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Mutual Fund Trading and Long-Term Price-Value Convergence

Yawen Qiu1, Rui Shen2, Marno Verbeek3 and Yu Wang4

ABSTRACT: In this paper, we examine whether or not mutual funds exploit long-term price-value

convergence measured by value-to-price (V/P) ratio. We find that in aggregate, mutual funds tend

to buy (sell) high (low) V/P stocks. However, only a subgroup of mutual funds actively trade on

strategy consistent with V/P strategy. We show that fund managers trading most aggressively

towards V/P strategy generate significantly positive risk-adjusted returns. We also show that

though mutual funds seem to help improving long-term market efficiency, their impact is very

limited.

1 National University of Singapore, yqiu@u.nus.edu 2 Nanyang Technological University, shenrui@ntu.edu 3 Erasmus University Rotterdam, mverbeek@rsm.nl 4 IMC Asset Management, yu.wang@imc.nl

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Mutual Fund Trading and Long-Term Price-Value Convergence

ABSTRACT: In this paper, we examine whether or not mutual funds exploit long-term price-value

convergence measured by value-to-price (V/P) ratio. We find that in aggregate, mutual funds tend

to buy (sell) high (low) V/P stocks. However, only a subgroup of mutual funds actively trade on

strategy consistent with V/P strategy. We show that fund managers trading most aggressively

towards V/P strategy generate significantly positive risk-adjusted returns. We also show that

though mutual funds seem to help improving long-term market efficiency, their impact is very

limited.

JEL classification: G10; G11; G14; G23; M41

Keywords: value-to-price ratio; intrinsic value; fund performance; long-term price-value

convergence

Data availability: Data are commercially available.

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I. INTRODUCTION

Institutional investors have become dominant in the US equity market (French 2008; Stein

2009), with their power even more prominent in trading. By 2002, nonretail investors accounted

for more than 96% of the New York Stock Exchange trading volume (Jones and Lipson 2004), but

it remains an open question whether institutional investors improve market efficiency (e.g. Bartov

2000; Collins et al. 2003; Ke and Ramalingegowda 2005; Boehmer and Kelly 2009; Richardson et

al. 2010). In this study, we provide new evidence on this topic through the behavior and

consequences of mutual funds trading in relation to long-term price-value convergence.

Institutional investors are regarded as sophisticated professionals (Stein 2009) capable of

exploiting arbitrage opportunities based on their analyses. However, in reality, institutional

investors operate under constraints arising from the serious agency issues between money

managers and their clients (e.g. Dasgupta and Prat 2008; He and Krishnamurty 2008; Dasgupta,

Prat, and Verardo 2011a, 2011b; Guoco and Kaniel 2011). Because clients cannot directly observe

money managers’ abilities, they rely on recent past performance to evaluate them, leading to

myopic trading behavior (Scharfstein and Stein 1990; Edeleen 1999). Shleifer and Vishny’s (1997)

analytical model shows that money managers’ fear of temporary money outflows may significantly

limit their trading effectiveness, specifically the ability to implement long-term strategies, even

though the returns from such strategies are positive and significant in the long run.

Although a large body of literature has been built on such theoretical arguments to provide

evidence regarding the role played by institutional investors, the results have been mixed.

Numerous studies have suggested that institutional investors improve market efficiency through

their sophistication and superior analytical skills (e.g. Collins et al. 2003; Ke and Ramalingegowda

2005; Boehmer and Kelly 2009). Ali et al. (2008) and Richardson et al. (2010) provide evidence

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that money managers do not trade on certain arbitrage opportunities, such as the accruals anomaly.5

In contrast to previous studies that have mainly focused on relatively short-term strategies, our

study adopts a strategy based on long-term price-value convergence. We provide direct evidence

of the theory proposed by Shleifer and Vishny (1997).

In this study, we focus on one particular class of institutional investors: mutual funds, that

accounts for a significant portion of the equity market. According to French (2008), the holding of

public traded equity of open-end mutual funds increased from 4.6% in 1980 to 32.4% in 2007. In

addition to their importance and data availability, mutual funds also offer additional advantage over

hedge funds and other active institutions because they are subject to more restrictions. In operation,

mutual funds are limited to using leverage, short-selling and charging performance-based fees – all

of which make them unattractive to top talent. Meanwhile, as the clients of mutual funds are largely

unsophisticated retail investors (compared with the clients of hedge funds and other active

institutions), mutual funds face greater risk of redemptions due to temporary underperformance.

Therefore, these characteristics of mutual funds provide a powerful test of Shleifer and Vishny’s

(1997) performance-based arbitrage theory.

To construct our long-term strategy of price-value convergence, we use a residual income

model first developed by Frankel and Lee (1998) and Lee et al. (1999) to obtain an empirical

estimate of a stock’s intrinsic value-to-price (V/P) ratio. According to Frankel and Lee (1998), V/P

anomalies are related to a long-term divergence of price and value (more than three years). V/P

ratio also differs from backward-looking multiples such as earnings-to-price ratio (E/P) or book-

to-market ratio (B/P) because it encompasses comprehensive fundamental analysis and

incorporates expected growth in earnings power. We empirically examine whether active mutual

5 Bartov et al. (2000) also find mixed evidence on the sophistication of institutional investors.

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fund managers typically trade on long-term mispricing indicated by the V/P ratio. By examining

the quarterly holdings of 2,537 distinct US active equity mutual funds from 1981 to 2008, we find

that mutual funds in aggregate tend to trade in a direction consistent with the V/P. However, we

also note that mutual funds do not generally hold very high V/P stocks because of the high volatility

of these stocks. Over time, there is evidence that mutual funds trade less consistently with a V/P

strategy suggesting a temporal shift because of increased competition (Stein 2009).

To further characterize the portfolio choices of mutual funds based on long-term price-value

convergence (proxied by V/P), we construct a fund-level V/P-timing measure, VPT, which is

conceived in the spirit of Grinblatt et al. (1995) and is similar to the accruals investing measure

developed by Ali et al. (2008). VPT is the value-weighted average V/P decile rank of all stocks

held by a mutual fund. A high VPT value indicates that the fund manager tilts his or her portfolio

toward underpriced stocks (with high V/P). To address the concern that some funds might

inadvertently have a high (low) VPT, we average the VPT scores of a particular fund for the

previous two years, denoted as AVGVPT. We sort all active mutual funds into ten decile portfolios

in ascending order (1-10) on the basis of AVGVPT.

We use fund returns before fees, net of realized transaction costs, to evaluate the association

between AVGVPT and fund performance. In univariate portfolio sorts, decile 10 (D10) funds with

the highest AVGVPT have an average return of 1.30%, 1.18% and 1.00% per month over each of

the three years from portfolio formation, and significantly outperform the lowest AVGVPT funds

in decile 1 (D1) by 0.42%, 0.35% and 0.21% per month, respectively. More interestingly, the

superior performance of D10 funds does not simply reflect higher risk-taking. The average monthly

risk-adjusted returns on D10 funds for each of the next three years are 0.33%, 0.25% and 0.19%

based on the capital asset pricing model (CAPM), 0.22%, 0.19% and 0.13% based on the Fama

and French three-factor model, and 0.18%, 0.14% and 0.11% based a four-factor model including

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momentum (t-stats of four-factor alphas are 2.02, 1.17 and 1.74, respectively). Hence, mutual funds

pursuing long-term strategies generate both statistically and economically significant profits.

Finally, we examine the influence of mutual funds on the V/P effect. Although the V/P effect

is generally smaller with more mutual funds trading or holding, a mutual fund’s influence is limited

and statistically insignificant, especially in the long run. These results suggest that mutual funds

contribute little to long-term market efficiency.

Our study contributes to the broad literature on institutional investors and market efficiency.

The existing evidence on this topic is mixed. Previous findings have indicated that institutional

investors improve market efficiency in the short run (e.g. Boehmer and Kelly 2009). In contrast,

this study provides several pieces of novel evidence regarding mutual funds and long-term market

efficiency. First, some mutual funds tend to exploit long-term mispricing opportunities, although

not very aggressively. Second, the mutual funds that exploit such opportunities the most can

generate risk-adjusted performance over a relatively long period. Third, the effect of mutual fund

trading on long-term price-value convergence is limited. Overall, our findings support the

performance-based arbitrage theory proposed by Shleifer and Vishny (1997).

Our study also contributes to the fundamental analysis literature. Bradshaw et al. (2001)

suggest that the price/earnings-to-growth (PEG) ratio is most commonly used among financial

analysts. Ali et al. (2008) document that on average, mutual funds do not exploit the accruals

anomaly. Based on their survey, Richardson et al. (2010) find that although practitioners and

academics regard value-related strategies as very successful, the use of residual income-based

models is less common among the former. In this study, we use a large sample to provide empirical

evidence that mutual funds in aggregate trade on mispricing consistent with the V/P anomaly. This

could indicate that practitioners are likely to use comprehensive fundamental analysis models

similar to residual income-based specifications without acknowledging it. Our results also show

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that a small portion of mutual funds try to exploit long-term trading strategies and that these mutual

funds benefit from their trading despite the transaction costs and short-sale constraints they face.

Our finding on this point contributes to the debate over the relevance of fundamental analysis to

real trading, underlining the importance of fundamental analysis in the real world.

The remainder of this paper is organized as follows. Section II introduces our residual income

model. Section III describes the data and the sample selection procedure, and reports summary

statistics. Section IV explores the relation between mutual fund trading and mispricing identified

by the V/P ratio. Section V provides evidence of the benefits of trading consistently with long-term

price-value divergence. Section VI presents additional analyses regarding how mutual fund trading

affects the profitability of V/P strategy and various robustness checks. We conclude our paper in

Section VII.

II. RESIDUAL INCOME MODEL

We use a standard discounted residual income approach to measure the divergence between

the price and value of a stock in the long run.6 A stock’s fundamental value is generally defined as

the present value of its expected future dividends conditional on all currently available information.

Specifically,

∑∞

=

+

+=

1

*

)1(][

ii

e

ittt r

DEV , (1)

where *tV is the stock’s fundamental value at time t, Et[Dt+i] is the expected future dividends for

period t+i based on information available at time t and re is the cost of equity.

6 The residual income model is also referred to as the Edwards-Bell-Ohlson (EBO) valuation technique. Ohlson (1990, 1995) and Feltham and Ohlson (1995) develop the model theoretically.

8

Under the clean surplus accounting assumption, the change in a firm’s book value is equal to

earnings minus net dividends. Following Frankel and Lee (1998), Equation (1) can be rewritten as

the reported book value plus the sum of an infinite series of discounted residual income:

ie

iteitt

it

ii

e

iteitttt r

BrROEEBr

BrNIEBV)1(

])[()1(

][ 1

11

1*

+−

+=+−

+= −++∞

=

∞

=

−++ ∑∑ , (2)

where Bt is the book value at time t, NIt+i is the net income for period t+i and ROEt+i is the after-

tax return on book equity for period t+i. Equation (2) shows that a firm’s intrinsic value can be

decomposed into an accounting measure of capital invested (Bt) and a measure of the present value

of future cash flows not captured in the current book value. Firms with an expected ROE higher

(lower) than their cost of equity (re) have intrinsic value greater (smaller) than their current book

value.

In practice, implementation of the model requires forecasts of ROE (FROE), the dividend

payout rate (k), current book value (Bt), cost of equity (re) and a terminal value, i.e. an estimate of

the value of the firm based on the residual income earned after the explicit forecasting horizon. To

calculate a stock’s intrinsic value, we strictly follow Frankel and Lee’s (1998) approach and use a

three-period expansion of the model:

222

121

*^

)1()1()1( ++

++

+−

++

−+

+−

+= tee

ett

e

ett

e

ettt B

rrrFROEB

rrFROEB

rrFROEBV , (3)

where

Bt: book value from the most recent financial statements;

Bt+i: forecast book value for period t+i: Bt+i = Bt+i-1 + FYt+i - FDIVt+i, where FDIVt+i denotes the

dividends forecast for year t+i, estimated using the dividend payout ratio k, which is

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computed as common stock dividends divided by net income before extraordinary items.7

We assume that FDIVt+i= FYt+i ×k;

re: industry-specific cost of equity estimated from a three-factor risk model according to Fama and

French (1997);8

FROEt+i: forecast ROE for period t+i. For the first two years, this variable is computed as FYt+i

/[(Bt+i-1+Bt+i-2)/2], where FYt+i is I/B/E/S consensus (mean) forecast i-years-ahead earnings.

For the third year, we use the five-year long-term growth rate to compute a three-years-ahead

earnings forecast: FROEt+2=FYt+2×(1+Ltg). When Ltg is missing from the I/B/E/S database,

we use FROEt+1 to proxy for FROEt+2.

The foregoing model provides a framework for analyzing the relation between accounting

numbers and firm value, reflects the importance of including forward-looking earnings information

in the valuation,9 and performs very well empirically. Previous studies have found this V/P ratio to

be a reliable predictor of cross-sectional (Frankel and Lee 1998) and time-series (Lee et al. 1999)

variation in US stock returns. Ali et al. (2003) further show that the V/P effect is mainly

concentrated around earnings announcements, consistent with the mispricing explanation for its

return predictive power. Jiang and Lee (2005) find that book values and earnings estimates derived

from the residual income model contain more useful information than those produced by the

traditional dividend discount model (DDM) for stock valuation. In the corporate finance literature,

researchers also note that the V/P ratio is a good mispricing measure in explaining corporate

takeover (Dong et al. 2006) and external financing (Dong et al. 2011) decisions.

7 For firms with negative earnings, we divide dividends by 5% of the total assets to derive an estimate of k, where 5% is the average long-term ROA in our sample period (see Table 1). 8 Frankel and Lee (1998), Abarbanell and Bernard (2000) and Dong et al. (2006) find that the choice of re has little effect on cross-sectional analysis. 9 Frankel and Lee (1998) and Lee et al. (1999) provide a detailed and comprehensive discussion of the insights gained from the model.

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III. SAMPLE DESCRIPTION AND SUMMARY STATISTICS

In this section, we describe the stock dataset used to analyze the V/P effect and the selection

criteria for our mutual fund sample. We then report summary statistics for our sample.

Stock Data

The sample of stocks examined in this study includes all U.S. domestic non-financial

companies traded on the NYSE, the AMEX, and NASDAQ included in the Compustat/CRSP

merged database from 1981 to 2008. We require firms to have valid accounting data (for Bt-1, Bt-2,

NIt-1 and DIVt-1) and data on stock prices and shares outstanding for the t-1 fiscal year-end and the

end of June in year t. We also require that firms have one-year-ahead and two-year-ahead earnings

forecasts from I/B/E/S. We use I/B/E/S forecasts announced in May and constrain our sample to

firms with fiscal year-ends between June and December, inclusive. This constraint ensures that

forecast earnings correspond to the correct fiscal year-end.10

To ensure that accounting variables are known to the public before portfolio formation, we

form and rebalance our stock portfolios at the end of June in year t using the V/P ratios computed

on the basis of the intrinsic value estimates and market equity values at the fiscal year-end of

calendar year t-1. To be consistent with Fama and French (1992), we calculate the book-to-market

ratio (B/M) based on the book value at the last fiscal year-end and market equity in December in

calendar year t-1. In estimating Equation (3), we remove firms with negative book values or

negative V, and eliminate firms with absolute FROE values above 100% and dividend payout ratios

higher than 100%. To mitigate the concern that our stock return tests might be influenced by return

10 I/B/E/S provides more comprehensive data after 1983. Our results are qualitatively and quantitatively similar if we exclude data for 1981 and 1982.

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outliers, we eliminate stocks with prices below $1.11 Taken together, our filters eliminate 4,636

observations (approximately 9%), leaving a final sample of 50,246 firm years.

Mutual Fund Sample Selection

We construct our mutual fund database by combining the Center for Research in Security

Prices (CRSP) Survivor-Bias-Free U.S. Mutual Fund Database (MFDB) and the CDA/Spectrum

Mutual Fund Holdings Database from Thomson Financial. 12 As we wish to examine the

informational advantages of mutual funds in stock markets, we include in our sample only active

mutual funds that invest primarily in US common stocks. In particular, we eliminate balanced,

bond, money market, international, index and sector funds and exclude funds not primarily invested

in equity securities (see the Appendix for details on how we select active US domestic equity funds).

Our final sample covers 2,537 distinct funds over the 1981-2008 period.

Data on the monthly returns, prices, and market values of common stocks traded on the

NYSE, the AMEX, and NASDAQ come from CRSP. Consistent with the literature, we exclude

closed-end funds, real estate investment trusts (REITs), American Depository Receipts (ADRs),

foreign companies, primes, and scores (we retain only shares with a code of 10 or 11).

Summary Statistics

Table 1 reports the summary statistics for our stock (Panel A) and mutual fund (Panel B)

samples. Their average characteristics are calculated at the end of each June from 1981 to 2007.

The average dividend payout ratio (k) for stocks in our stock sample decreases from 0.33 in 1981

11 These firms typically have unstable B/M and V/P ratios and poor market liquidity. 12 Our merging procedure uses the MFLINKS dataset maintained by Russ Wermers and Wharton Research Data Services (WRDS).

12

to 0.11 in 2007. The average ROE and ROA also exhibit a decreasing pattern over time, although

their falls are not strictly monotonic. The average ROE ranges from 0.04 to 0.16, whereas the

average ROA varies from 0.01 to 0.07. These results illustrate the stability of the key model inputs

over time. Using the residual income model to estimate intrinsic stock value, we observe that the

average V/P ratio displays a generally declining trend over our sample period, falling from 1.54 in

1981 to 0.65 in 2007. Panel A of Table 1 also shows that in an average year, mutual funds in

aggregate hold 1,542 stocks out of the 1,587 stocks with valid V/P computation data. The mutual

fund holdings data thus cover the majority of our stock sample. Furthermore, mutual funds increase

their ownership of an average stock (defined as the proportion of outstanding shares in a stock held

by all mutual funds) almost monotonically from 2.77% in 1981 to 17.26% in 2007. The

corresponding number of funds holding the stock also rises sharply from eight to 70 over the sample

period. These numbers illustrate that mutual funds have become more important as common equity

shareholders over recent decades.

[Insert Table 1 about here]

Panel B of Table 1 presents average mutual fund characteristics by year. We observe that the

active equity mutual fund industry has expanded rapidly; that is, the number of actively managed

equity funds in our sample increases from 179 in 1981 to 1,518 in 2007, with average total assets

(TNA) under management growing from $195.51 million to $1,743.51 million. These funds invest

an average of 90% of their assets in common stocks, which suggests that our sample is highly

representative of the universe of US active funds with a domestic equity investment focus. The

expansion of mutual funds over our sample period outpaced that of stock markets, causing such

funds to become increasingly important common equity shareholders. Panel B of Table 1 also

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reveals initially increasing trends in 12b1 fees, expense ratios, and fund turnover ratios, followed

by slight decreases after 2003.

IV. DO MUTUAL FUNDS TRADE ON LONG TERM V/P STRATEGY?

In this section, we first document that intrinsic stock value reveals information concerning

future stock returns over our sample period. Next, and more importantly, we investigate whether

mutual funds trade on long-term price-value convergence measured by the V/P ratio.

Stock Characteristics across V/P Quintiles

Because Frankel and Lee (1998) examine an earlier stock sample from 1976 to 1993, we first

confirm the V/P effect for stocks in our sample covering the 1981 to 2008 period. We follow

Frankel and Lee (1998) by using public information to compute V/P ratios for our sample of stocks

at the end of June in year t. We then sort the stocks into five quintile portfolios numbered in

ascending order based on their V/P ratios for the fiscal year ending in calendar year t-1. To

minimize the potential influence of analyst forecast errors on more opaque/smaller firms, we

compute value-weighted portfolio returns, as value-weighting is considered a more conservative

approach to revealing superior trading strategies.13 We report portfolio returns for the years t+1,

t+2 and t+3, respectively. The results reported in Table 2 show that over the first year (July in year

t - June in year t+1) firms in the highest V/P quintile (Q5) outperform those in the lowest V/P

quintile (Q1) by 0.80%, 0.81% and 0.44 per month on a value-weighted basis after making

adjustments according to the CAPM, the three-factor model and the four-factor model,

13 Fama and French (2008) point out that equal-weighted portfolio returns may be driven by tiny stocks that although numerous, have little economic significance. Value-weighting can also mitigate the potential influence of analyst bias, because analysts tend to issue more optimistic earnings forecasts for small firms (Gu and Wu 2003).

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respectively.14 Over the second year (July in year t+1 - June in year t+2) and the third year (July in

year t+2 - June in year t+3), the V/P strategy earns stronger risk-adjusted returns. In terms of four-

factor adjusted returns, the firms in the highest V/P quintile (Q5) outperform those in the lowest

V/P quintile (Q1) by 0.74% and 0.63% in the second and third years, respectively (the t-stats are

2.98 and 2.69, respectively). The return patterns are consistent with those in Frankel and Lee (1998).

Specifically, firms in the highest V/P quintile (Q5) have superior and statistically significant

abnormal returns (alpha) in all three years. This finding is important for our subsequent analysis of

mutual fund trading because mutual funds’ informational advantage should be most conspicuous

among their long positions due to short-sale constraints.

[Insert Table 2 about here]

We now examine the characteristics of stocks with low and high V/P ratios. We present

univariate results for each of the quintile portfolios in Table 3. Specifically, we use the same

portfolio sorts to calculate the cross-sectional averages of stock characteristics before reporting

their time-series means. The results show that the average V/P ratio increases from 0.40 in Quintile

1 to 1.77 in Quintile 5, whereas there is a much lower degree of divergence in the corresponding

B/M ratio across the V/P quintiles. Furthermore, we find that the most underpriced stocks in

Quintile 5 tend to be small-cap stocks with an average size quintile rank value of 2.17 based on

NYSE market-cap breakpoints numbered in ascending order; they also have a slight tendency to

be growth stocks and winners in the past year. Stocks in the two extreme quintiles exhibit a high

14 In the event of a stock delisting, we use CRSP delisting returns when such observations are not missing; otherwise, we follow Shumway (1997) by replacing missing delisting returns with -30% if the delisting is performance-related (CRSP delisting codes 500 and 520-584).

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degree of return volatility and a high rate of turnover. This is especially so among underpriced

stocks, which have an average return volatility of 13.80% per year and an average annual turnover

of 164.94%.

Average mutual fund ownership of both underpriced and overpriced stocks tends to be

smaller than that of the rest of the stock universe. A typical stock in Quintile 5 (Quintile 1) with

the highest (lowest) V/P ratio has an average mutual fund ownership of 8.60% (8.57%), which is

lower than the average mutual fund ownership of 9.22% for a typical stock in Quintile 3 with a

medium V/P ratio. A similar pattern is also found in the average number of mutual funds holding

a stock. However, we observe an interesting pattern when looking at the change in mutual fund

ownership of a stock from June in year t-1 to June in year t. We observe that both the change in

mutual fund ownership and the change in the number of funds holding a stock increase with the

V/P ratio. On average, mutual funds tend to buy (sell) underpriced (overpriced) stocks based on

their fundamental stock valuations, and start trading on such information during the year before the

release of all public financial reports. The last two columns of Table 3 suggest that mutual funds

continue to exploit intrinsic stock values after financial information is released at the end of June

each year. We explore this issue in more detail in the next subsection.

[Insert Table 3 about here]

Mutual Fund Trading and V/P Strategy

According to DeLong et al. (1990) and Campbell and Kyle (1993), mutual funds can behave

as informed traders by trading on mispricing opportunities and bringing about market efficiency.

However, Shleifer and Vishny (1997) argue that delegated portfolio managers may become capital-

constrained when they tilt their portfolios toward severely mispriced securities, especially for long-

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term strategies. Moreover, mispricing based on long-term price-value convergence measured by

V/P is associated with high return volatility, as shown in Table 3. Hence, fund managers might

have weak incentives to exploit intrinsic stock value. In this subsection, we examine in more detail

how mutual funds trade in response to the information content of the V/P ratio.

We first use an event study approach to illustrate how mutual funds trade on V/P information.

We form five quintile portfolios of stocks based on their V/P ratios at the end of June each year

between 1981 and 2006, calculated using value and price information at the fiscal year-end of year

t-1. Quintile 1 consists of the most overpriced stocks (lowest V/P firms) and Quintile 5 the least

(highest V/P firms). To examine the trading activities of mutual funds in more detail, we calculate

time-series average changes in mutual fund ownership for the quintile portfolios over the same

ranking and holding periods. To avoid the instability of aggregate mutual fund ownership

documented by Gompers and Metrick (2001), we cross-sectionally demean (market-adjusted) firm-

level ownership changes before computing the average changes in mutual fund ownership at the

portfolio level.

Figure 1 plots equally weighted, market-adjusted changes in mutual fund ownership for

different V/P portfolios. Quarter 0 denotes the April to June period in year t, and Quarter -2 denotes

September to December in year t-1. The results suggest that in aggregate, mutual fund trading is

consistent with the information contained in V/P ratios. Mutual funds start to increase their

ownership of underpriced stocks from Quarter -1 (January to March in year t) and appear to stop

trading on the same information after Quarter 3 (July to September in year t). In contrast, mutual

funds tend to reduce their ownership of overpriced stocks dramatically during a shorter period

(from Quarter -1 to Quarter 1). These results indicate that as an investor group, mutual funds exhibit

trading behavior consistent with the mispricing opportunities based on V/P ratio. More importantly,

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mutual funds appear to trade on such valuation information from January to June (in year t) when

such information is gradually released.

[Insert Figure 1 about here]

To provide a more comprehensive picture of mutual fund trading behavior in response to

fundamental analysis, we run multivariate panel regressions for calendars quarter between 1981

and 2007 that relate changes in mutual fund ownership of a given stock to V/P while controlling

for other stock characteristics.15 We control for the quintile ranks of B/M and E/P, accruals and

earnings changes as alternative fundamental strategies which might be exploited by mutual funds

(Ali et al. 2008; Richardson et al. 2010; Ali et al. 2012). Accruals are constructed following Sloan

(1996) and Ali et al. (2008) using balance sheet approach. Earnings changes are computed as the

change in actual earnings for the last fiscal year scaled by price at the last fiscal year-end (Bernard

and Thomas 1990). The quintile ranks of V/P, B/M, E/P, accruals and earnings changes are

determined at the last fiscal year-end and assigned to each quarter in the next calendar year. We

include contemporaneous analyst forecast revisions (Analyst Rev) and contemporaneous stock

returns (Rt) to control for the new information coming to the market during the quarter. Analyst

Rev is calculated as the change of the consensus analyst earnings forecasts through the quarter

scaled by the stock price at the beginning of the quarter. Rt is the quarterly stock returns from CRSP.

Because mutual funds tend to hold stocks with bigger size, smaller volatility and higher liquidity,

we control for firms size (Log(ME)), idiosyncratic volatility (Idio Vol) and turnover ratio

(Turnover), respectively. Log(ME) is the logarithm of firms’ market cap at the beginning of the

15 The results are qualitatively and quantitatively similar when using Fama-MacBeth cross-sectional regressions (Fama and MacBeth 1973).

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quarter. We measure Idio Vol by regressing daily stock returns against daily Fama-French factors

in quarter t-1 and using the standard deviation of the residuals as the residual volatility of the stock

(Idio Vol). We require at least 40 daily stock return observations to be available. Turnover is

computed as total stock trading volume in the last quarter divided by the average of the stock prices

at the beginning and end of the last quarter. We further include past one year returns (Pr1Yr) to

control for mutual funds chasing momentum stocks. Finally, to control for clientele effects, we

include mutual funds holding at the beginning of the quarter (MFO) as a control variable. We run

panel regressions and report coefficients and corresponding t-statistics in Panel A of Table 4

(Quarter -1 to Quarter +2, where Quarter 0 denotes the April to June period). Consistent with the

pattern established in the event study, mutual fund trades are positively and significantly associated

with V/P ranks in the first three calendar quarters of a year, even after controlling for fund return

chasing behavior by including contemporaneous quarterly stock returns (Rt). The quintile ranks of

other fundamental-to-price ratios such as B/M and E/P are either negatively or insignificantly

associated with aggregate mutual fund trading, suggesting that mutual fund managers do not trade

in the direction of these simple financial ratios. The coefficient of Accruals is statistically

insignificant in quarter 0 and is negatively significant in quarter -1. The coefficients of analyst

revisions flip over quarters, thus suggesting that the reaction of active mutual funds to short-term

cash flow information is mixed. In aggregate, mutual funds tend to exploit mispricing revealed by

long-term information and more comprehensive valuation models. Our results are not driven by a

few years of observations. In robustness tests, we use Fama-MacBeth regressions instead of panel

regressions. Untabulated V/P rank coefficient estimates are positive in 22 out of 27 years for

Quarter 0, 18 out of 27 years for Quarter -1, and in 17 out of 27 years for Quarter 1. When we

replace the V/P ranks with dummy variables indicating quintile membership, the results show that

mutual funds trade largely on intrinsic value in the second calendar quarter. Funds tend to sell

19

overpriced stocks (Q1, low V/P stocks) and buy underpriced stocks (Q5, high V/P) in Quarter 0.

This positive association is robust to the inclusion of other return predictors such as firm size (ME),

one-year return (Pr1Yr), idiosyncratic volatility (Idio Vol) and the turnover ratio (Turnover).

Therefore, in aggregate mutual funds tend to trade more intensively in the direction of V/P during

the first half of each calendar year. In an untabulated analysis, we further examine three types of

active mutual funds: aggressive growth, growth, and growth and income.16 We find similar results

across all three types of mutual funds.

[Insert Table 4 about here]

The Temporal Shift of Mutual Fund Trading and V/P Strategy

As documented in French (2008), mutual fund industry has boomed in the past three decades.

Stein (2009) proposes a theoretical model suggesting that the dominance of institutions might be

associated with crowding and leverage effects. Because of not knowing other smart money

institutions strategies and the fear of crashes caused by fire sale of other institutions, mutual fund

managers may choose to stay away from strategies involving long horizon payoffs and highly

volatile stocks. So it is possible that as more and more mutual funds compete in the market, their

tendency of trading on long-term strategy such as V/P strategy has been weakened. To explore this

possibility, we examine whether or not there is a time trend of aggregate mutual fund trading on

V/P strategy. Trend is defined as the calendar year minus 1981. In this test, we focus on Quarter -

1 and Quarter 0 because most mutual funding trading regarding V/P strategy happens in these two

16 We obtain fund investment objectives from the CDA database.

20

quarters.17 The results of the possible temporal shift of mutual fund trading on V/P strategy are

reported in Panel B of Table 4. When focusing on the quintile rank of V/P, we find that the

coefficient of the intersection between Trend and V/P rank is negative and significant for Quarter

-1. This suggests that mutual funds significantly reduce their trading related to V/P strategy in

Quarter -1 as time passes. The corresponding effect is negative but insignificant for Quarter 0.

When we use dummy variables (Q1 and Q5), we find that mutual funds significantly reduce trading

on high V/P stocks (Q5) for Quarter -1. For Quarter 0, we find that as time passes, mutual funds

sell more low V/P stocks (Q1) and buy less high V/P stocks (Q5). Two combined forces can explain

these results. The learning effect over time enables mutual fund managers to get rid of overpriced

stocks. However, the crowding and leverage effects suggested by Stein (2009) make mutual fund

managers hesitate to exploit the opportunities in underpriced stocks. Overall, our results are

consistent with a temporal shift in mutual fund trading related to V/P strategy.

V. DO MUTUAL FUNDS PROFIT FROM EXPLOITING LONG-TERM STRATEGY?

In section IV, we have shown that in aggregate, mutual funds tend to trade on the information

content of the V/P ratio. However, as indicated in Table 3, mutual funds on average still hold less

high V/P stocks than average stocks. It is also unclear whether or not mutual funds can make real

profit by exploiting long-term strategies after the costs arising from trading and fire sale (Edelen

1999). In this section, we present evidence regarding the payoffs mutual funds earn by taking bet

on long-term price-value convergence.

Mutual Fund V/P Timing Measure

17 In untabulated results, we find insignificant effect of time trend on mutual fund trading related to V/P strategy in Quarter 1 and 2.

21

To measure cross-sectional dispersion in how actively mutual funds trade on long-term value

strategy as measured by their adoption of V/P trading strategy, we construct a V/P timing measure

modeled on the momentum investing measure of Grinblatt et al. (1995) and similar to the accruals

investing measure of Ali et al. (2008). At the end of each June, we rank all stocks in our sample

into decile portfolios based on V/P and assign a rank of between 1 and 10 to each stock, with 1

representing the most overpriced 10% of stocks and 10 the most underpriced 10% of stocks.18 The

V/P timing measure for fund i at time t, VPTi,t, is defined as the weighted average V/P rank of all

stocks held by the fund:

∑=

=itN

jtjtjiit PRankVwVPT

1,,, / (4)

where V/P Rankj,t is the decile rank of stock j in ascending order based on the V/P ratio; Ni,t is the

number of stocks held by mutual fund i at time t; and wi,j,t is the weight of stock j in the fund i

portfolio at time t.19 A high VPT indicates that the fund tilts its portfolio toward underpriced or

high V/P stocks.20 To avoid the possibility that some funds achieve a high (low) VPT by chance,

we take the average VPT score for a particular fund in years t and t-1 to construct AVGVPT as a

measure of the fund’s adoption of long-term value strategy.21

18 We use decile ranks to increase the variation of VPT. In an unreported analysis, we replace the decile ranks with quintile ranks and find that the main results are not affected. 19 Because of the variable restrictions in calculating V/P, there are some stocks held by mutual funds without a valid V/P ratio. In calculating VPT, we ignore the stocks held by mutual funds but without V/P. We will elaborate and present evidence on this point in Section VI. 20 Mutual funds tend to have very persistent VPT over time. The correlation between VPT in year t+1 and year t is 0.757. 21 To calculate AVGVPT, we require that mutual funds have information in both year t and year t-1. In robustness checks (untabulated), we replace a missing VPT score in year t-1 with 5.5 (the average score) or the same VPT score for the same fund in year t, and find that our conclusions are not affected. We also try other definitions of high-skill funds. Alternative high- (low-) skill funds definitions include funds in the top (bottom) quintile or decile by VPT rank in both year t and year t-1, and funds in the top (bottom) AVGVPT decile and the top (bottom) half of funds by VPT rank in both year t and year t-1. All our results are robust to each alternative definition of high- (low-) skill funds.

22

Characteristics of Funds with Extreme AVGVPT

Mutual funds have different flavors in their trading. It is not necessary that mutual funds have

to trade on long-term value strategy to be successful. It might be interesting to know whether or

not mutual funds’ trading on V/P strategy is associated with certain fund characteristics. To achieve

this goal, we examine the characteristics of mutual funds across AVGVPT decile portfolios. We use

Fama-MacBeth regressions to analyze the possible association between AVGVPT and fund

characteristics. At the end of each June, we calculate AVGVPT and sort mutual funds into deciles

based on their AVGVPT scores in ascending order. We then compute the cross-sectional averages

of fund characteristics and report their time-series means. Table 5 reports the results based on the

univariate sorts. D5 funds have an average AVGVPT of 5.47. As the average AVGVPT across all

funds is 5.50, the holdings of D5 funds appear to be neutral to a V/P strategy. In contrast, the

average AVGVPT of D1 funds is 4.29, whereas the average AVGVPT for D10 funds is 7.00,

suggesting that D10 funds trade on the V/P effect, whereas D1 funds trade against it. The results

also show that funds in the two extreme VPT deciles tend to be newer funds with higher expense

ratios. Furthermore, high-VPT funds in Decile 10 are smaller and have higher turnover ratios. A

typical fund in Decile 10 with the highest VPT has average total assets (TNA) of $562 million,

which is substantially lower than average TNA in any other decile portfolio. These high AVGVPT

funds also have the highest average turnover ratio (100.07%) among all deciles. We observe no

apparent relation between AVGVPT and 12b1 fees.

[Insert Table 5 about here]

We next run Fama-MacBeth regressions to develop a better understanding of the association

between using V/P strategy and other strategies. In particular, we examine three fund skills

23

documented in prior studies. Active Share measures the extent to which the makeup of the fund

portfolio deviates from that of its benchmark (Cremers and Petajisto 2009). Following Baks et al.

(2007), we use the normalized Herfindahl index (Portfolio Concentration) to measure the fund

manager’s willingness to take big bets on a relatively small number of stocks. Return Gap is the

difference between the reported fund return and the return on a portfolio that invests in the

previously disclosed fund holdings, and captures the fund’s unobserved intra-quarter trading

activities (Kacperczyk et al. 2008). We use the average monthly return differential over the

previous year in our regressions. We further control for fund characteristics such as fund size

(Log(TNA)), the fund expense ratio (Expense Ratio) and the fund turnover ratio (Turnover Ratio)

as fund characteristics might be associated with their trading strategies. We also include fund past

performance (Past Fund Performance). We regress AVGVPT on these fund characteristics and

three fund performance predictors (Active Share, Portfolio Concentration and Return Gap) at the

end of each June and report the time-series average coefficients in Table 6. Among the three fund

performance predictors, the Return Gap is significantly and negatively associated with AVGVPT.

Intuitively, this suggests that mutual funds that rely on frequent interim/short-term trades do not

exploit investment opportunities presented by long-run price-value convergence. Portfolio

Concentration is also negatively associated with AVGVPT. Because there is too much uncertainty

in the long run, it is possible that funds taking big bets on a small number of stocks tend to exploit

short-term opportunities. We do not find significant association between Active share and

AVGVPT.22

[Insert Table 6 about here]

22 In untabulated results, we do not find any intersection effect between different strategies. This result might not be surprising because as shown in Table 5, the variation of AVGVPT is not very large across funds.

24

Aggressiveness of Funds Trading Towards V/P Strategy

As Table 3 reveals, stocks with extreme V/P ratios have small market capitalizations and high

idiosyncratic volatility, which makes them relatively unattractive to mutual funds. To gain more

insights into how aggressive mutual funds trade on long-term value strategy, we examine how

funds exploit fundamental mispricing across V/P deciles. At the end of each June, we calculate for

each AVGVPT decile the aggregate portfolio weight of each V/P stock decile. Specifically, for D10

funds, the aggregate portfolio weight within a V/P decile is computed as the total value of stocks

in the V/P decile held by D1 funds divided by the total value of their equity holdings. We report

the time-series averages of the portfolio weights for D1, D5 and D10 funds in Table 5. Consistent

with our expectations, D5 funds that are neutral to the V/P strategy invest almost equally in all ten

V/P deciles. Relative to these neutral funds, D10 funds tend to overweight stocks in the highest V/P

decile (16.99%) and underweight stocks in the lowest V/P decile (3.40%). The reverse pattern can

be observed for D1 funds, which overweight low V/P stocks and underweight high V/P stocks. The

portfolio weight differences between D10 and D1 funds and between D10 and D5 funds in the two

extreme V/P deciles are statistically significant. Note that D10 funds are generally small funds

(with an average TNA of $515 million, see Table 5). Although these high AVGVPT funds place

large bets on underpriced stocks, their total investments in these stocks cannot be substantial. More

importantly, even for the funds with highest AVGVPT (D10 funds), they do not trade on long-term

value strategy very aggressively. This is consistent with the prediction of limits of arbitrage.

[Insert Table 7 about here]

Do Funds Profit from Exploiting Long-term Value Strategy?

25

We have shown that mutual funds’ trading of long-term value strategy varies a lot cross-

sectionally. However, an efficient market and/or the transaction costs associated with

implementing trading strategy may prevent funds earning abnormal profits from such strategies.

Because highly underpriced stocks are generally small and have high return volatility, mutual funds

buying such stocks may face major trading friction and large transactions costs. At the same time,

mutual funds are restricted to take short positions so that they cannot take profit by short selling

overpriced stocks. Therefore, it is of great importance to evaluate the profitability of fund trading

based on V/P in practice to gain a better understanding of the trading behavior of mutual funds and

the associated impact.

To do so, we first compute AVGVPT scores in June of year t and use the results to sort all

active mutual funds into decile portfolios. We then track mutual fund performance in years t+1,

t+2 and t+3 by computing monthly TNA-weighted fund portfolio performance.23 We use size-

weighted portfolio performance because we try to focus on funds with large impact on the market.

In untabulated results, we use equal-weighted fund portfolio performance and the results are

qualitatively similar. For the performance evaluation, because we are interested in whether or not

mutual funds can earn abnormal profit in addition to risk taking through exploiting long-term value

strategy, we use mutual fund performance before fees (by adding the back expense ratio/12 to the

net fund return reported by CRSP) adjusted by conventional risk factors as a measure of investment

profitability (Cohen et al. 2005).

Table 8 reports the fund performance results. Panels A, B and C of Table 8 display the fund

performance results in years t+1, t+2 and t+3, respectively. Over the first year (July in year t - June

in year t+1), D10 funds generate a significant return of 1.30% per month and significantly

23 The returns are calculated from July in year t+i to June in year t + i + 1, i = 0, 1, 2 respectively for performance in years t+1, t+2 and t+3.

26

outperform their D1 counterparts by 0.42% per month. We also examine how well D10 funds

perform relative to D5 funds (with an AVGVPT score of 5.5) supposedly neutral to fundamental

analysis. The return spread between D10 and D5 funds is statistically significant at 0.33% per

month. The significant return spreads are robust to various forms of risk adjustment. Qualitatively

similar results are also found for fund performance in years t+2 and t+3. More importantly, the

average return for D10 funds, which have the highest AVGVPT, is significantly positive from year

t+1 to year t+3. In terms of Fama-French 3-factor alpha, D10 funds earn 0.22%, 0.19% and 0.13%

per month from year t+1 to year t+3, with t-statistics of 2.83, 2.66 and 2.22, respectively. It is not

surprising that the alphas are smaller after controlling for momentum, because D10 funds are likely

to be past winners and to continue being winners after portfolio formation. This abnormal

performance is net of transaction costs, and thus represents the net benefits of fundamental analysis

skills. As mutual funds in our sample can only hold long positions in stocks and the profits of many

trading strategies are from the short side, this evidence is particular significant. We observe

negative risk-adjusted returns for D1 funds, although the results are not significantly different from

zero. It is possible that poor performing funds are more likely to improve their skills in later periods

or change their managers.

[Insert Table 8 about here]

The above results suggest that active mutual funds exploiting long-term value strategy benefit

from their trading and generate both statistically and economically significant profits, net of actual

transactions costs and before fund expenses, over at least a three-year horizon. Overall, our

evidence suggests that a subgroup of mutual funds that are trying to exploit long-term value strategy

profit from their trading.

27

VI. ADDITIONAL ANALYSES

In this section, we conduct additional analyses regarding the impact of mutual funds on long-

term market efficiency and provide various robustness tests.

Mutual Fund Trading and Price Convergence to Fundamental Value

Given that mutual funds in aggregate tend to trade in the direction of V/P, their trading

activities might mitigate mispricing by pushing stock prices back toward fundamental value.

However, evidence in Section V suggests only a subgroup of mutual funds really trade on long-

term strategy measured by V/P and even for the subgroup, their trading is not very aggressive. Thus

it is unclear whether or not mutual funds trading can have a significant impact on long-term price-

value convergence process. This section provides additional evidence on this aspect.

The idea we develop in this part of the paper is whether or not the V/P effect is less (more)

pronounced among stocks more (less) exploited by mutual funds. We use mutual fund ownership

(MFO), change of number of mutual funds holding the stock (∆NoF) and change of mutual fund

ownership (∆MFO) as three measures to proxy for the mutual funds exploitation for the mispricing

of a particular stock. In particular, we examine whether or not stocks with higher V/P ratios and

lower mutual fund exploitation to have higher abnormal future returns comparing to those with

lower mutual fund ownership. If mutual funds have significant impact on the price-value

convergence process, we expect a lower level of fund exploitation (in the direction of V/P) to result

in a stronger V/P effect in the future.

We use a two-way independent sorting procedure to test the foregoing predictions. Along

one dimension, we first sort stocks into five quintiles on the basis of V/P at the end of each June.

In Panel A, we sort stocks into three tertiles based on mutual fund ownership in June and fund

28

trading during the past six months, respectively. We hold the 15 fractile portfolios for year t+1, t+2

and t+3 and compute their value-weighted monthly portfolio returns, respectively. The portfolios

are rebalanced at the end of the following June. In Panel B and C, we sort stocks based on the

change in the number of funds holding a stock in the past six months and the change in the mutual

funds ownership in the past six months, respectively. The Carhart 4-factor alphas for these

portfolios are reported in Table 9. In most cases (eight of nine), we find that stocks with less mutual

funds exploitation show stronger V/P effect than those with more mutual funds exploitation. The

only exception is in year t+3 when we use ∆NOF as the mutual funds exploitation measure.

However, the difference of V/P effect between high and low mutual funds exploitation is largely

insignificant. Overall, our results suggest that mutual funds help reducing the divergence between

price and intrinsic value, but that their impact is very limited.

[Insert Table 9 about here]

Mismatch between V/P Effect and Long-term Fund Portfolio Returns

Frankel and Lee (1998) find that abnormal returns of V/P strategy are stronger in year t+2 and

year t+3 than those in year t+1. As shown in Table 2, we confirm their finding in our sample period.

In particular, abnormal returns (Carhart 4-factor alphas) are highest in year t+2. However, in Table

8, we find that fund portfolio returns are highest in year t+1 and are declining in the following

years. This creates a mismatch between the V/P effect and fund returns. We conjecture that this is

because mutual funds usually do not hold the same position for a very long period. As we can see

from Table 1, the average turnover ratio is more than 83%. In particular, as shown in Table 5, funds

with highest VPT have an average turnover ratio around 100% suggesting that these funds on

average hold a position for one year. We expect that when mutual funds pursuing long-term

29

strategy hold stocks for a longer horizon, the patterns of their fund portfolio returns should be more

consistent with those of V/P effect. To examine this argument, we use a two-way independent

sorting procedure as we did in Table 9. Along one dimension, we first sort stocks into five quintiles

on the basis of V/P at the end of each June. Along another dimension, we sort stocks into three

tertiles based on mutual fund turnover ratio during the past year. The results reported in Table 10

support our conjecture. For mutual funds with lowest turnover ratio, funds with highest VPT

generate highest abnormal performance in year t+2 (monthly Carhart 4-factor alpha is 0.19% and

t-stat is 3.35) and then in year t+3 (monthly Carhart 4-factor alpha is 0.12% and t-stat is 2.68).

These funds only generate marginally significant abnormal performance in year t+1 (monthly

Carhart 4-factor alpha is 0.10% and t-stat is 1.70). These results are consistent with our conjecture

that the mismatch in V/P effect and fund portfolio returns is because of the frequent trading of

mutual funds.

[Insert Table 10 about here]

Analyst Forecast Bias

As shown in Frankel and Lee (1998), V/P is vulnerable to analyst forecast bias. In order to

examine the impact of analyst forecast bias on our results, we following Frankel and Lee (1998) to

construct a predicted analyst forecast bias variable using percentile rank of past five year sales

growth (RK_SG), of book to market ratio (RK_BP), of the measure OP in Frankel and Lee (1998)

(RK_OP), and of analyst consensus long-term earnings growth (RK_Ltg). OP is a measure of

analyst optimism defined as (Vf – Vh) / |Vh|. Vf is the intrinsic value used in calculating V/P ratio

before. Vh is calculated using earnings forecasts based on time-series models instead of analyst

forecasts. We regress analyst forecast error in year t+2 (FErrt+2) measured by subtracting actual

30

ROEt+2 from forecasted FROEt+2 on RK_SGt, RK_BPt, RK_OPt, and RK_Ltgt. Consistent with the

result in Table 7 of Frankel and Lee (1998), we find that FErrt+2 is positively and significantly

correlated with RK_SGt, RK_OPt, and RK_Ltgt and is insignificantly correlated with RK_BPt

(untabulated results). However, in further analyses, the predicted forecast errors cannot predict

future abnormal returns in our sample period. They are not associated with mutual fund trading and

fund portfolio returns either (untabulated results). Overall, the evidence suggests that our results

are not influenced by potential analyst forecast bias.

Other Accounting Based Anomalies

Prior studies suggest that exploiting other anomalies such as accrual anomaly or Post-

Earnings-Announcement-Drift (PEAD) can also affect the future performance of mutual funds (Ali

et al. 2008, 2012). We do not expect that exploiting trading strategies based on accrual anomaly or

PEAD will affect our results. The reason is that accrual anomaly and PEAD predict returns in a

relative short period (usually less than one year). However, V/P strategy is a long-term strategy

extending to three years. In untabulated results, we regress fund returns in year t+1, t+2 and t+3 on

decile rank of AVGVPT, AIM and PEADT. AVGVPT, AIM and PEADT are timing measure of

accrual anomaly and PEAD which are constructed in the same spirit of VPT. The decile rank of

AVGVPT are positively and significantly associated with fund returns in year t+1, t+2 and t+3. We

further control for fund characteristics such as fund size, fund age, expense ratio and fund turnover

ratio and our results hold.

Stocks without Valid V/P

31

As the construction of V/P ratio requires long-term analyst forecasts, there are some stocks

held by mutual funds without a valid V/P ratio.24 In previous analyses, we ignore these stock in

constructing VPT and AVGVPT. This practice might induce some selection bias in stocks. To

address this concern, we use Vh to construct V/P when Vf is missing. As discussed earlier, Vh is the

intrinsic value measure based on time-series forecasts. By replacing missing V/P with Vh/P, we

repeat the analyses in Table 8 and report the results in Table 11. The results are largely similar to

those in Table 8. Overall, our results are robust after considering various potential problems.

VII. CONCLUSIONS

This paper explores how effectively active mutual funds trade on and profit from long-term

price-value convergence. Over the 1981 to 2008 sample period, we find that in aggregate active

funds tend to trade on V/P anomalies as documented by Frankel and Lee (1998). The V/P ratio

measures the extent to which a stock is mispriced relative to its intrinsic value based on a

comprehensive valuation model: the residual income model. We use the residual income model

and analyst earnings forecasts to measure a firm’s intrinsic value, and show that mutual funds start

to exploit such mispricing opportunities. However, further analyses show that only a subgroup of

mutual funds do overweight underpriced stocks (high V/P stocks) and even this subgroup of mutual

funds does not appear to exploit the V/P anomaly very aggressively. Using fund return data before

fees, we show that funds that have the highest weights on underpriced stocks generate significant

risk-adjusted alpha over a three-year horizon. We also find evidence consistent with the notion that

mutual funds help improving long-term market efficiency. However, the impact of mutual funds

on long-term market efficiency is very limited.

24 We find that on average V/P ratio is missing for 30% of stocks held by mutual funds.

32

Appendix: Mutual Fund Sample Selection

We start with all U.S. equity mutual funds that appear in both the CRSP mutual fund

database and the CDA/Spectrum mutual fund holdings database. We use the MFLINKS data set

available from the WRDS to link the two databases. Our sample of stock holdings spans the 1981

to 2008 period.

Because we wish to capture active mutual funds that invest primarily in U.S. equities, we

follow Pastor and Stambaugh (2002) and Kacperczyk et al. (2008) by eliminating balanced, bond,

money market, sector and international funds, as well as funds that do not primarily invest in U.S.

common equity. We use the following specific steps in our sample selection process. We select

funds with the following Lipper class codes provided by the CRSP: EIEI, G, I, LCCE, LCGE,

LCVE, MCCE, MCGE, MCVE, MLCE, MLGE, MLVE, SCCE, SCGE or SCVE. If a fund does

not have any of these Lipper class codes, we select funds with the following Strategic Insight

objectives: SCG, GRO, AGG, ING, GRI or GMC. If both codes are missing for a fund, we pick

funds with the following Wiesenberger objectives: SCG, AGG, G, G-S, S-G, GRO, LTG, I, I-S,

IEQ, ING, GCI, G-I, G-I-S, G-S-I, I-G, I-G-S, I-S-G, S-G-I, S-I-G, GRI or MCG. If none of the

objective codes are available, we require that a fund have a CS policy code.

We eliminate funds with any of the following investment objectives provided by

CDA/Spectrum: international, municipal bonds, bond and preferred, and balanced. Furthermore,

we use portfolio composition data provided by CRSP MFDB to exclude funds that invest an

average of less than 80% or more than 105% of their funds under management in common equity.

To address the incubation bias documented by Elton et al. (2001) and Evans (2010), we exclude

observations prior to the reported fund inception date, observations for which the names of the

funds are missing from the CRSP database, and funds with net assets that fall below $5 million. To

33

prevent outliers from driving our results, we also require that a fund have at least 10 stock holdings

to be eligible for consideration in our analysis.

To ensure that we capture active mutual funds, we eliminate index funds with names that

include the following keywords: INDEX, INDE, INDX, INX, IDX, DOW JONES, ISHARE, S&P,

S &P, S& P, S & P, 500, WILSHIRE, RUSSELL, RUSS or MSCI. To lessen errors due to

abbreviation and misspelling, we manually inspect fund names and filter out the remaining

international, sector, tax-managed, fixed income, balanced and real estate funds, in addition to

annuities.

34

REFERENCES

Ali, A., L. Hwang, and M. Trombley. 2003. Residual-income-based valuation predicts future stock

returns: Evidence on mispricing vs. risk explanation. The Accounting Review 78, 377-396.

Ali, A., X. Chen, T. Yao, and T. Yu. 2008. Do mutual funds profit from accruals anomaly? Journal

of Accounting Research 46, 1-26.

——————. 2012. Mutual fund competition and profiting from the post earnings announcement drift.

Working Paper. Available at SSRN: http://dx.doi.org/10.2139/ssrn.2020662.

Baks, K., J. Busse, and T. Green. 2007. Fund managers who take big bets: Skilled or overconfident.

AFA 2007 Chicago Meetings Paper. Available at SSRN:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=891727.

Bartov, E., S. Radhakrishnan, and I. Krinksy. 2000. Investor sophistication and patterns in stock

returns after earnings announcements. The Accounting Review 75, 43–63.

Bernard, V., and J. Thomas. 1990. Evidence that stock prices do not fully reflect the implications

of current earnings for future earnings. Journal of Accounting and Economics 13, 305-340.

Boehmer, E., and E. Kelley. 2009. Institutional investors and the informational efficiency of prices.

Review of Financial Studies 22, 3563-3594.

Bradshaw, M., S. Richardson, and R. Sloan. 2001. Do analysts and auditors use information in

accruals? Journal of Accounting Research 39, 45–74.

Campbell, J., and A. Kyle. 1993. Smart money, noise trading, and stock price behavior. Review of

Economic Studies 60, 1-34.

Campbell, J., T. Ramadorai, and A. Schwartz. 2009. Caught on tape: Institutional trading, stock

returns and earnings announcements. Journal of Financial Economics 92, 66-91.

Carhart, M. 1997. On persistence in mutual fund performance. Journal of Finance 52, 57-82.

35

Cohen, R., J. Coval, and L. Pastor. 2005. Judging fund managers by the company they keep.

Journal of Finance 60, 1057-1096.

Collins, D., G. Gong and P. Hribar. 2003. Investor sophistication and the mispricing of accruals.

Review of Accounting Studies 8, 251-276.

Cremers, M., and A. Petajisto. 2009. How active is your fund manager? A new measure that

predicts performance. Review of Financial Studies 22, 3329-3365.

Daniel, K., M. Grinblatt, S. Titman, and R. Wermers. 1997. Measuring mutual fund performance

with characteristic-based benchmarks. Journal of Finance 52, 1035-1058.

Dasgupta, A., and A. Prat. 2008. Information aggregation in financial markets with career concerns.

Journal of Economic Theory 143, 83-113.

Dasgupta, A., A. Prat, and M. Verardo. 2011a. Institutional trade persistence and long-term equity

returns. Journal of Finance 66, 635-653.

——————. 2011b. The price impact of institutional herding. Review of Financial Studies 24, 892-925.

DeLong, J., A. Shleifer, L. Summers, and R. Waldmann. 1990. Noise trader risk in financial

markets. Journal of Political Economy 98, 703-738.

Edelen, R. 1999. Investor flows and the assessed performance of open-end mutual funds. Journal

of Financial Economics 53, 439-466.

Elton, E., M. Gruber, and C. Blake. 2001. A first look at the accuracy of the CRSP mutual fund

database and a comparison of the CRSP and Morningstar mutual fund databases. Journal of

Finance 56, 2415-2430.

Evans, R. 2010. Mutual fund incubation. Journal of Finance 65, 1581-1611.

Fama, E., and K. French. 1992. The cross-section of expected stock returns. Journal of Finance 46,

427-466.

——————. 1997. Industry costs of equity. Journal of Financial Economics 43, 153-193.

36

——————. 2008. Dissecting anomalies. Journal of Finance 63, 1653-1678.

——————. 2010. Luck versus skill in the cross section of mutual fund returns. Journal of Finance 65,

1915-1947.

Fama, E., and J. Macbeth. 1973. Risk and return: Empirical tests. Journal of Political Economy 81,

607-636.

Feltham, G., and J. Ohlson. 1995. Valuation and clean surplus accounting for operating and

financial activities. Contemporary Accounting Research 11, 689-731.

Frankel, R., and C. Lee. 1998. Accounting valuation, market expectation, and cross-sectional stock

returns. Journal of Accounting and Economics 25, 283-319.

French, K. 2008. Presidential address: the cost of active investing. Journal of Finance 63, 1537–

1573.

Gompers, P., and A. Metrick. 2001. Institutional investors and equity prices. Quarterly Journal of

Economics 116, 229-259.

Grinblatt, M., S. Titman, and R. Wermers. 1995. Momentum investment strategies, portfolio

performance, and herding: A study of mutual fund behavior. American Economic Review 85,

1088-1105.

Gu, Z., and J. Wu. 2003. Earnings skewness and analyst forecast bias. Journal of Accounting and

Economics 35, 5-29.

He, Z., and A. Krishnamurthy. 2012. A model of capital and crises. Review of Economic Studies

79, 735-777.

Jiang, X., and B. Lee. 2005. An empirical test of the accounting-based residual income model and

the traditional dividend discount model. Journal of Business 78, 1465-1504.

Jones, C., and M. Lipson. 2005. Are retail orders different? Working Paper. Available at:

http://www.darden.virginia.edu/web/Faculty-Research/Directory/Full-time/Marc-L-Lipson/

37

Kacperczyk, M., and A. Seru. 2007. Fund manager use of public information: New evidence on

managerial skills. Journal of Finance 62, 485-528.

Kacperczyk, M., C. Sialm, and L. Zheng. 2008. Unobserved actions of mutual funds. Review of

Financial Studies 21, 2379-2416.

Ke, B., and S. Ramalingegowda. 2005. Do institutional investors exploit the post-earnings

announcement drift? Journal of Accounting and Economics 39, 25-53.

Lee, C., J. Myers, and B. Swaminathan. 1999. What is the intrinsic value of the Dow? Journal of

Finance 54, 1693-1741.

Ohlson, J. 1990. A synthesis of security valuation theory and the role of dividends, cash flows, and

earnings. Contemporary Accounting Research 6, 648-676.

Ohlson, J. 1995. Earnings, book values, and dividends in security valuation. Contemporary

Accounting Research 11, 661-687.

Pastor, L., and R. Stambaugh. 2002. Mutual fund performance and seemingly unrelated assets.

Journal of Financial Economics 63, 313-349.

Richardson, S., I. Tuna and P. Wysocki. 2010. Accounting anomalies and fundamental analysis: A

review of recent research advances. Journal of Accounting and Economics 50, 410-454.

Scharfstein, D., and J. Stein. 1990. Herd behavior and investment. American Economic Review 80,

465-479.

Shleifer, A., and R. Vishny. 1997. The limits of arbitrage. Journal of Finance 52, 35-55.

Shumway, T. 1997. The delisting bias in CRSP data. Journal of Finance 52, 327-340.

Sloan, R. 1996. Do stock prices fully reflect information in accruals and cash flows about future

earnings? The Accounting Review 71, 289-316.

Stein, J. 2009. Presidential address: sophisticated investors and market efficiency. Journal of

Finance 64, 1517-1548.

38

Swaminathan, B. 1996. Time-varying expected small firm returns and closed-end fund discounts.

Review of Financial Studies 60, 249-282.

39

Figure 1: Equal-weight, market-adjusted change of mutual fund ownership This figure corresponds to the end of each quarter. Quarter 0 is the second calendar quarter of each calendar year. Using the same portfolio sorting procedure, we compute the equal-weight average of cross-sectionally demeaned change of mutual fund ownership of stocks in each quintile portfolio from Quarter -2 to Quarter +8. Change of mutual fund ownership is defined as the quarterly changes of the fraction of shares held by all mutual funds. This figure plots time-series average change of ownership numbers.

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

0.002

-2 -1 0 1 2 3 4 5 6 7

Mar

ket-A

dj C

hang

e of

Mut

ual

Fund

Ow

ners

hip

Event Quarters

Lowest V/P

Higest V/P

40

Table 1: Summary Statistics: Stocks and Mutual Funds This table presents summary statistics for our stock (Panel A) and mutual fund (Panel B) data (see the Appendix for details on sample selection). We compute equal-weight average characteristics at the end of each June from 1981 to 2007. In Panel A, V is the intrinsic value of a stock, and is estimated based on the residual income model developed by Frankel and Lee (1998). The value-to price ratio (V/P) is computed by dividing the analyst-based intrinsic value of a firm by its market capitalization at the fiscal year-end in the last calendar year. k is the dividend payout ratio, computed as common stock dividends divided by earnings to common shareholders. For firms with negative earnings, k is computed as common stock dividends divided by (total assets * 0.05). ROE is the return on equity for the last fiscal year, computed as net income divided by average book equity. ROA is the return on assets for the last fiscal year. We also compute the number of distinct stocks in the Compustat/CRSP merged database that have valid data available to compute V/P ratios, and the number of these stocks held by mutual funds. We also present mutual fund ownership and the number of distinct mutual funds that hold a stock in each year. Mutual fund ownership in a stock is calculated as the fraction of outstanding shares held by all mutual funds. The above calculations exclude stocks with prices lower than $1 at the end of each June. In Panel B, we calculate the cross-sectional averages of various fund characteristics in each year, including the number of distinct mutual funds, total net assets, 12b1 fees, expense ratio, turnover ratio and the percentage of fund common stock holdings. These fund characteristics are extracted from the CRSP fund summary database. 12b1 fees data in CRSP start from 1993, and fund turnover ratios for 1992 are missing from CRSP. The last row of the table presents time-series average annual cross-sectional means.

41

Panel A: Stock Characteristics Panel B: Mutual Fund Characteristics

Year V/P k ROE ROA

No. of Stocks (V/P

Universe)

No. of Stocks (V/P & Held by Funds)

Average Mutual Fund

Ownership (%)

No. of Funds

Holding the Stock

No. of Mutual Funds

TNA ($millions)

12b1 Fees (%)

Expense Ratio (%)

Turnover Ratio (%)

% of Common

Stock Holdings

1981 1.54 0.33 0.16 0.07 938 836 2.77 8 179 195.51 0.95 73.81 88.57 1982 1.40 0.32 0.16 0.07 1043 934 2.68 7 176 187.35 0.90 71.09 83.58 1983 1.31 0.33 0.12 0.06 1070 979 3.35 7 203 209.39 1.00 79.56 86.31 1984 1.11 0.29 0.11 0.05 1276 1181 3.81 7 211 280.93 0.89 78.92 87.30 1985 1.17 0.26 0.13 0.06 1273 1200 4.21 8 242 264.57 0.95 74.83 85.38 1986 0.99 0.25 0.10 0.05 1305 1242 4.75 9 263 333.89 0.98 80.73 85.91 1987 0.95 0.24 0.09 0.04 1305 1231 4.77 10 299 366.27 0.98 80.65 85.63 1988 1.10 0.22 0.11 0.05 1298 1225 4.70 11 311 365.61 1.03 91.77 86.03 1989 1.07 0.21 0.14 0.06 1361 1307 4.71 13 344 371.25 1.21 78.93 85.13 1990 0.96 0.22 0.13 0.06 1371 1314 5.30 14 365 446.21 1.25 77.41 86.19 1991 1.12 0.24 0.12 0.05 1368 1298 5.67 16 389 395.01 1.27 82.54 85.09 1992 0.92 0.23 0.09 0.04 1411 1324 5.76 15 431 540.76 1.06 86.97 1993 0.87 0.21 0.10 0.04 1543 1448 6.99 21 566 552.25 0.18 1.22 68.69 86.29 1994 0.84 0.19 0.09 0.04 1768 1754 8.14 26 703 602.26 0.17 1.18 71.32 87.67 1995 0.98 0.17 0.11 0.05 1909 1894 9.04 29 813 588.74 0.17 1.20 77.75 90.97 1996 0.88 0.15 0.11 0.05 2075 2063 9.82 29 894 804.72 0.16 1.23 81.77 90.94 1997 0.85 0.14 0.10 0.04 2171 2143 10.42 31 1018 950.73 0.17 1.25 84.21 92.19 1998 0.81 0.12 0.09 0.04 2294 2276 11.62 32 1138 1165.31 0.19 1.24 86.27 93.40 1999 0.86 0.12 0.08 0.03 2175 2142 11.39 34 1180 1419.84 0.20 1.25 87.12 93.71 2000 0.89 0.12 0.10 0.04 1867 1846 12.06 47 1347 1646.00 0.31 1.27 91.40 92.91 2001 0.87 0.11 0.10 0.04 1638 1633 13.30 58 1417 1514.64 0.32 1.26 100.74 92.42 2002 0.69 0.11 0.04 0.01 1619 1613 15.47 65 1485 1279.09 0.33 1.30 105.25 93.56 2003 0.76 0.11 0.05 0.02 1653 1644 15.03 66 1512 967.75 0.32 1.34 105.34 94.08 2004 0.67 0.10 0.06 0.02 1778 1771 16.19 66 1542 1278.23 0.31 1.36 92.51 95.25 2005 0.66 0.11 0.11 0.05 1785 1782 16.50 70 1556 1466.28 0.29 1.30 83.94 94.19 2006 0.70 0.11 0.11 0.05 1782 1780 17.31 69 1556 1536.13 0.27 1.27 83.71 96.43 2007 0.65 0.11 0.10 0.04 1785 1778 17.26 70 1518 1743.51 0.24 1.24 83.52 96.80

Average 0.95 0.19 0.10 0.05 1587 1542 9.00 31.05 802.15 795.27 0.24 1.16 83.61 89.74

42

Table 2: V/P and Future Stock Returns: Quintile Portfolios This table presents the performance of the quintile portfolios formed on the basis of the value-to-price ratio, V/P. V is an intrinsic value measure derived from a residual income model using the current I/B/E/S consensus earnings forecast available prior to June 30 of each year. Specifically, at the end of each June from 1981 to 2007, we sort stocks into quintiles in ascending order based on V/P and compute the average monthly value-weight portfolio return in the subsequent three years. We also present the risk-adjusted performance of these portfolios based on the CAPM, the Fama and French (1993) three-factor model, and the Carhart (1997) four-factor model. Stocks with prices lower than $1 at the time of portfolio formation are excluded. T-statistics are computed using Newey-West standard errors. *** represents statistical significance at the 1% level, ** represents statistical significance at the 5% level, and * represents statistical significance at the 10% level.

Panel A: Value-Weighted Post-Ranking Portfolio Return from July in year t to June in year t+1 (%/month)

(%/month)

Panel B: Value-Weighted Post-Ranking Portfolio Return from July in year t+1 to June in year t+2

(%/month)

Panel A: Value-Weighted Post-Ranking Portfolio Return from July in year t+2 to June in year t+3

(%/month)

V/P Quintile

Average Return

CAPM Alpha

FF Alpha Carhart Alpha

Average Return

CAPM Alpha

FF Alpha Carhart Alpha

Average Return

CAPM Alpha

FF Alpha Carhart Alpha

1 0.74 -0.37 -0.36 -0.11 0.80 -0.21 -0.22 -0.18 0.68 -0.23 -0.26 -0.23 (2.47) (-3.82) (-3.73) (-0.99) (2.54) (-2.24) (-2.30) (-1.54) (2.31) (-2.35) (-2.59) (-2.19) 2 0.91 -0.09 -0.02 -0.02 0.88 -0.08 -0.05 0.03 0.90 0.03 0.00 0.07 (3.68) (-1.24) (-0.35) (-0.37) (3.26) (-0.91) (-0.58) (0.27) (3.45) (0.37) (-0.02) (0.73) 3 1.06 0.12 0.10 0.05 0.97 0.07 0.06 0.01 0.88 0.03 0.05 0.08 (4.83) (1.61) (1.52) (0.78) (3.76) (0.98) (0.88) (0.14) (3.27) (0.28) (0.56) (0.95) 4 1.13 0.19 0.18 0.08 1.07 0.16 0.19 0.20 0.94 0.10 0.13 0.18 (5.1) (1.89) (1.96) (0.92) (4.24) (1.67) (2.00) (1.99) (3.56) (1.12) (1.51) (2.26) 5 1.46 0.44 0.46 0.33 1.41 0.43 0.60 0.56 1.12 0.24 0.37 0.40 (6.31) (2.73) (3.33) (2.69) (4.51) (2.87) (4.19) (3.47) (3.39) (1.35) (2.29) (2.39)

Q5-Q1 0.72*** 0.80*** 0.81*** 0.44** 0.61*** 0.65*** 0.82*** 0.74*** 0.44* 0.47** 0.63*** 0.63*** (3.29) (3.65) (4.24) (2.39) (3.13) (3.20) (4.12) (2.98) (1.94) (1.98) (2.76) (2.69)

43

Table 3: Stock Characteristics across V/P Quintiles At the end of each June from 1981 to 2007, we compute for each stock a measure of mispricing, V/P, which is the value-to-price ratio based on a residual income model. We then sort stocks into quintiles in ascending order based on V/P and calculate the stock characteristics for each quintile portfolio. This table reports time-series averages of the cross-sectional mean characteristics. Our set of characteristic variables includes the average value-to-price ratio V/P, the average book-to-market ratio, the average market cap, book-to-market, the past one-year return (11-month cumulative return over the t-11 to t-1 period), average total return volatility and stock turnover in the past year, and levels of and changes in mutual fund ownership of a stock (or the number of funds holding a stock) in the past year and in the following year. The market capitalization of a stock is computed by multiplying the stock price by the number of outstanding shares at each quarter-end (in millions). The V/P ratio is computed at the fiscal year-end in the last calendar year. The book-to-market ratio is determined for each stock at the end of the last calendar year using the book value of the stock at the end of the last fiscal year and the market value of the stock at the end of the last calendar year (see Fama and French (1992)). Stock volatility (Volatility) is calculated as the standard deviation of monthly returns in the past year (we require at least six monthly stock return observations to be available). Stock turnover (Turnover) is computed as total stock trading volume in the past year divided by the average of the stock prices at the beginning and end of the period. To facilitate comparison across deciles, we score for each year the size, book-to-market ratio and past returns from 1 to 5, with 5 representing the quintile with the largest market capitalization (based on NYSE breakpoints), the highest book-to-market ratio, and the highest past one-year return. Mutual fund ownership (MFO) of a stock is the fraction of outstanding shares owned by all mutual funds. The change in mutual fund ownership (∆MFO) of a stock and the number of funds holding a stock are measured yearly at the end of June. Stocks with prices lower than $1 at the end of each June are excluded.

V/P Quintile V/P B/M

ME Score (1~5)

BM Score (1~5)

Pr1Yr Score (1~5)

Volatility (%)

Turnover (%) MFOt (%)

No. of Funds (NoFt)

∆MFOt (%) ∆NoFt

∆MFOt+1 (%) ∆NoFt+1

1 0.40 0.62 2.40 2.70 2.44 13.30 155.29 8.57 26.56 0.08 -0.16 -0.24 0.29 2 0.67 0.58 2.80 2.59 2.86 10.78 124.98 9.40 35.46 0.26 1.03 -0.11 1.02 3 0.84 0.63 2.79 2.86 3.02 10.12 116.13 9.22 33.86 0.31 1.59 -0.14 1.10 4 1.05 0.66 2.66 2.92 3.14 10.75 126.70 9.22 33.04 0.43 2.14 -0.03 1.09 5 1.77 0.73 2.17 2.82 3.46 13.80 164.94 8.60 26.34 0.65 2.91 0.13 1.58

Q5-Q1 1.37 0.10 -0.23 0.12 1.02 0.50 9.65 0.03 -0.22 0.57 3.07 0.37 1.29

44

Table 4: V/P and Mutual Fund Trading: Fama and Macbeth (1973) Cross-Sectional Regressions This table presents the relation between the value-to-price ratio, V/P, of a stock at the end of each June and mutual fund trading in the stock over the prior two quarters and in the subsequent two quarters, controlling for other stock characteristics using the pool regressions. The dependent variable is the quarterly change in mutual fund ownership of a given stock. MFO is the fraction of shares held by mutual funds. We rank stocks at the end of June into five quintiles based on V/P, and use the ranks from 1 to 5 as the regression inputs for Models 1, 3, 5 and 7. We also construct two dummy variables, Q1 (Q5), which are equal to one when a stock is in Quintile 1 (5) and zero otherwise. We also construct quintile ranks for accruals, earnings changes, B/M ratios, and E/P ratios at the end of the last fiscal year-end in a similar way to V/P. Analyst earnings forecast revisions (Analyst Rev) are the contemporaneous changes of consensus forecasts. Market cap (ME), the book-to-market ratio (B/M), the past one-year return (Pr1Yr) and the stock turnover ratio (Turnover) are defined as previously. The E/P ratio is calculated by dividing earnings by market capitalization at the last fiscal year-end. Stock turnover is calculated on a quarterly basis. We also regress daily stock returns against daily Fama-French factors in a given quarter and use the standard deviation of the residuals as the residual volatility of the stock (Idio Vol) for that quarter (we require at least 40 daily stock return observations to be available). We also include the contemporaneous quarterly stock return (Rt) to control for funds’ return-chasing behavior. Stocks with prices lower than $1 at the beginning of each quarter are excluded. Standard errors are clustered by firm and year. *** represents statistical significance at the 1% level, ** represents statistical significance at the 5% level, and * represents statistical significance at the 10% level.

45

Panel A. Mutual fund trading and V/P strategy

Dependent Variable: ∆MFOt (%) Quarter (-1) Quarter (0) Quarter (+1) Quarter (+2) Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8 V/P Rank 0.023** 0.064*** 0.029*** -0.004 (2.42) (5.61) (2.82) (-0.36) Q1 -0.066** -0.129*** -0.064* 0.035 (-2.11) (-3.45) (-1.71) (0.90) Q5 0.018 0.139*** 0.047 0.014 (0.53) (3.44) (1.39) (0.39) B/M Rank -0.038*** -0.037*** -0.002 -0.001 -0.007 -0.007 -0.012 -0.013 (-4.10) (-4.08) (-0.16) (-0.08) (-0.73) (-0.69) (-1.12) (-1.14) E/P Rank 0.012 0.013 -0.045*** -0.041*** 0.001 0.003 0.021* 0.022* (1.20) (1.31) (-3.55) (-3.34) (0.10) (0.28) (1.71) (1.81) Accrual Rank -0.018** -0.018** 0.000 -0.000 -0.007 -0.007 0.021** 0.021** (-2.03) (-2.06) (0.01) (-0.01) (-0.75) (-0.77) (2.11) (2.11) Earnings Changes Rank 0.013 0.013 -0.023** -0.023** -0.029*** -0.028*** -0.020** -0.021** (1.38) (1.42) (-2.12) (-2.12) (-3.15) (-3.12) (-2.07) (-2.09) Analyst Rev 0.000** 0.000** -0.000*** -0.000*** -0.000*** -0.000*** -0.000*** -0.000*** (2.02) (2.02) (-8.90) (-7.63) (-7.68) (-6.87) (-5.70) (-4.93) Log(ME)t-1 0.031*** 0.030*** 0.025** 0.025** 0.013 0.012 -0.023** -0.023** (3.67) (3.53) (2.27) (2.19) (1.40) (1.29) (-2.01) (-1.97) Pr1Yrt-1 0.059** 0.059** 0.353*** 0.353*** 0.252*** 0.255*** 0.322*** 0.322*** (2.35) (2.36) (9.33) (9.33) (9.08) (9.15) (9.04) (9.05) Idio Volt-1 -2.302** -2.181** -9.594*** -9.553*** -6.698*** -6.615*** -9.799*** -9.891*** (-2.16) (-2.04) (-5.28) (-5.28) (-5.24) (-5.21) (-7.00) (-6.98) Turnovert-1 0.042 0.044 0.047 0.048 0.019 0.020 0.049 0.047 (0.81) (0.85) (0.54) (0.55) (0.46) (0.50) (0.85) (0.82) MFOt-1(%) -3.235*** -3.238*** -3.640*** -3.641*** -3.464*** -3.466*** -4.754*** -4.748*** (-14.61) (-14.59) (-12.07) (-12.05) (-12.93) (-12.87) (-10.02) (-9.96) Rt 0.733*** 0.740*** 0.761*** 0.765*** 0.845*** 0.847*** 0.491*** 0.492*** (12.27) (12.32) (8.34) (8.40) (12.89) (12.91) (7.05) (7.05) Intercept 0.288*** 0.365*** 0.548*** 0.728*** 0.438*** 0.523*** 0.774*** 0.749*** (3.42) (4.40) (4.90) (6.57) (4.30) (4.70) (7.70) (7.58) Adj-R2 2.42% 2.42% 3.12% 3.14% 2.78% 2.79% 3.39% 3.39%

46

Panel B. The temporal shift of mutual fund trading and V/P strategy Dependent Variable: ∆MFOt (%) Quarter (-1) Quarter (0) Model 1 Model 2 Model 3 Model 4 V/P Rank 0.059*** 0.072*** (3.78) (4.30) Q1 -0.043 0.061 (-0.80) (1.14) Q5 0.230*** 0.350*** (4.24) (5.72) Trend * V/P Rank -0.003*** -0.001 (-2.65) (-0.56) Trend * Q1 -0.001 -0.013*** (-0.28) (-3.11) Trend * Q5 -0.015*** -0.015*** (-4.00) (-3.44) Trend 0.049*** 0.044*** 0.047*** 0.051*** (12.49) (19.50) (10.89) (18.27) B/M Rank -0.057*** -0.057*** -0.022** -0.020* (-6.17) (-6.09) (-2.02) (-1.85) E/P Rank 0.009 0.010 -0.048*** -0.045*** (0.88) (0.98) (-3.81) (-3.62) Accrual Rank -0.020** -0.020** -0.003 -0.003 (-2.35) (-2.39) (-0.27) (-0.30) Earnings Changes Rank 0.015* 0.016* -0.021* -0.020* (1.65) (1.70) (-1.87) (-1.84) Analyst Rev 0.000*** 0.000*** -0.000*** -0.000*** (2.97) (3.10) (-7.28) (-5.91) Log(ME)t-1 -0.004 -0.005 -0.012 -0.013 (-0.48) (-0.60) (-1.14) (-1.20) Pr1Yrt-1 0.060** 0.060** 0.361*** 0.362*** (2.46) (2.49) (9.62) (9.62) Idio Volt-1 -6.389*** -6.217*** -14.241*** -14.167*** (-5.94) (-5.75) (-7.84) (-7.81) Turnovert-1 -0.023 -0.017 -0.007 -0.001 (-0.45) (-0.34) (-0.08) (-0.01) MFOt-1(%) -4.888*** -4.913*** -5.549*** -5.586*** (-18.76) (-18.80) (-15.78) (-15.80) Rt 0.769*** 0.775*** 0.714*** 0.718*** (12.77) (12.84) (7.86) (7.93) Intercept 0.161* 0.296*** 0.492*** 0.616*** (1.78) (3.57) (4.25) (5.61) Adj-R2 3.62% 3.63% 4.22% 4.24%

47

Table 5: Fund Characteristics across VPT –Sorted Decile Portfolios At the end of each June from 1981 to 2007, we compute for each fund a measure of V/P timing, VPT, which is defined as the weighted average V/P decile rank of individual stocks held by the mutual fund. We take average VPT in years t and t-1 to construct the average VPT score AVGVPT. We then sort mutual funds into deciles in ascending order based on AVGVPT and calculate equal-weight average fund characteristics for each decile portfolio. D1 (decile 1) has funds with the lowest AVGVPTs and D10 (decile 10) has funds with the highest AVGVPTs. This table reports time-series average cross-sectional mean fund characteristics. Our set of characteristic variables includes the average V/P timing measure VPT, the average fund age (in years), the average fund size (TNA), 12b1 fees (12b1 Fees), the expense ratio (Expense Ratio) and the fund turnover ratio (Turnover Ratio). All fund characteristics are extracted from the CRSP MFDB fund summary database. Stocks with prices lower than $1 at the end of each June are excluded.

Decile AVGVPT Age (years)

TNA ($Millions)

12b1 Fees (%)

Expense Ratio (%)

Turnover Ratio (%)

1 4.29 15.36 997 0.25 1.18 65.85 2 4.83 17.32 982 0.23 1.14 70.77 3 5.11 17.92 935 0.24 1.14 75.95 4 5.31 18.89 963 0.26 1.14 80.08 5 5.47 19.42 937 0.24 1.09 80.58 6 5.67 19.16 814 0.25 1.12 84.89 7 5.86 18.76 872 0.26 1.13 86.68 8 6.10 18.76 904 0.23 1.14 88.28 9 6.37 18.14 802 0.24 1.14 89.92

10 7.00 14.26 562 0.23 1.27 100.72 D10 - D1 2.72 -1.10 -435 -0.02 0.09 34.87

48

Table 6: Association between AVGVPT and other fund performance predictors: Cross-Sectional Regressions This table presents the relation between the fund V/P timing measure, AVGVPT, at the end of each June and other mutual fund performance predictors, controlling for other fund characteristics at the end of June from 1981 to 2007 and following the Fama and MacBeth (1973) procedure. The dependent variable is AVGVPT, which is defined as the weighted average V/P decile rank of individual stocks held by the mutual fund in years t and t-1. Fund age (Log(Age)), fund size (TNA), the fund expense ratio (Expense Ratio), the fund turnover ratio (Turnover Ratio) and fund past performance (Past Fund Performance) are included as control variables. Three fund performance predictors documented in prior studies are examined: average Active Share in the past year, Portfolio Concentration, and average Return Gap in the past year. Active Share is a measure of the extent to which the fund portfolio deviates from its benchmark, and was developed by Cremers and Petajisto (2009). We follow Baks, Busse, and Green (2007) by measuring Portfolio Concentration using a normalized Herfindahl index. The return gap is the difference between the return on a hypothetical holdings-based portfolio and the realized fund return (see Kacperczyk, Sialm, and Zheng, 2008). For these regressions, we restrict our sample period to 1990-2006 because the Active Share data are available from 1990Q1 to 2006Q4 from the website of Antti Petajisto. Stocks with prices lower than $1 are excluded when calculating the measures. Time-series average coefficients are reported in the table. T-statistics are computed using Newey-West standard errors. *** represents statistical significance at the 1% level, ** represents statistical significance at the 5% level, and * represents statistical significance at the 10% level.

Dependent Var: AVGVPT Log(Age) -0.0152 (-1.05) Log(TNA) -0.0043 (-0.51) Expense Ratio -0.0109 (-0.45) Turnover Ratio 0.0013*** (5.34) Past Fund Performance 0.0156** (2.44) Active Share 0.2109 (0.83) Portfolio Concentration -0.0466* (-2.03) Return Gap -0.2094** (-2.50) Intercept 5.1473*** (23.70) Adj-R2 20.08%

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Table 7: Portfolio Weights of D1, D5 and D10 Mutual Funds across V/P Stock Deciles At the end of each June from 1981 to 2007, we compute for each fund a measure of V/P timing, AVGVPT, which is defined as the weighted average V/P decile rank of individual stocks held by the mutual fund in years t and t-1. We then sort mutual funds into deciles in ascending order based on AVGVPT and calculate equal-weight average fund characteristics for each decile portfolio. D1 (decile 1) has funds with the lowest AVGVPTs, and D10 (decile 10) has funds with the highest AVGVPTs. This table reports the portfolio weights in each stock V/P decile for different groups of mutual funds: D1, D5 and D10 funds respectively. The portfolio weight of a stock V/P decile is the total value of the funds’ equity holdings. We report the time-series means of the portfolio weights. The t-statistics in parentheses are computed using Newey-West standard errors.

V/P Decile

D1 Fund Portfolio Weights

(%)

D5 Fund Portfolio Weights

(%)

D10 Fund Portfolio Weights

(%) D10-D1 D10-D5 1 20.43 10.27 3.97 -16.46 -6.29 (-10.96) (-6.88) 2 16.94 10.85 3.09 -13.85 -7.76 (-9.85) (-10.35) 3 13.27 11.09 3.41 -9.86 -7.68 (-8.68) (-8.75) 4 9.87 11.65 5.18 -4.69 -6.47 (-4.02) (-5.80) 5 9.03 10.81 6.13 -2.89 -4.68 (-2.94) (-4.90) 6 6.72 10.96 7.95 1.23 -3.01 (1.32) (-2.93) 7 5.73 10.95 9.29 3.56 -1.65 (3.02) (-1.30) 8 5.14 10.28 10.79 5.66 0.51 (4.04) (0.40) 9 4.15 9.74 13.72 9.57 3.98 (8.02) (3.06)

10 5.34 9.36 16.24 10.90 6.88 (6.84) (3.92)

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Table 8: AVGVPT and Fund Performance: Decile Portfolios This table presents the performance of the decile portfolios formed on the basis of the V/P timing measure, AVGVPT, which is the weighted average V/P decile rank of individual stocks held by the mutual fund in years t and t-1. D1 (decile 1) includes funds with the lowest AVGVPTs, and D10 (decile 10) comprises funds with the highest AVGVPTs. For each June from 1981 to 2007, we sort funds into deciles in ascending order based on AVGVPT and compute their average monthly fund size-weight portfolio returns for the year t+1, t+2 and t+3 (year t+1 is from June in year t to June in year t+1). Panels A, B and C present the results for the next three years. We also present the risk-adjusted performance of these portfolios based on the CAPM, the Fama and French (1993) three-factor model and the Carhart (1997) four-factor model. *** represents statistical significance at the 1% level, ** represents statistical significance at the 5% level, and * represents statistical significance at the 10% level.

Panel A: Size-Weighted Fund Portfolio Returns from July in year

t to June in Year t+1 (%/month) Panel B: Size-Weighted Fund Portfolio Returns from July in year

t+1 to June in Year t+2 (%/month) Panel C: Size-Weighted Fund Portfolio Returns from July in year

t+2 to June in Year t+3 (%/month)

Decile Average Return CAPM Alpha FF Alpha

Carhart Alpha

Average Return CAPM Alpha FF Alpha

Carhart Alpha

Average Return CAPM Alpha FF Alpha

Carhart Alpha

1 0.88 -0.18** -0.06 -0.03 0.83 -0.17** -0.10* -0.11* 0.79 -0.06 0.04 -0.03 (3.08) (-2.24) (-1.01) (-0.41) (2.73) (-2.43) (-1.70) (-1.67) (2.62) (-0.84) (0.68) (-0.47) 2 0.89 -0.11 -0.09 -0.05 0.92 -0.05 -0.04 -0.04 0.75 -0.08 -0.04 -0.09 (3.56) (-2.01) (-1.58) (-0.89) (3.27) (-0.86) (-0.76) (-0.63) (2.66) (-1.31) (-0.63) (-1.47) 3 0.95 -0.07 0.00 -0.03 0.84 -0.14 -0.10 -0.09 0.76 -0.07 -0.04 -0.06 (3.71) (-1.33) (0.10) (-0.58) (2.96) (-2.87) (-2.16) (-1.73) (2.77) (-1.38) (-0.94) (-1.22) 4 0.96 -0.03 0.02 0.00 0.86 -0.10 -0.07 -0.07 0.75 -0.07 -0.07 -0.09 (3.99) (-0.92) (0.49) (0.08) (3.15) (-2.26) (-1.80) (-1.52) (2.75) (-1.64) (-1.59) (-1.88) 5 0.98 -0.01 -0.01 -0.03 0.97 0.02 0.02 0.00 0.79 -0.03 -0.03 -0.02 (4.11) (-0.37) (-0.15) (-0.77) (3.63) (0.66) (0.62) (0.03) (2.95) (-0.88) (-0.77) (-0.37) 6 1.05 0.07 0.04 -0.01 0.94 -0.00 -0.03 -0.05 0.85 0.04 0.04 0.03 (4.44) (1.30) (0.98) (-0.28) (3.59) (-0.11) (-0.77) (-1.17) (3.22) (0.88) (1.03) (0.81) 7 1.09 0.12 0.06 0.00 0.98 0.04 0.03 -0.00 0.80 -0.01 -0.03 -0.02 (4.73) (1.95) (1.42) (0.06) (3.79) (1.07) (0.87) (-0.02) (3.05) (-0.15) (-0.69) (-0.46) 8 1.12 0.13 0.09 0.04 1.07 0.12 0.11 0.08 0.91 0.09 0.08 0.07 (4.66) (1.95) (1.69) (0.84) (4.05) (2.71) (2.53) (1.8) (3.37) (2.16) (2.02) (1.71) 9 1.11 0.14 0.11 0.06 1.10 0.15 0.12 0.11 0.87 0.06 0.02 0.07 (4.70) (2.01) (1.67) (0.8) (4.00) (2.62) (2.20) (2.04) (3.29) (0.94) (0.31) (1.09)

10 1.30 0.33*** 0.22*** 0.18** 1.18 0.25*** 0.19*** 0.14* 1.00 0.19** 0.13** 0.11* (5.29) (3.00) (2.83) (2.02) (4.5) (2.90) (2.66) (1.71) (3.67) (2.57) (2.22) (1.74)

D10-D1 0.42*** 0.51*** 0.28** 0.20* 0.35*** 0.42*** 0.30*** 0.25** 0.21* 0.25** 0.09 0.14 (2.77) (3.25) (2.53) (1.66) (2.88) (3.67) (2.92) (2.33) (1.82) (2.28) (0.91) (1.48)

D10-D5 0.33*** 0.34*** 0.23*** 0.21** 0.20** 0.23*** 0.17** 0.14 0.22*** 0.22*** 0.16** 0.13* (3.26) (3.24) (2.7) (2.16) (2.38) (2.64) (2.15) (1.58) (2.89) (2.92) (2.58) (1.81)

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Table 9: Mutual Fund Trading and the Return-Predictive Power of V/P This table presents the performance of the quintile portfolios formed on the basis of the value-to-price ratio, V/P, conditional on a mutual fund trading in the past six months. V/P, MFO, and the number of funds holding a stock (NoF) are defined as previously. We use independent two-way sorts. Specifically, at the end of each June from 1981 to 2007, we sort stocks into five quintile portfolios in ascending order based on V/P, and independently sort these stocks again into three tertiles in ascending order based on mutual fund aggregate holding and trading information in the past six months (we use mutual fund ownership to measure fund holdings (Panel A) and use the change in ownership or the change in the number of funds holding a stock to measure mutual fund trading (Panels B and C)). We then compute average monthly value-weighted portfolio returns in the subsequent three years. This table presents the risk-adjusted performance of these portfolios based on the Carhart (1997) four-factor model. Stocks with prices lower than $1 at the time of portfolio formation are excluded. T-statistics are computed using Newey-West standard errors. *** represents statistical significance at the 1% level, ** represents statistical significance at the 5% level, and * represents statistical significance at the 10% level.

Value-Weighted Post-Ranking Portfolio Return (Carhart Alpha %/month) Ranking Var V/P Year t+1 ( from July in year t to June in Year t+1) Year t+2 ( from July in year t+1 to June in Year t+2) Year t+3 ( from July in year t+2 to June in Year t+3

Panel A: MFO Low 3 High High - Low Low 3 High High -

Low Low 3 High High - Low

Low -0.17 0.11 0.42** 0.59** -0.16 -0.03 0.49 0.65*** -0.10 0.07 0.51 0.61*** (-0.92) (0.7) (2.04) (2.1) (-1.09) (-0.17) (3.02) (2.59) (-0.68) (0.47) (2.62) (2.79)

Median -0.13 0.05 0.37** 0.50** -0.26 0.02 0.75 1.02*** -0.26 0.03 0.37 0.63** (-1.02) (0.55) (2.11) (2.26) (-1.90) (0.21) (3.05) (3.09) (-1.92) (0.32) (1.99) (2.52)

High -0.07 -0.03 0.36 0.43 -0.05 -0.03 0.19 0.24 -0.22 0.16 0.18 0.41 (-0.47) (-0.24) (1.45) (1.51) (-0.32) (-0.21) (1.14) (0.96) (-1.50) (1.23) (0.82) (1.46)

High - Low 0.09 -0.14 -0.06 0.11 0.00 -0.30 -0.12 0.09 -0.32 (0.46) (-0.67) (-0.19) (0.52) (0.02) (-1.27) (-0.78) (0.53) (-1.01)

Panel B: ∆NoF Low 3 High High - Low Low 3 High High -

Low Low 3 High High - Low

Low 0.00 0.08 0.73*** 0.73*** -0.17 0.02 0.75 0.92*** 0.01 -0.07 0.62 0.61** (0.04) (0.61) (3.38) (3.02) (-0.97) (0.12) (4.01) (3.05) (0.12) (-0.71) (2.40) (2.19)

Median -0.12 0.03 0.17 0.29 -0.27 0.30 0.45 0.72*** -0.28 0.13 0.19 0.46* (-0.84) (0.17) (0.91) (1.14) (-1.45) (1.52) (2.04) (3.01) (-1.78) (0.93) (1.15) (1.88)

High -0.04 0.06 0.25 0.29 -0.16 -0.06 0.45 0.61** -0.36 0.15 0.33 0.69*** (-0.27) (0.8) (1.6) (1.25) (-1.17) (-0.65) (2.68) (2.43) (-2.66) (1.38) (1.75) (2.62)

High - Low -0.04 -0.01 -0.48* 0.01 -0.07 -0.31 -0.37*** 0.22 -0.29 (-0.27) (-0.08) (-1.89) (0.05) (-0.42) (-1.60) (-2.59) (1.28) (-1.07)

Panel C: ∆MFO Low 3 High High - Low Low 3 High High -

Low Low 3 High High - Low

Low -0.05 0.01 0.52*** 0.57** -0.18 0.05 0.78 0.96*** -0.06 0.13 0.49 0.55**

52

(-0.32) (0.05) (3.17) (2.3) (-1.07) -0.32 (4.02) (3.62) (-0.58) (1.16) (2.00) (2.15) Median -0.01 -0.00 0.10 0.11 -0.17 -0.06 0.60 0.77** -0.28 0.01 0.44 0.72**

(-0.04) (-0.01) (0.57) (0.4) (-1.21) (-0.55) (2.69) (2.31) (-1.91) (0.11) (1.79) (2.30) High -0.17 0.05 0.37 0.54 -0.12 -0.03 0.25 0.37* -0.27 0.15 0.19 0.45*

(-1.05) (0.42) (1.42) (1.57) (-0.87) (-0.30) (1.53) (1.67) (-1.76) (1.19) (0.99) (1.91) High - Low -0.12 0.04 -0.15 0.06 -0.09 -0.52** -0.21 0.02 -0.30

(-0.53) (0.28) (-0.5) (0.40) (-0.40) (-2.42) (-1.25) (0.10) (-0.94)

53

Table 10: Mutual Fund Turnover and the Fund Returns based on VPT This table presents the performance of the quintile portfolios formed on the basis of the mutual fund timing measure VPT, conditional on a mutual fund turnover ratio in the past year. VPT and Turnover Ratio are defined as previously. We use independent two-way sorts. Specifically, at the end of each June from 1981 to 2007, we sort stocks into five quintile portfolios in ascending order based on VPT, and independently sort these stocks again into three tertiles in ascending order based on mutual fund turnover ratio in the past year. We then compute average monthly value-weighted portfolio returns in the subsequent three years. This table presents the risk-adjusted performance of these portfolios based on the Carhart (1997) four-factor model. Stocks with prices lower than $1 at the time of portfolio formation are excluded. T-statistics are computed using Newey-West standard errors. *** represents statistical significance at the 1% level, ** represents statistical significance at the 5% level, and * represents statistical significance at the 10% level.

Value-Weighted Post-Ranking Portfolio Return (Carhart Alpha %/month) Ranking Var VPT Year t+1 ( from July in year t to June in Year t+1) Year t+2 ( from July in year t+1 to June in Year t+2) Year t+3 ( from July in year t+2 to June in Year t+3

Turnover Ratio Low 3 High High - Low Low 3 High High -

Low Low 3 High High - Low

Low -0.04 -0.01 0.10 0.14 -0.05 -0.01 0.19 0.24*** -0.03 0.04 0.12 0.15* (-0.77) (-0.31) (1.70) (1.52) (-1.08) (-0.32) (3.35) (3.05) (-0.54) (0.89) (2.68) (1.92)

Median 0.02 -0.02 0.12 0.11 -0.06 -0.03 0.06 0.12 -0.02 -0.01 0.06 0.08 (0.23) (-0.60) (1.42) (1.00) (-0.77) (-0.57) (0.92) (1.22) (-0.32) (-0.27) (0.96) (0.82)

High -0.11 -0.01 0.01 0.12 -0.12 -0.10 0.02 0.13 -0.09 -0.03 0.09 0.18* (-1.18) (-0.13) (0.16) (1.20) (-1.32) (-1.62) (0.21) (1.41) (-1.01) (-0.51) (1.25) (1.70)

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Table 11: Replacing Missing V/P with Vh/P This table presents the performance of the decile portfolios formed on the basis of the V/P timing measure, AVGVPT, which is the weighted average V/P decile rank of individual stocks held by the mutual fund in years t and t-1. In contrast to Table 8, we replace missing V/P with Vh/P to construct VPT. Vh is the measure of intrinsic value using time-series forecasts instead of analyst forecasts. D1 (decile 1) includes funds with the lowest AVGVPTs, and D10 (decile 10) comprises funds with the highest AVGVPTs. For each June from 1981 to 2007, we sort funds into deciles in ascending order based on AVGVPT and compute their average monthly fund size-weight portfolio returns for the year t+1, t+2 and t+3 (year t+1 is from June in year t to June in year t+1). Panels A, B and C present the results for the next three years. We present the risk-adjusted performance of these portfolios based on the Carhart (1997) four-factor model. *** represents statistical significance at the 1% level, ** represents statistical significance at the 5% level, and * represents statistical significance at the 10% level.

Panel A: Size-Weighted Fund Portfolio Returns from July in

year t to June in Year t+1 (%/month) Panel B: Size-Weighted Fund Portfolio Returns from July in

year t+1 to June in Year t+2 (%/month) Panel C: Size-Weighted Fund Portfolio Returns from July in

year t+2 to June in Year t+3 (%/month)

Decile Carhart Alpha Carhart Alpha Carhart Alpha 1 -0.02 -0.12 -0.04 (-0.31) (-1.69) (-0.67) 2 -0.09 -0.03 -0.12 (-1.49) (-0.46) (-1.80) 3 -0.02 -0.08 -0.09 (-0.42) (-1.45) (-1.98) 4 0.03 -0.09 -0.09 (0.87) (-1.89) (-1.77) 5 -0.03 -0.01 -0.04 (-0.78) (-0.29) (-0.90) 6 0.00 -0.03 0.04 (0.09) (-0.62) (0.83) 7 0.01 0.00 0.00 (0.13) (0.01) (0.00) 8 0.06 0.10 0.11 (1.20) (1.97) (1.94) 9 0.04 0.07 0.03 (0.69) (1.21) (0.52)

10 0.19 0.11 0.13 (2.17) (1.71) (1.81)

D10-D1 0.21 0.23** 0.17* (1.62) (2.13) (1.74)

D10-D5 0.22** 0.12 0.16** (2.30) (1.61) (2.00)