) and (7), and next four quarter

cumulative return for column (4) and (8). The main independent variable of interest is Dispw, the

disproportionate holdings adjustment variable. We include fund characteristic variables as controls, and also

variables that have shown to predict fund performance, including the Carhart four-factor fund alpha estimated

using previous 24 months fund return; flow, the capital flow to the mutual fund in the previous quarter; 𝑅2,

estimated using previous 24 months return following Amihud and Goyenko (2013); Retgap as defined based

on Kacperczyk, Sialm and Zheng (2007), and also the nine style dummies defined in Amihud and Goyenko

(2013). 1%, 5%, and 10% statistical significance is indicated with ∗∗∗,∗∗, and ∗, respectively.

36

Table 6. Dispw on stock selectivity and timing

Characteristics Selectivity Characteristic Timing Market Timing

(1) (2) (3) (4) (5) (6) (7) (8) (9)

(6 m) (9 m) (12 m) (6 m) (9 m) (12 m) (6 m) (9 m) (12 m)

𝐷𝑖𝑠𝑝𝑤 0.561 0.539 0.590 0.488 0.503 0.727 0.769 0.788 0.831

(2.51)** (2.65)*** (3.11)*** (2.25)** (2.48)** (3.74)*** (3.56)*** (3.81)*** (4.24)***

𝐿𝑜𝑔(𝑇𝑁𝐴) -0.015 -0.018 -0.019 -0.024 -0.025 -0.022 0.019 0.018 0.019

(1.88)* (2.23)** (2.38)** (2.93)*** (2.92)*** (2.41)** (2.27)** (2.05)** (2.13)**

[𝐿𝑜𝑔(𝑇𝑁𝐴)]2 0.000 0.001 0.001 0.000 0.000 0.000 -0.002 -0.002 -0.002

(0.61) (0.91) (1.12) (0.46) (0.61) (0.42) (3.30)*** (3.04)*** (3.04)***

Turnover -0.007 -0.008 -0.009 -0.023 -0.023 -0.025 0.016 0.015 0.016

(1.33) (1.49) (1.70)* (3.97)*** (4.15)*** (4.87)*** (3.10)*** (3.07)*** (3.40)***

Expense 0.004 -0.001 -0.004 -0.034 -0.034 -0.028 0.103 0.098 0.098

(0.42) (0.06) (0.44) (4.05)*** (3.97)*** (3.15)*** (9.98)*** (9.77)*** (9.87)***

Log(nholds) -0.001 -0.002 -0.003 0.004 -0.000 0.006 0.004 0.002 0.001

(0.22) (0.39) (0.56) (0.68) (0.05) (1.18) (0.58) (0.25) (0.11)

𝐿𝑜𝑔(𝑎𝑔𝑒) 0.028 0.026 0.022 0.011 0.006 0.003 -0.004 -0.006 -0.009

(5.62)*** (5.38)*** (4.66)*** (2.43)** (1.26) (0.53) (0.71) (1.05) (1.73)*

𝐹𝑙𝑜𝑤 0.155 0.110 0.059 -0.189 -0.280 -0.318 -0.016 -0.056 -0.084

(6.51)*** (4.96)*** (3.20)*** (8.77)*** (12.48)*** (14.51)*** (0.91) (3.30)*** (5.21)***

Intercept -0.005 0.019 0.040 0.129 0.153 0.148 0.469 0.493 0.521

(0.13) (0.52) (1.09) (3.43)*** (4.07)*** (3.70)*** (10.64)*** (11.39)*** (11.93)***

R2_A 0.12 0.12 0.12 0.93 0.92 0.91 0.87 0.86 0.84

N 96,850 96,850 96,850 96,850 96,850 96,850 96,850 96,850 96,850

This table reports OLS regressions of future fund characteristic selectivity (CS), characteristic timing (CT), and market timing (MT). The dependent

variable is the next 6 to 12 months monthly average CS, CT and MT. We calculate CS and CT following DGTW(1997), where the holdings of the fund

each quarter is based on its beginning of quarter holdings. And MT is calculated following Kacperczyk et al. (2014). The main independent variable of

interest is Dispw, the disproportionate holdings adjustment variable. We include time fixed effects and fund characteristic variables as controls. The

standard errors are clustered at fund level. 1%, 5%, and 10% statistical significance is indicated with ∗∗∗,∗∗, and ∗, respectively.

37

Table 7. Prediction of capital flows

Dep.Var: Forward Capital Flows

Fama-Macbeth Regression

Pooled OLS

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

(1st Qtr) (2

nd Qtr) (3

rd Qtr) (4

th Qtr)

(1

st Qtr) (2

nd Qtr) (3

rd Qtr) (4

th Qtr)

𝐷𝑖𝑠𝑝𝑤 0.505 0.552 0.368 0.339

0.372 0.328 0.203 0.088

(6.73)*** (5.78)*** (3.38)*** (3.90)***

(6.57)*** (5.86)*** (3.73)*** (1.64)

𝐿𝑜𝑔(𝑇𝑁𝐴) -0.031 -0.034 -0.036 -0.038

-0.057 -0.061 -0.069 -0.065

(7.37)*** (6.69)*** (8.50)*** (9.30)***

(10.59)*** (10.98)*** (11.95)*** (11.81)***

[𝐿𝑜𝑔(𝑇𝑁𝐴)]2 0.002 0.002 0.002 0.002

0.002 0.002 0.002 0.001

(6.20)*** (5.37)*** (6.67)*** (7.44)***

(5.06)*** (3.94)*** (3.99)*** (2.83)***

Turnover 0.004 0.002 0.006 0.006

0.005 0.003 0.007 0.008

(1.60) (1.00) (2.39)** (2.09)**

(2.90)*** (1.60) (2.81)*** (3.65)***

Expense -0.009 -0.013 -0.013 -0.015

-0.010 -0.011 -0.014 -0.016

(2.79)*** (4.08)*** (3.62)*** (4.44)***

(1.98)** (2.03)** (2.44)** (2.73)***

Log(nholds) 0.014 0.015 0.012 0.009

0.014 0.008 0.007 0.002

(6.24)*** (7.06)*** (5.67)*** (3.87)***

(5.39)*** (3.16)*** (2.41)** (0.79)

𝐿𝑜𝑔(𝑎𝑔𝑒) -0.012 -0.010 -0.009 -0.007

-0.035 -0.023 -0.019 -0.012

(10.91)*** (8.86)*** (8.21)*** (6.45)***

(10.88)*** (6.94)*** (5.08)*** (3.44)***

𝐹𝑙𝑜𝑤 0.253 0.166 0.128 0.090

0.213 0.116 0.062 0.041

(14.35)*** (11.25)*** (9.02)*** (7.39)***

(19.89)*** (16.88)*** (10.15)*** (6.86)***

Alpha 5.083 4.459 3.905 3.273

4.200 3.372 2.863 2.206

(12.70)*** (13.07)*** (11.69)*** (9.40)***

(14.34)*** (12.79)*** (11.84)*** (10.50)***

𝑅2 -0.045 -0.056 -0.055 -0.038

-0.048 -0.027 0.011 0.033

(2.20)** (3.03)*** (3.16)*** (2.41)**

(2.89)*** (1.61) (0.67) (2.03)**

Retgap 0.100 0.194 0.109 0.107

-0.096 0.090 0.019 0.164

(1.01) (1.63) (0.96) (1.02)

(1.23) (1.07) (0.22) (2.32)**

Intercept 0.131 0.152 0.184 0.184

0.238 0.283 0.235 0.263

(3.93)*** (4.18)*** (5.50)*** (5.52)***

(9.68)*** (10.52)*** (8.40)*** (9.63)***

Style YES YES YES YES

R2 0.23 0.17 0.15 0.13

0.23 0.18 0.17 0.17

N 93,995 91,173 88,392 85,653

93,995 91,173 88,392 85,653

This table shows the regression of the realized cash flows for the 1st to 4

th quarters against the last quarter

Dispw for the sample period 1984-2012. We include last quarter end fund characteristics and capital flows as

controls. Column (1) to (4) show the Fama-Macbeth regression results, and column (5) to (8) show the pooled

OLS regression with fund fixed effect and time fixed effect. Standard errors are clustered at fund level. 1%,

5%, and 10% statistical significance is indicated with ∗∗∗,∗∗, and ∗, respectively

38

Table 8. Information content of stocks held by High Dispw funds

Panel A. Average monthly excess return (6 months, in %)

Underweight Overweight New Initiate Over - Under New - Under

Low Dispw (Decile 0) 1.218 1.157 1.165 -0.061 (1.16) -0.053 (0.81)

High Dispw (Decile 9) 1.055 1.200 1.097 0.145*** (2.75) 0.042 (0.66)

Over - Under -0.163 0.043 -0.068 0.206*** (2.81) 0.095 (1.06)

Panel B. Average monthly FF3F Alpha (6 months, in %)

Underweight Overweight New Initiate Over - Under New - Under

Low Dispw (Decile 0) -0.060 -0.130 -0.014 -0.070 (1.14) 0.047 (0.60)

High Dispw (Decile 9) -0.145 0.034 -0.028 0.180*** (2.68) 0.117 (1.57)

Over - Under -0.085 0.164 -0.015 0.249*** (2.70) 0.070 (0.59)

This table shows the average monthly excess return and FF3F alpha for the stocks over-weighted, under-

weighted, and newly initiated by high and low Dispw funds. We rank all funds into deciles each quarter end

based on their disproportionate portfolio adjustment Dispw, and high (low) Dispw funds are those funds in the

top (bottom) decile of Dispw. We then sort the cross sectional of stocks into terciles for each fund each quarter

end based on the current quarter trade (sharesi,j,t

𝑠ℎ𝑎𝑟𝑒𝑠𝑖,𝑗,𝑡−1− 1). Underweight (overweight) stocks are those stocks in

the bottom (top) tercile.

39

Table 9. Predicting future fund return (net expenses) using Dispw

Panel A. Sorting on Dipw

Mutual funds ranked by Dispw

Decile Excess

return

3-factor

alpha

4-factor

alpha

5-factor

alpha Excess

return

3-factor

alpha

4-factor

alpha

5-factor

alpha

Excess

return

3-factor

alpha

4-factor

alpha

5-factor

alpha

Excess

return

3-factor

alpha

4-factor

alpha

5-factor

alpha

Formation Qtr.

m1-3

m1-6

m1-12

1 6.37% -1.04% -0.71% -1.40%

6.39% -0.79% -0.36% -1.01%

6.00% -0.98% -0.61% -1.31%

6.51% -0.80% -0.48% -1.21%

10 10.05% 2.51% 2.05% 3.44%

9.28% 1.93% 1.49% 2.60%

8.66% 1.86% 1.42% 2.76%

8.42% 1.13% 0.69% 1.92%

10-1 3.69% 3.55% 2.76% 4.84%

2.89% 2.71% 1.85% 3.61%

2.66% 2.85% 2.03% 4.07%

1.91% 1.92% 1.17% 3.13%

(3.52) (4.89) (3.98) (6.64)

(2.29) (3.01) (2.13) (3.92)

(2.32) (3.75) (2.81) (5.45)

(1.78) (2.99) (1.92) (4.94)

Panel B. Regression analysis

Dep.Var: Forward Cumulative Fund Quarterly Return (net expenses, in %)

Fama-Macbeth Regression Pooled OLS

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

(Qtr.1) (Qtr.2) (Qtr.3) (Qtr.4) (Qtr.1) (Qtr.2) (Qtr.3) (Qtr.4)

𝐷𝑖𝑠𝑝𝑤 5.622 11.926 16.652 20.022 7.395 13.461 19.229 24.476

(2.76)*** (4.00)*** (5.02)*** (4.72)*** (6.70)*** (7.72)*** (7.85)*** (7.84)***

𝐿𝑜𝑔(𝑇𝑁𝐴) -0.231 -0.415 -0.619 -0.844 -0.089 -0.157 -0.282 -0.359

(2.78)*** (3.08)*** (4.00)*** (4.80)*** (2.32)** (2.16)** (2.60)*** (2.47)**

[𝐿𝑜𝑔(𝑇𝑁𝐴)]2 0.013 0.022 0.034 0.047 -0.001 -0.005 -0.003 -0.004

(1.90)* (2.01)** (2.65)*** (3.28)*** (0.44) (0.72) (0.29) (0.35)

Turnover 0.150 0.212 0.270 0.358 -0.006 -0.050 -0.090 -0.137

(1.57) (1.49) (1.60) (1.71)* (0.28) (1.11) (1.37) (1.57)

Expense -0.273 -0.517 -0.763 -0.920 -0.255 -0.506 -0.773 -1.016

(3.31)*** (3.78)*** (4.42)*** (4.47)*** (5.78)*** (5.85)*** (5.95)*** (5.70)***

40

Log(nholds) 0.142 0.322 0.432 0.461 0.288 0.534 0.712 0.853

(2.39)** (3.83)*** (3.85)*** (3.33)*** (10.41)*** (10.76)*** (10.10)*** (9.27)***

𝐿𝑜𝑔(𝑎𝑔𝑒) 0.078 0.158 0.212 0.271 0.132 0.231 0.299 0.365

(2.33)** (3.55)*** (4.32)*** (4.61)*** (6.42)*** (5.85)*** (5.11)*** (4.70)***

𝐹𝑙𝑜𝑤 0.011 -0.470 -0.730 -1.127 0.232 0.034 -0.526 -1.169

(0.05) (1.04) (1.29) (1.85)* (1.97)** (0.20) (2.17)** (4.10)***

Alpha 44.761 75.967 95.754 105.453 26.231 35.157 31.227 13.264

(2.75)*** (3.44)*** (4.06)*** (4.24)*** (4.31)*** (3.82)*** (2.43)** (0.87)

𝑅2 0.137 -0.432 -0.458 -0.340 -3.576 -6.901 -8.979 -10.656

(0.13) (0.28) (0.24) (0.16) (10.35)*** (11.13)*** (10.00)*** (9.15)***

Retgap 5.235 0.738 4.527 11.238 -1.582 -0.285 12.795 31.078

(1.20) (0.11) (0.54) (1.17) (0.68) (0.09) (2.52)** (5.34)***

Intercept 2.889 6.320 9.218 13.008 4.842 10.031 14.031 18.358

(2.61)** (3.57)*** (4.30)*** (5.52)*** (14.39)*** (13.53)*** (11.51)*** (11.18)***

Style dummies YES YES YES YES YES YES YES YES

R2_A 0.24 0.25 0.24 0.23 0.81 0.80 0.79 0.78

N 96,796 96,197 95,307 94,331 96,796 96,197 95,307 94,331

This table replicates table 4&5 using mutual funds return net expenses as directly reported by CRSP MFDB. Panel A reports the association between our

disproportionate holdings adjustment variable Dispw and mutual fund future returns net expenses. At the end of each quarter, we form calendar time

portfolios by sorting all mutual funds into deciles based on 𝐷𝑖𝑠𝑝𝑖,𝑡, the disproportionate holdings adjustment of the mutual fund in the quarter. The

portfolios are rebalanced every quarter and are held for corresponding time periods. Monthly returns with different risk adjustments are reported: the

return in excess of the risk-free rate, the Fama-French three-factor alpha, and the Carhart four-factor alpha. Panel B replicates table 5 by replacing the

dependent variable with the future fund returns net expenses for the following one to four quarters. T -statistics, shown in parentheses, are computed

based on standard errors with Newey-West corrections of corresponding lags. 1%, 5%, and 10% statistical significance is indicated with ∗∗∗,∗∗, and ∗,

respectively

41

Table 10. Predicting future fund return, controlling for Activeshare

Dep.Var: Forward Cumulative Fund Quarterly Return (in %)

Fama-Macbeth Regression Pooled OLS

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

(Qtr.1) (Qtr.2) (Qtr.3) (Qtr.4) (Qtr.1) (Qtr.2) (Qtr.3) (Qtr.4)

𝐷𝑖𝑠𝑝𝑤 6.993 10.338 11.796 16.222 13.506 17.461 22.834 27.876

(1.20) (1.88)* (1.87)* (2.37)** (5.99)*** (5.15)*** (4.85)*** (4.83)***

𝐴𝑐𝑡𝑖𝑣𝑒𝑠h𝑎𝑟𝑒 1.186 2.548 3.680 4.844 3.243 6.602 10.149 13.907

(1.16) (1.64) (2.09)** (2.38)** (13.01)*** (15.45)*** (15.61)*** (16.51)***

𝐿𝑜𝑔(𝑇𝑁𝐴) -0.256 -0.615 -0.915 -1.151 -0.279 -0.459 -0.732 -0.993

(1.53) (2.89)*** (3.35)*** (3.71)*** (2.51)** (2.49)** (2.68)*** (2.88)***

[𝐿𝑜𝑔(𝑇𝑁𝐴)]2 0.013 0.034 0.049 0.063 0.012 0.015 0.027 0.040

(0.89) (1.80)* (2.09)** (2.33)** (1.34) (1.01) (1.22) (1.40)

Turnover 0.154 0.269 0.362 0.468 0.053 0.055 0.072 0.097

(1.10) (1.42) (1.61) (1.85)* (1.30) (0.79) (0.69) (0.73)

Expense 0.081 0.063 -0.102 -0.068 -0.014 -0.015 -0.143 -0.283

(0.50) (0.27) (0.35) (0.21) (0.16) (0.09) (0.60) (0.91)

Log(nholds) 0.361 0.694 1.003 1.255 0.659 1.170 1.721 2.241

(2.21)** (3.13)*** (3.65)*** (4.04)*** (10.50)*** (11.02)*** (11.01)*** (11.22)***

𝐿𝑜𝑔(𝑎𝑔𝑒) 0.130 0.256 0.308 0.306 0.111 0.183 0.227 0.228

(2.21)** (3.67)*** (3.41)*** (3.03)*** (2.74)*** (2.58)*** (2.16)** (1.70)*

𝐹𝑙𝑜𝑤 0.945 0.266 0.648 -0.453 -0.359 -1.131 -1.726 -2.637

(1.20) (0.31) (0.59) (0.40) (1.80)* (3.71)*** (4.24)*** (5.20)***

Intercept 0.990 2.565 4.542 6.419 -2.586 -4.417 -6.320 -8.030

(0.73) (1.25) (1.71)* (2.04)** (5.04)*** (5.02)*** (4.83)*** (4.84)***

R2_A 0.13 0.12 0.11 0.11 0.55 0.62 0.61 0.61

N 60,155 59,602 58,974 58,332 60,155 59,602 58,974 58,332

This table reports Fama-MacBeth and Pooled OLS forecasting regressions of future fund returns, controlling

for Activeshare. Our activeshare data comes from Petajisto website

http://www.cfapubs.org/doi/pdf/10.2469/faj.v69.n4.7. And we focus on the Activeshare_min defined as the

active share of the fund relative to the index that produced the lowest Active Share for a fund as of each report

date. The results using active share with respect to fund’s official index is stronger. The sample period is from

1984-2009, as the Activeshare data is updated through 2009. The dependent variable is the next quarter return

for column (1) and (5), next two quarter cumulative return for column (2) and (6), next three quarter

cumulative return for column (3) and (7), and next four quarter cumulative return for column (4) and (8). The

main independent variable of interest is Dispw, the disproportionate holdings adjustment variable. We include

fund characteristic variables as controls. 1%, 5%, and 10% statistical significance is indicated with ∗∗∗,∗∗, and

∗, respectively.

42

Table 11. Information environment for stocks held by high Dispw funds

Low Dispw (Decile 0) High Dispw (Decile 9) Low - High (t-stat)

IOR 40.17% 35.01% -5.16% (4.54***)

Resid_IOR 6.41% 2.08% -4.34% (3.93***)

Coverage 9.38 7.73 -1.65 (5.33***)

Turnover 48.17% 63.04% 14.88% (7.46***)

Idivol 0.14% 0.16% 0.03% (3.36***)

PRC 23.83 26.41 2.57 (0.82)

NYSE SizeDecile 3.51 3.59 0.08 (0.59)

This table shows the information environment for the stocks held by high and low Dispw funds. We rank all

funds into deciles each quarter end based on their disproportionate portfolio adjustment Dispw, and high (low)

Dipw funds are those funds in the top (bottom) decile of Dispw. We then look into the characteristics of the

stocks held solely by high and low Dispw funds respectively (Stocks that are held simultaneously by high and

low Dispw funds are excluded). IOR is the institutional ownership, and Resid_IOR denotes the residual

institutional ownership orthogonalizing with respect to firm size. Coverage refers to the number of analysts

following the firm. Turnover is the last year total trading volume scaled by shares outstanding. Idivol is the

stocks’ idiosyncratic volatility based on the market model. And PRC and NYSE Size decile refer to the last

quarter end stock price and NYSE Size decile group.

43

Figure 1. Histogram of Dispw and Disp

This Figure shows the histogram of Dispw and Disp which measures fund disproportionate holdings adjustment for the sample period 1984-2012. Dispw

is calculated as the cross sectional weighted average standard deviation of funds’ existing holdings change (𝑠ℎ𝑎𝑟𝑒𝑠𝑖,𝑗, 𝑡

𝑠ℎ𝑎𝑟𝑒𝑠𝑖,𝑗,𝑡−1

𝑠𝑝𝑙𝑖𝑡𝑎𝑑𝑗− 1) at each quarter end, with

the weights being the quarter beginning portfolio weights ( 𝐷𝑖𝑠𝑝𝑖,𝑡 = 𝑆𝑡𝑑𝑖,𝑡(𝑤𝑖,𝑗,𝑡(𝑠ℎ𝑎𝑟𝑒𝑠𝑖,𝑗, 𝑡

𝑠ℎ𝑎𝑟𝑒𝑠𝑖,𝑗,𝑡−1

𝑠𝑝𝑙𝑖𝑡𝑎𝑑𝑗− 1))). Disp is the non-weighted standard deviation of

existing holdings change ( 𝐷𝑖𝑠𝑝𝑖,𝑡 = 𝑆𝑡𝑑𝑖,𝑡(𝑠ℎ𝑎𝑟𝑒𝑠𝑖,𝑗, 𝑡

𝑠ℎ𝑎𝑟𝑒𝑠𝑖,𝑗,𝑡−1

𝑠𝑝𝑙𝑖𝑡𝑎𝑑𝑗− 1)).

.

44

Figure 2. The migration of Dispw – Average decile ranks of Dispw in event times

This figure presents the average mutual fund Dispw decile rank in event time, where quarter zero is the

portfolio formation period. That is, for each quarter, we form ten decile portfolios by ranking mutual funds

based on their current quarter end disproportionate portfolio adjustment Dispw. Holding the portfolios fixed

for the next 12 quarters, we compute the average Dispw rank for each portfolio. For example, in 1990Q1, we

sort funds into ten groups based on their 1990Q1 Dispw. For each quarter from 1990Q1 to 1994Q1, we

compute the average Dispw decile rank for each of the group based on the event quarter Dispw. We repeat this

process of sorting and averaging for every quarter in our sample horizon.

45

Figure 3. Return patterns of Dispw

This figure shows cumulative returns to the hedge portfolios ranked by mutual fund disproportionate

adjustment variable Dispw. At the end of each quarter, all mutual funds are sorted into deciles based on Dispw

Mutual funds in the top decile are equal weighted to form the long portfolio, and funds in the bottom decile are

equal weighted to form the short portfolio. These decile portfolios are then rebalanced every quarter and are

held for two years. The curve shows cumulative returns to the hedge portfolio. We include both versions of

fund returns, the raw return from funds’ perspective and the return net expenses from investors’ perspective.

46

Figure 4. Stock performance around event time for high and low Dispw funds

This figure shows the normalized price around event time for the stocks over-weighted and under-weighted by

high and low Dispw funds respectively. We rank all funds into deciles each quarter end based on their

disproportionate portfolio adjustment Dispw, and high (low) Dipw funds are those funds in the top (bottom)

decile of Dispw. We then sort the cross sectional of stocks into terciles for each fund each quarter end based on

the current quarter trade (𝑠ℎ𝑎𝑟𝑒𝑠𝑖,𝑗, 𝑡

𝑠ℎ𝑎𝑟𝑒𝑠𝑖,𝑗,𝑡−1

𝑠𝑝𝑙𝑖𝑡𝑎𝑑𝑗− 1). Underweight (overweight) stocks are those stocks in the bottom

(top) tercile. We form equal weighted portfolios for stocks over-weighted (under-weighted) by high (low)

Dispw funds, and look at their return dynamics for the -6 to 6 months’ period around the formation quarter. We

normalize the price of the portfolio to 1 at the formation quarter for easiness of comparison.