Where are the smart investors? New evidence of the smart money effect

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Where are the smart investors? New evidence of the smart money effect

Hsin-Yi Yu

Department of Finance, National University of Kaohsiung, 700, Kaohsiung University Rd., Nanzih District, 811, Kaohsiung, Taiwan

a r t i c l e i n f o

a b s t r a c t

Article history:

Received 11 January 2011

Received in revised form 5 September 2011 Accepted 28 September 2011

Available online 6 October 2011

Previous research debates whether investors are smart enough to invest in funds that sub-sequently outperform. This paper documents a robust smart money effect among top-performing small fund investors, even after controlling for the momentum factor. I further ex-plore the reason for the smart money effect and find that such outperformance comes from the market-timing ability of smart investors. Market-timing ability distinguishes smart investors from investors who naively chase the winners.

© 2011 Elsevier B.V. All rights reserved.

JEL classification: G11

G20

Keywords: Smart money effect Fund cash flow Fund performance Timing ability

1. Introduction

Do smart investors invest in poor-performing funds? Recent studies debate whether investors are smart enough to invest in funds that will outperform in the future, so-called the“smart money” effect (Gruber, 1996; Keswani and Stolin, 2008; Sapp and

Tiwari, 2004; Wermers, 2003; Zheng, 1999). To provide evidence for the smart money effect, most studies focus on the fund flow

of all equity fund investors in the aggregate. However, if investors are really smart, they will pick top-performing funds as their final destination and stay with them. That is, the top-performing fund group should be the best place to identify smart investors. This paper provides evidence for the above argument. Furthermore, I also find that the risk-adjusted returns earned by smart investors stem from market-timing ability. In other words, the smart investors not only perceive which fund to invest in but also detect when to invest.

Research concerning the smart money effect in the mutual fund context was initiated byGruber (1996), confirmed byZheng

(1999), challenged bySapp and Tiwari (2004), and recently re-examined byKeswani and Stolin (2008).Gruber (1996) and Zheng

(1999)coined the term smart money effect; they find evidence that a group of sophisticated investors seem to identify the superior

funds and invest accordingly to outperform the market. However, after controlling for the momentum effect,Sapp and Tiwari

(2004)demonstrate that the smart money effect is no longer significant. They conclude that the outperformance is due to

the momentum effect rather than the intelligence of investors. Subsequently,Keswani and Stolin (2008)attribute the insignificant

☆ The research data were collected during the study in the University of Edinburgh.This paper has benefited from discussions with and comments from David Stolin, Robin Luo, Wikrom Prombutr, an anonymous referee, the participants at the European Financial Management Association 2010 conference and the 2010 Financial Management Association annual meeting, and the colleagues in the University of Edinburgh. I am especially grateful to Li-Wen Chen for technical as-sistance. I also acknowledgefinancial support from the National Science Council.

⁎ Tel.: +886 7 5919709; fax: +886 7 5919329. E-mail address:hyyu@nuk.edu.tw.

0927-5398/$– see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jempfin.2011.09.005

Contents lists available atSciVerse ScienceDirect

Journal of Empirical Finance

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smart money effect demonstrated bySapp and Tiwari (2004)to the use of quarterly data and the weight they place on the pre-1991 period.Keswani and Stolin (2008)confirm the smart money effect in the U.K. based on monthly data.

It is interesting to note that previous studies, whether they support or reject the smart money effect, focus on the sample that covers all fund investors in the market, including naive investors who simply chase the star funds (Guercio and Tkac, 2008). Thus, the smart money effect may be diluted by the winner chasers. In addition, observing the samples in previous studies, researchers implicitly assume that smart investors can be found in bottom-performing funds. However, smart investors should be able to avoid bottom-performing funds and invest in top-performing funds. Therefore, unlike previous studies, I investigate the smart money effect by examining the risk-adjusted returns of investors in different fund groups ranked by excess returns. If investors who invest in top performers can make significant risk-adjusted returns even after the momentum effect is controlled for, it suggests that these investors are indeed smart and possess undiscovered skills for earning abnormal returns.

The sample covers the complete universe of 9,607 diversified U.S. equity mutual funds for the period from January 1993 to September 2008 in the CRSP Survivor-Bias Free U.S. Mutual Fund Database. Similar toZheng (1999), this paper begins with an examination of the GT measure (Grinblatt and Titman, 1993). The result indicates that investors who invest in funds whose total net assets (TNA) are in the lowest 20% can profit by tilting their portfolio weights over time in favor of assets with higher expected returns and away from assets with lower expected returns. Due to the absence of practical implementation of the GT measure, I subsequently follow the method ofZheng (1999)to construct ten trading strategies to further investigate the practical implications of fund flow information by using small funds whose TNA are in the lowest 20%. These portfolios are weighted by unexpected flows that measure the differences between the actual flows and expected flows.

The results suggest that the smart investors can be found in the top-performing funds. After I rank the small funds into quintiles based on past excess returns, only the group with the top performance exhibits the significantly positive risk-adjusted return, and such outperformance cannot be subsumed by the momentum factor. However, the trading strategies of the entire small fund group do not exhibit the significant risk-adjusted returns over the market. This shows that using the entire sample would dilute the smart money effect, as I argue above. In addition, the result also indicates that the smart money effect is short lived.

Because the behavior of flocking to the top-performing funds is itself momentum, it is surprising to find that the risk-adjusted returns of the top-performing small fund group cannot be explained by the momentum effect. Hence, the smart investors should possess undiscovered skills for distinguishing themselves from the momentum-style investors who simply chase the recent winners.

But what kind of skills do these investors possess? If both smart investors and momentum-style investors can identify superior funds, the potential difference between smart investors and momentum-style investors is the time of trading these superior funds, i.e., timing ability. For example, suppose there is a fund that performs very well from t + 1 to t + 12. Smart investors would buy it at the beginning of t + 1 and sell it at the end of t + 12. On the other hand, momentum-style investors, who chase the winners based on, for instance, the past three-month returns, can still identify this fund. However, the momentum strategy would lead them to buy this fund at the beginning of t + 4 and sell it at the end of t + 15. Obviously, both the smart investors and momentum-style investors invest in this fund from t + 4 to t + 12, but the smart investors would obtain higher returns than momentum-style investors due to better timing ability. Owing to the overlap of holding periods, it is possible that smart investors are misidentified as momentum-style investors when using all fund investors in the market as the sample. Following this vein, I further examine whether timing ability is the determinant of earning abnormal returns for smart investors. Four timing models are used to observe whether smart investors possess timing ability. If the risk-adjusted returns earned by the smart investors can be fully explained by timing factors, we can conclude that smart investors possess timing skills.

The result provides evidence that the smart money effect comes from the market-timing ability of smart investors. After the influence of timing activities is considered in the performance evaluation model, the risk-adjusted returns in the top-performing small fund group are no longer significant. This finding is also complemented by the short-lived smart money effect presented above. The short-lived phenomenon implies that the skill owned by smart investors might be a skill that appears occasionally rather than continuously or can only be practiced within a short time period. Market-timing ability corresponds to these characteristics.

In summary, this paper provides evidence that smart investors appear in the top-performing small funds. Additionally, they possess market-timing ability to distinguish themselves from those who naively flock to winners. The significant risk-adjusted returns earned by the smart investors with market-timing ability provide a partial answer for the question posed byGruber

(1996): why do investors buy actively managed mutual funds when mutual funds, on average, offer a negative risk-adjusted return?

This is because a group of smart investors seems to identify superior funds by the fact that the flow information predicts future performance. The result also provides a rationale for the growth in actively managed mutual funds.

The paper is organized as follows. I describe the related literature briefly inSection 2and introduce the methodology inSection 3.

Section 4outlines the data.Section 5presents the results.Section 6gauges the robustness of the results.Section 7concludes.

2. Literature review

The four key studies concerning the smart money effect are those ofGruber (1996), Zheng (1999), Sapp and Tiwari (2004),

and Keswani and Stolin (2008). Gruber's aim is to understand the continued expansion of the actively managed mutual fund sector

despite widespread evidence that, on average, active fund managers do not add value. He finds evidence that a group of sophisticated investors seems to identify the superior funds. Thus, money appears to be smart. Expanding the dataset,Zheng (1999)claims that

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funds that experience positive new money flows significantly outperform those that experience negative new money flows, and new flows into small rather than large funds can be used to make risk-adjusted returns.

However,Sapp and Tiwari (2004)attribute this outperformance to the momentum effect documented byJegadeesh and Titman

(1993)and conclude that the smart money effect is an artifact of return continuation. The smart money debate was raised again by

the recent work ofKeswani and Stolin (2008). Keswani and Stolin re-examine the smart money issue with the U.K. data. They find that the portfolios of new money weighted by inflows outperform those weighted by outflows. They also provide evidence that the smart money effect in the U.K. is due to the fund buying (but not sales) of both individual and institutional investors. They finally ascribe the insignificance of the smart money effect inSapp and Tiwari (2004)to the use of quarterly data and the weight they place on the pre-1991 period. However, the smart money effect in the U.K. can only be documented by using the long-short strategy. The risk-adjusted return of a single portfolio is negative, which implies that buying behavior alone in the UK is not smart enough. Furthermore,Sawicki and Finn (2002)confirm that the smart money effect is neither size-neutral nor age-neutral. Investors respond more strongly to recent performance of small (young) funds than to recent performance of large (old) funds. On the contrary,Frazzini

and Lamont (2008)suggest that poor fund selection decisions end up costing longer-term investors approximately 0.84% per year, a

result they dub the“dumb money” effect. Along the avenue of timing ability, the work ofFriesen and Sapp (2007)examine the timing ability of mutual fund investors at the individual fund level. They find that fund investor timing decisions reduce fund investor returns by 1.56% annually.

In summary, prior studies do not exploit the possibility that smart investors are more likely to be identified in top-performing funds. To fill the gap, this paper focuses on the investors in top-performing funds to observe whether these investors possess undiscovered skills to earn significant risk-adjusted returns.

3. Methodology

3.1. The GT measure of performance

To estimate the aggregate abilities of investors in selecting mutual funds and switching between them, the GT measure introduced by Grinblatt and Titman (1993)is employed. The GT performance measure for a given month t is calculated as follows: GT Measuret¼ ∑ N i¼1 Ri;tþ1 wi;t−wi;t−1   ð1Þ where wi, tis the portfolio weight for fund i at time t, which is equal to the TNA for fund i divided by the total TNA for all domestic

equity funds. The change of portfolio weight for fund i, i.e., (wi,t−wi,t− 1), is called the GT weight; it will be utilized to construct

portfolios in a later section. Ri,t + 1is the return of fund i between time t and t + 1. Note that the calculation of the GT measure

requires that a fund must survive for more than two months. However, the zero-cost portfolio assumption implicitly assumes that the investor can short sell assets to finance the purchase of others when short-selling cannot be implemented by fund investors. Therefore, similar toZheng (1999), ten trading strategies are constructed to explore the practical implications of fund flows.

3.2. Unexpectedflows

Monthly new cash flows into a fund are defined as the dollar change in TNA with an adjustment for increases in fund TNA due to mergers and then divided by the TNA at the immediately preceding month. New money is assumed to come at the end of each month. Defunct funds are not excluded from the sample before they disappear, and this mitigates survivorship bias.

flowi;t¼

TNAi;t−TNAi;t−1× 1þ Ri;t

 

−MGTNAi;t

TNAi;t−1 ð2Þ

where Ri,tis the raw return of fund i during month t, TNAi,trefers to fund i's TNA at the end of month t, and MGTNAi,tstands for

changes in fund i's TNA due to merging of other funds into fund i.

Based on the new cash flows in Eq.(2), I compute the unexpected flows with a procedure similar to that used byCoval and

Stafford (2007). Unexpected flows are the differences between the actual flows and expected flows, which are estimated by

lagged fund raw returns and new cash flows from the previous 12 months (Chevalier and Ellison, 1997; Coval and Stafford,

2007; Sirri and Tufano, 1998). A simple Fama and MacBeth (1973)regression model in Eq. (3)is used to forecast fund

flows. flowi;t¼ a þ ∑ 12 k¼1 bk⋅flowi;t−kþ ∑ 12 h¼1 ch⋅Ri;t−hþ εi;t ð3Þ

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where the residualεi, tis the unexpected flow and Ri, t− his the past raw return of fund i. To obtain the most reliable data, I limit the

changes in TNA so that they cannot be too extreme:−3:0 ≤ TNAFLOWi;t

i;t−1 ≤ 3:0.

1In total, 189 cross-sectional regressions throughout the 16-year observation period are included.

3.3. Trading strategies

Consistent with the work ofZheng (1999), I construct ten hypothetical trading strategies. Portfolio 1 Equally weighted portfolio of all available funds.

Portfolio 2 In all available funds and weighted by current TNA of the fund.

Portfolio 3 Equally weighted portfolio of all available funds with positive unexpected flows. Portfolio 4 Equally weighted portfolio of all available funds with negative unexpected flows.

Portfolio 5 In all available funds with positive unexpected flows and weighted in proportion to the unexpected flow of the fund. Portfolio 6 In all available funds with negative unexpected flows and weighted in proportion to the unexpected flow of the fund. Portfolio 7 Equally weighted portfolio of all available funds with above-median unexpected flows.

Portfolio 8 Equally weighted portfolio of all available funds with below-median unexpected flows.

Portfolio 9 In all available funds with positive GT weights and weighted in proportion to GT weights of the funds. Portfolio 10 In all available funds with negative GT weights and weighted in proportion to GT weights of the funds.

To take the spirit of the GT measure into consideration, portfolios 9 and 10 are weighted by the GT weight, i.e., (wi, t−wi, t− 1),

calculated in the GT measure. All trading portfolios are constructed at the beginning of each month, based on the relevant information of the immediately preceding month. These portfolios are held for one month. The risk-adjusted returns of portfolios are evaluated by the three-factor model inFama and French (1993)and the four-factor model inCarhart (1997).2The factor data are collected from the website of Kenneth R. French.

3.4. Timing ability

This paper uses four models based onTreynor and Mazuy (1966) and Henriksson and Merton (1981)to investigate whether the aggregate risk-adjusted returns can be fully explained by the timing factors.

Revised Treynor–Mazuy model (TM):

ri;t¼ αiþ βi⋅RMRFtþ si⋅SMBtþ hi⋅HMLtþ pi⋅PR1YRtþ γ1;i⋅RMRFt2þ εi;t ð4Þ

Revised Henriksson–Merton model (HM):

ri;t¼ αiþ βi⋅RMRFtþ si⋅SMBtþ hi⋅HMLtþ pi⋅PR1YRtþ γ1;i⋅RMRFtþ εi;t ð5Þ

RMRFt¼ I RMRFf tN 0g⋅RMRFt

Treynor–Mazuy–Carhart factor timing model (TMC):

ri;t¼ αiþ βi⋅RMRFtþ si⋅SMBtþ hi⋅HMLtþ pi⋅PR1YRtþ γ1;i⋅RMRF2t þ γ2;i⋅SMB2tþ γ3;i⋅HML2tþ γ4;i⋅PR1YR2tþ εi;t ð6Þ

Henriksson–Merton–Carhart factor timing model (HMC):

ri;t¼ αiþ βi⋅RMRFtþ si⋅SMBtþ hi⋅HMLtþ pi⋅PR1YRtþ γ1;i⋅RMRFtþ γ2;i⋅SMBtþ γ3;i⋅HMLtþ γ4;i⋅PR1YRtþ εi;t ð7Þ

RMRFt¼ I RMRFf tN 0g⋅RMRFt

SMBt¼ I SMBf tN 0g⋅SMBt

HMLt¼ I HMLf tN 0g⋅HMLt

PR1YRt ¼ I PR1YRf tN 0g⋅PR1YRt

where ri, tis the excess return of the mutual fund i at month t (net return minus one-month T-bill return), I{condition} is an indicator

function that equals one if the condition is true, and zero otherwise. FollowingVolkman (1999), Bollen and Busse (2001), and Chen et

al. (2009), the factor timing models in Eqs.(6) and (7)measure three extra timing skills: SMBtmeasures the ability to choose between

1

For some mutual funds, the new cashflows are hundreds of times the TNA, which is not possible or can occur only in very special situations. For funds that cannot conform to the data requirements, I delete the observation for fund i at time t. The results are not altered without such winsorization.

2

In addition to the factor models, an alternative approach is whatZheng (1999)terms the“fund regression approach”. However, the fund regression approach only includes funds with a sufficiently long return history. This means that using the fund regression approach may ignore many funds that do not survive suf-ficiently long. For this reason and for comparability with portfolio results inZheng (1999) and Sapp and Tiwari (2004), this paper shows the results obtained under the factor models, although the results of using the fund regression approach are similar.

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small- and large-capitalization companies, HMLtcaptures the ability to choose between value and growth stock, and PR1YRtreveals

the ability to choose between momentum and contrarian strategies.

4. Data and samples

The data were collected from the Center for Research in Security Prices (CRSP) mutual fund database. The sample includes all domestic equity funds that existed during the period from January 1993 to September 2008.3I exclude international funds, sector funds, specialized funds, and balanced funds because these funds may have risk characteristics that are not spanned by the factors driving the returns of most other mutual funds. In summary, the sample has a total of 9607 fund entities and 868,190 fund months.

Table 1presents descriptive statistics. The average (median) fund size measured by TNA is $466.28 ($37.8) million. Evidently,

the sample is somewhat skewed by larger funds. I therefore classify the funds into quintiles based on TNA. In the unreported results, the average (median) fund size of the top quintile ranking by TNA is $2131.46 ($744.9) million, whereas the average (median) fund size of the bottom quintile is $1.29 ($0.8) million. It is obvious that the variation of fund size is large enough to produce different results.

5. Empirical results

5.1. GT measure

Zheng (1999)finds that all equity funds in the aggregate demonstrate a positive GT measure, but she does not examine

whether the finding is size neutral. This section investigates whether the significant GT measure can be ascribed to the small fund group.

I sort funds into quintiles based on TNA.Table 2presents the GT measure estimates in different size quintiles. Unfortunately, unlike the findings ofZheng (1999), the GT measure for the entire sample is not significant. However, after ranking the entire sample into quintiles by TNA, we can observe that the GT measure for the bottom quintile is significant, whereas it is insignificant for the other four quintiles. For the bottom quintile, the GT measure is 2.36 basis points per month (approximately 28.69 basis points annually), which is smaller than that found inZheng (1999). This finding provides evidence that only investors in the bottom quintile show significant ability of switching assets. Other investors do not significantly switch their money to assets with increasing expected returns. In this regard, the smart money effect is not an overall phenomenon but rather can only be observed in the bottom size quintile.

This finding can be attributed to two possible interpretations. First, based on the model ofHuang et al. (2007), the costs of information collection and redemption, the so-called participation costs, affect fund flows. Funds with different participation costs possess different sensitivities of flows to past performance. A large well-known fund has a lower information barrier such that investors can overcome hurdles even if fund performance is mediocre. However, a small no-name fund has a high information barrier and thereby can only attract investors by means of a superior past performance. Therefore, investors would notice and invest their money in small no-name funds only when these small funds exhibit superior past performance. Given this, investors would unwittingly benefit from the ex post good performance of these small funds. This line of thinking implies that the returns earned by investing in small funds with good past performance would be explained by the momentum effect (Sapp and Tiwari, 2004).

3I base the selection criteria on two objective codes: the Strategic Insights Objective Code and the Lipper Objective Code. Because the Strategic Insights

Objec-tive Code generally provides fund objecObjec-tive codes from 1993 to 1998, while the Lipper ObjecObjec-tive Code does so from 1998 to 2008, I selected the observations based on a union of the two codes.

Table 1

Descriptive statistics for the mutual fund sample.

Mean Median 25th percentile 75th percentile Standard deviation

TNAs ($ millions) 466.28 37.80 6.20 187.20 2643.00

Monthly new cash flow 0.02 0.00 −0.02 0.03 0.13

Monthly new cash flow without size adjustment ($ millions) 1.77 0.04 −1.19 2.24 167.65

Monthly raw return (basis point) 61.72 93.70 −202.47 348.78 522.45

Monthly excess return (basis point) 32.92 65.47 −229.48 318.75 522.27

Unexpected flow (%) −0.19 −0.95 −2.96 1.70 11.35

This table presents a summary of the descriptive statistics. The sample includes all U.S. equity mutual funds from January 1993 to September 2008. The monthly excess return is defined as the monthly raw return minus the one-month Treasury bill rate. The monthly new cash flow is measured as flowi, t= [TNAi, t−TNAi, t− 1×

(1 + Ri, t)−MGTNAi, t]/TNAi, t− 1. The terms TNAi, t− 1and TNAi, trepresent the TNA for the fund at the end of month t−1 and t, Ri, trepresents the fund's raw return in

month t, and MGTNAi, trepresents the increase in the fund's TNA due to mergers during month t. The new cash flow without size adjustment is computed as the

monthly new cash flow without dividing by the TNA at the beginning of the month. Unexpected flows are the differences between the actual flows and expected flows, which are estimated by lagged fund raw returns and new cash flows from the previous year.

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Alternatively, fund size may affect trading strategy. Investors might be more cautious when investing in small funds than in larger funds (Zheng, 1999). In addition, funds with different sizes may attract different investors. Small funds generally have less media coverage and higher participation costs (Huang et al., 2007; Jain and Wu, 2000); thus, the small fund investors are more likely to trade for sophisticated reasons rather than because of newspaper or analyst recommendations. If this argument were true, the risk-adjusted returns earned by the small fund investors would still be significant when the momentum factor is controlled.

5.2. The performance of trading strategies

This section observes portfolio performance to distinguish between the two interpretations raised in the former section and examine whether the significant GT measure can be converted to significant risk-adjusted returns. Therefore, the sample here only covers the small funds, whose TNA are in the lowest 20% among all domestic equity funds. To examine whether smart investors gather in top-performing funds, small funds are sorted into quintiles on excess returns at the beginning of each month.

Table 3presents the results. For brevity, I only report the signs and significance levels here.4Two features stand out. First and

foremost, Carhart's four-factor risk-adjusted returns of the top performance quintiles in portfolios 5 and 9 are positive at the 1% and 5% significance levels, even when the momentum factor is controlled. This finding lends further credence to the interpretation

inSection 5.1that fund size may affect investor strategy. Secondly, unlikeZheng (1999), I do not observe any significantly positive

risk-adjusted returns by using all funds in the bottom size quintile.

It is interesting to note that the phenomenon of dumb money can be observed as well. After including the momentum factor, the relatively poor-performing funds, i.e., the first, second, or third performance quintiles, possess significant negative risk-adjusted returns in almost all portfolios. Contrary to the smart investors, there is a group of investors who will invest in funds that underperform in the future. Such investors are more likely to be found in poor-performing funds. This finding supports the argument that smart investors gather in top-performing funds, whereas dumb investors are trapped in poor-performing funds. A potential explanation lies in the disposition effect, where fund investors are reluctant to sell past losers and continue to lose on their investment.

In addition to the bottom size quintile,Table 4repeats the analysis inTable 3for the other size quintiles. For brevity,Table 4

illustrates only the signs and significance levels of Carhart's four-factor risk-adjusted returns of portfolios by performing a double partition along the size and excess return dimensions. As expected, the significantly positive risk-adjusted returns can only be observed in the subsamples covering the relatively small and top-performing fund group. It appears that the smart money effect is neither size-neutral nor return-neutral. Moreover, asTable 4reveals, the dumb money effect still prevails in poor-performing funds. The negative risk-adjusted returns can be identified in almost all portfolios of the funds in the bottom and second performance quintiles, regardless of fund size.

In addition to the double partition, I also sort funds into quintiles on excess returns to examine the smart money effect in different performance quintiles. Consistent with the finding inSapp and Tiwari (2004), the untabulated results demonstrate that Carhart's four-factor risk-adjusted returns are not significant in the ten portfolios for each performance quintile. All of these results provide sufficient evidence that inappropriate samples would color the identification of the smart money effect.

Panel A ofTable 5shows the returns of all portfolios. The sample here covers the small funds whose performances are ranked in the top quintile. The monthly four-factor risk-adjusted return for portfolio 5 is 54.59 basis points per month, or approximately 6.55% per year. Meanwhile, the risk-adjusted returns of similar portfolios examined byZheng (1999) and Sapp and Tiwari (2004)

are very small and insignificant—0.3 basis points and −0.3 basis points per month, respectively.5

The difference demonstrates that the smart money effect is mainly attributed to the unexpected fund flows of top-performing small funds.

Panel B ofTable 5reports the returns earned by the long-short strategy, where one buys the positive portfolios and sells the corresponding negative portfolios. In Carhart's four-factor model, portfolio 5 significantly outperforms portfolio 6 by 45.07 basis

4

To control for idiosyncratic variations in mutual fund returns,Kosowski et al. (2006)use the bootstrap method to analyze the significance of alphas. I also apply the bootstrap method ofKosowski et al. (2006)to reconstruct the distribution of the model coefficients and then use this distribution to test for statistical significance instead of employing the standard t-test. The results of using the bootstrap method are similar to those when using the standard t-test.

5The portfolios inZheng (1999), Sapp and Tiwari (2004), and portfolio 5 in this paper are similar but not identical. Portfolio 5 in this paper is grouped and

weighted by the funds’ unexpected flows but by new cash flows without size adjustment inZheng (1999)and new cashflows in Equation (2) inSapp and Tiwari (2004).

Table 2

GT measure for the size-sorted fund portfolios.

Quintiles 1 (Small) 2 3 4 5 (Big) All funds

GT measure 2.36* 1.26 0.93 0.72 0.51 0.54

(1.72) (1.63) (1.32) (1.01) (1.02) (1.03)

[0.09] [0.10] [0.19] [0.31] [0.31] [0.30]

This table presents the numbers and significance levels of the GT measures in different fund groups. Performance measures are in basis points per month. All equity funds are ranked into quintiles by their total net assets (TNA). The GT Performance measure is∑Ri,t + 1(wi,t−wi,t− 1), where wi,tis the portfolio weight

for fund i at time t, and Ri,t + 1is the raw return of fund i between time t and t + 1. The t statistics in parentheses test whether the GT measures are

significantly different from mean zero. The t statistics corrected for autocorrelation by the Newey–West adjustment are in parentheses, and the p values are in brackets.

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points per month, or 5.54% annually, which is significant at the 1% level. The risk-adjusted returns of the long-short strategies do not correspond to implementable strategies because investors are normally not allowed to short sell funds. The significant difference, however, still provides evidence for the argument that the investors in the top-performing small funds are smart.

Two implications emerge. First, the unexpected flows of investors in the small and top-performing fund group contain information that can be used to make risk-adjusted returns. Secondly, the risk-adjusted returns created by these smart investors cannot be fully attributed to the phenomenon of momentum. Specifically, in addition to naively chasing the winners, the investors in the small and top-performing fund group have undiscovered skills. In previous studies, which include all equity funds as the sample, it is difficult to distinguish these smart investors from winner chasers.

5.3. The span and accumulation of effective information

The above analyses are based on a one-month holding period, and this raises two immediate questions: How long is the information of unexpected flows (or GT weights) effective? Do accumulative unexpected flows (or GT weights) carry more information than those of a single period? This section repeats previous tests by using the accumulative unexpected flows and GT weights as weights.

Table 3

The sign and significance of portfolio performance for small funds.

P1. average fund Raw

ret

Excess ret

CAPM Fama French

Carhart P2. weighted by total net asset (VW) Raw ret Excess ret CAPM Fama French Carhart 1 (Worst) −−− −−− −−− 1 (Worst) −−− −−− −−− 2 + −− −−− −−− 2 ++ −− −−− −−− 3 ++ −−− −−− 3 ++ −−− −−− 4 ++ 4 +++ 5 (Best) +++ ++ + + 5 (Best) +++ ++ + + All ++ −− −− All ++ −− −− P3. positive unexpected flows (EW) Raw ret Excess ret CAPM Fama French

Carhart P4. negative unexpected flows (EW) Raw RET Excess ret CAPM Fama French Carhart 1 (Worst) −−− −−− −−− 1 (Worst) −− −−− −−− 2 −−− −−− −−− 2 + − −−− −−− 3 ++ −−− −−− 3 ++ −−− −−− 4 ++ 4 ++ 5 (Best) +++ + 5 (Best) +++ ++ All ++ −−− −− All ++ −− −−− P5. positive unexpected flows (CW) Raw ret Excess ret CAPM Fama French

Carhart P6. negative unexpected flows (CW) Raw ret Excess ret CAPM Fama French Carhart 1 (Worst) −−− −−− −−− 1 (Worst) −− −−− −− 2 + −− − 2 + − −−− −−− 3 ++ 3 ++ −−− −−− 4 ++ 4 +++ 5 (Best) +++ +++ +++ +++ +++ 5 (Best) +++ + All ++ All ++ −− −−− P7. upper 50% of unexpected flows (CW) Raw ret Excess ret CAPM Fama French

Carhart P8. lower 50% of unexpected flows (CW) Raw ret Excess ret CAPM Fama French Carhart 1 (Worst) −−− −−− −−− 1 (Worst) −− −−− −−− 2 −−− −−− −−− 2 + −−− −−− 3 ++ −− −−− −−− 3 ++ − −− 4 ++ 4 ++ 5 (Best) +++ + 5 (Best) +++ ++ All + − −−− −−− All ++ − −−− P9. positive GT weights (GW) Raw ret Excess ret CAPM Fama French

Carhart P10. negative GT weights (GW)

Raw ret

E. ret CAPM Fama French Carhart 1 (Worst) − −− −− 1 (Worst) − − 2 ++ −− −− 2 + −− −−− −−− 3 +++ 3 ++ −−− −− 4 +++ + 4 ++ 5 (Best) +++ +++ +++ +++ ++ 5 (Best) +++ ++ All +++ + All ++ −− −

This table presents the signs and significance levels of returns for the 10 portfolios. The sample covers the funds whose TNAs are in the bottom quintile of all equity funds from January 1993 to September 2008. At the beginning of each month, these small funds are further sorted into five quintiles based on past excess returns in the immediately preceding month, where one is the worst-performing fund group and five is the best-performing fund group. Portfolios 1 to 10 are portfolios constructed according to different criteria. EW, VW, CW, and GW denote equal, value, unexpected flow, and GT weight, weighted respectively. The GT weight, i.e.,(wi, t−wi, t− 1), is calculated in the GT measure. Unexpected flows are the differences between the actual flows and expected flows, which are

estimated by lagged fund raw returns and new cash flows from the previous year. The Fama–French three-factor alpha is calculated as the intercept from the monthly time-series regression of portfolio excess returns on the market excess return (RMRF) and mimicking portfolios for size (SMB) and book-to-market (HML) factors. Carhart's four-factor model shares the same calculation by including the above three factors and the extra momentum factor (PR1YR). +++, ++, and + denote positive returns with significance levels of 1%, 5%, and 10%, respectively, based on t statistics. Conversely,−−−, −−, and − present negative returns with the significance levels of 1%, 5%, and 10%, respectively. The t statistics are adjusted for autocorrelation using the Newey–West covariance matrix.

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Table 6examines the performance of portfolios 5 and 9 by using the accumulative unexpected flows as weights.6Rows describe the length of the accumulation period (AL) from one to six months (AL1 ~ AL6). Columns indicate the starting time of the accumulation period. For example, the element (t–3, AL4) in Panel A ofTable 6measures the performance of a portfolio, which is weighted in proportion to the accumulative unexpected flows of the past four months, beginning from t− 3, i.e., the sum of unexpected flows from t − 3 to t− 6. Similarly, the element (t − 2, AL3) in Panel B ofTable 6measures the performance of the portfolio weighted by the accumulative GT weights of the past three months, beginning from t−2, i.e., the sum of GT weights from t− 2 to t− 4. Following this logic, the element (t− 1, AL1) only uses the unexpected flow or GT weight at time t− 1 as the weights. Therefore, the results of (t− 1, AL1) are identical with those inTable 5.

Apparently, the risk-adjusted return of (t−1, AL1) is the highest and most significant in Panel A ofTable 6. The significance levels of risk-adjusted returns reduce as further unexpected flows are included. For example, the abnormal returns of (t−1, AL4) and (t−1, AL5) are no longer significant. The performance of (t−1, AL1) also reaches a peak in Panel B ofTable 6. The results support the notion that the accumulative unexpected flows and GT weights do not carry more information of smart investors. The results can also be interpreted as suggestive evidence that the smart money effect is short-lived, which is consistent with the argument ofKeswani

and Stolin (2008).

In terms of the short-lived smart money effect, the following question seems both obvious and compelling: Why is it that these investors are smart but their intelligence lasts for only a short period? Similar to fund manager returns, fund investor returns can also be classified as fund selection and timing abilities. If both smart investors and momentum-style investors flock to superior funds, the major difference between smart investors and momentum-style investors is the time of trading. That is, unlike

6The performance of the portfolios other than portfolios 5 and 9 are also tested by using the accumulative unexpectedflows as weights, but these

perfor-mances are not reported. In brief, the risk-adjusted returns of the other portfolios are all insignificant, regardless of how long the accumulation period is. Table 4

The sign and significance of portfolio performance under independent double-partition along size and excess return dimensions.

P1. Average funds 1

(Small)

2 3 4 5

(Big)

P2. weighted by total net asset (VW) 1 (Small) 2 3 4 5 (Big) 1 (Worst) −−− −−− −−− −−− −−− 1 (Worst) −−− −−− −−− −−− −−− 2 −−− −−− −−− −−− −−− 2 −−− −−− −−− −−− −− 3 −−− −−− −−− −−− −−− 3 −−− −−− −−− −−− −−− 4 4 5 (Best) 5 (Best) P3. positive unexpected flows (EW) 1 2 3 4 5 P4. negative unexpected flows (EW) 1 2 3 4 5 1 (Worst) −−− −−− − −−− −−− 1 (Worst) −−− −−− −−− −−− −−− 2 −−− −− −−− −−− −− 2 −−− −−− −−− −−− −− 3 −−− −− −−− −− −− 3 −−− −−− −−− −−− −−− 4 4 5 (Best) 5 (Best) P5. positive unexpected flows (CW) 1 2 3 4 5 P6. negative unexpected flows (CW) 1 2 3 4 5 1 (Worst) −−− −− − −− −−− 1 (Worst) −− −−− −−− −−− −−− 2 − −−− −−− −− 2 −−− −− −− − −− 3 3 −−− −− −− − −−− 4 4 5 (Best) +++ 5 (Best) P7. upper 50% of unexpected flows (CW) 1 2 3 4 5 P8. lower 50% of unexpected flows (CW) 1 2 3 4 5 1 (Worst) −−− −−− −−− −−− −−− 1 (Worst) −−− −−− −−− −−− −−− 2 −−− −−− −−− −−− −−− 2 −−− −−− −−− −−− −−− 3 −−− −− −−− −−− −−− 3 −− −−− −−− −−− −−− 4 4 5 (Best) 5 (Best)

P9. Positive GT weights (GW) 1 2 3 4 5 P10. Negative GT weights (GW) 1 2 3 4 5

1 (Worst) −− −−− −− −−− −−− 1 (Worst) −−− −− −− −−−

2 −− −− −− −−− 2 −−− −− −−− −−− −−

3 3 −− −− −−− −− −−−

4 4

5 (Best) ++ ++ + 5 (Best)

This table presents the signs and significance levels of Carhart's four-factor risk-adjusted returns for the 10 portfolios under the double partition. At the beginning of each month from January 1993 to September 2008, mutual funds are independently sorted to quintiles based on size and excess returns. EW, VW, CW, and GW denote equal, value, unexpected flow, and GT weight, weighted respectively. The GT weight, i.e.,(wi, t−wi, t− 1), is calculated in the GT measure. Unexpected flows

are the differences between the actual flows and expected flows, which are estimated by lagged fund raw returns and new cash flows from the previous year. Carhart's four-factor risk-adjusted return is calculated as the intercept from the monthly time-series regression of portfolio excess returns on the market excess return (RMRF) and mimicking portfolios for size (SMB), book-to-market (HML) and momentum (PR1YR) factors. +++, ++, and + denote positive returns with significance levels of 1%, 5%, and 10%, respectively, based on t statistics. Conversely,−−−, −−, and − present negative returns with the significance levels of 1%, 5%, and 10%, respectively. The t statistics are adjusted for autocorrelation using the Newey–West covariance matrix.

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momentum-style investors, smart investors can decide when to invest and redeem their money, i.e., time the market, to enhance their returns. Hence, four timing models are introduced in the following section to examine whether smart investors possess timing ability.

5.4. The skills of smart investors

The basic idea behind timing activity relates to the ability to forecast future market states and weight equity exposure accordingly. Because portfolios 5 and 9 are the only two portfolios that can earn significant risk-adjusted returns, it is more possible for them to possess timing ability.Table 7shows the test results of portfolios 5 and 9 based on four models: the revised Treynor–Mazuy model

Table 5

Portfolio performance for the top-performing small funds.

Raw ret Excess ret CAPM Fama–French Carhart

Panel A: portfolio performance

P1. average fund 104.24 73.13 29.53 25.58 19.35

(3.20) (2.25) (1.81) (1.74) (1.29)

[0.00] [0.03] [0.07] [0.08] [0.20]

P2. weighted by total net asset (VW) 104.95 73.85 30.39 26.68 20.03

(3.23) (2.28) (1.85) (1.81) (1.34)

[0.00] [0.02] [0.07] [0.07] [0.18]

P3. positive unexpected flows (EW) 96.83 65.18 23.01 21.42 17.91

(2.83) (1.91) (1.33) (1.35) (1.10)

[0.01] [0.06] [0.18] [0.18] [0.27]

P4. negative unexpected flows (EW) 96.88 65.23 24.55 18.71 10.61

(2.94) (1.99) (1.50) (1.25) (0.71)

[0.00] [0.05] [0.14] [0.21] [0.48]

P5. positive unexpected flows (CW) 131.82 100.17 57.36 61.12 54.59

(3.57) (2.72) (2.67) (3.12) (2.73)

[0.00] [0.01] [0.01] [0.00] [0.01]

P6. negative unexpected flows (CW) 95.25 63.59 22.72 17.80 9.52

(2.81) (1.88) (1.26) (1.09) (0.58)

[0.01] [0.06] [0.21] [0.28] [0.56]

P7. upper 50% of unexpected flows (CW) 95.26 63.61 22.47 19.74 16.69

(2.87) (1.92) (1.37) (1.30) (1.07)

[0.00] [0.06] [0.17] [0.20] [0.29]

P8. lower 50% of unexpected flows (CW) 98.61 66.96 25.56 20.67 12.37

(2.93) (2.00) (1.50) (1.34) (0.80) [0.00] [0.05] [0.13] [0.18] [0.43] P9. positive GT weights (GW) 127.02 95.86 50.55 47.48 38.08 (3.60) (2.72) (2.58) (2.67) (2.12) [0.00] [0.01] [0.01] [0.01] [0.04] P10. negative GT weights (GW) 104.75 73.60 30.70 25.93 20.94 (3.03) (2.13) (1.49) (1.40) (1.10) [0.00] [0.03] [0.14] [0.16] [0.27]

Panel B: performance difference

P3–P4 −0.05 −1.54 2.71 7.30 (−0.01) (−0.28) (0.50) (1.36) [0.99] [0.78] [0.62] [0.17] P5–P6 36.57 34.65 43.32 45.07 (3.74) (3.54) (4.54) (4.61) [0.00] [0.00] [0.00] [0.00] P7–P8 −3.35 −3.09 −0.93 4.33 (−0.66) (−0.60) (−0.18) (0.87) [0.51] [0.55] [0.86] [0.39] P9–P10 22.27 19.84 21.55 17.13 (1.74) (1.55) (1.63) (1.27) [0.08] [0.12] [0.10] [0.21]

This table presents the simple excess returns and risk-adjusted returns for 10 portfolios. At the beginning of each month from January 1993 to September 2008, the entire fund universe is first divided into 25 cells by a two-way independent sort by firm size and excess return. The sample in this table covers top-performing funds whose TNAs are in the lowest 20%. Panel A evaluates the performance of each portfolio. Performance measures are in basis points per month. EW, VW, CW, and GW denote equal, value, unexpected flow, and GT weight, weighted respectively. The GT weight, i.e.,(wi, t−wi, t− 1), is calculated in the GT measure.

Unexpected flows are the differences between the actual flows and expected flows, which are estimated by lagged fund raw returns and new cash flows from the previous year. The excess returns are calculated as raw returns minus the one-month Treasury bill rate. The Fama–French three-factor portfolio alpha is calculated as the intercept from the monthly time-series regression of portfolio excess returns on the market excess return (RMRF) and mimicking portfolios for size (SMB) factor and book-to-market (HML) factor. Carhart's four-factor portfolio shares the same calculation by including the above three factors and the extra momentum factor (PR1YR). Panel B demonstrates the results by using the long-short strategy to test whether the performance difference between the positive and negative portfolios is significantly different from zero. The t statistics adjusted by the Newey–West adjustment are in parentheses, and the p values are in brackets.

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(TM), the revised Henriksson–Merton model (HM), the Treynor–Mazuy–Carhart factor timing model (TMC), and the Henriksson– Merton–Carhart factor timing model (HMC). After including the timing skill coefficients, the alphas in all four timing models are no longer significant. This result implies that the superior performance is attributable to timing skills. In practical terms, the investors in the top-performing small funds can choose superior funds among all funds and purchase and sell them in a timely manner.

If the investors in the top-performing small funds have timing ability, what kind of timing ability do they have? Concerning portfolio 5, the TM and HM models in Panels A and B show that these smart investors possess market-timing ability. The market-timing coefficients of portfolio 5 are 1.717 and 1.318 at the 5% level of significance. The market-timing coefficients of portfolio 9 in Panels A and B are also significant at the 5% level. After including the other three timing factors in Panels C and D, the market-timing coefficients of portfolio 5 are still significant at the 5% and 10% significance levels. In untabulated results, which adopt the bootstrapping methods used byKosowski et al. (2006), the coefficients of market-timing in two portfolios are always significant at the 1% level.

Overall, the results reveal that smart investors possess market-timing skills. They can purchase (sell) top-performing small funds just as market returns are about to increase (decrease). Given this, the fact that the smart money effect is short-lived is not surprising. Market-timing ability mainly comes from an outlook of aggregate market or economic conditions within a short period followed by a decision of whether to invest quickly. It is not an ability that can be practiced and observed at all times. Therefore, the short-lived smart money effect and the argument that top-performing small fund investors have market-timing ability mutually reinforce each other.

Table 6

The span and the accumulation of effective information.

AL1 AL2 AL3 AL4 AL5 AL6

Panel A: portfolio 5, positive unexpected flows (CW)

t−1 54.59 39.66 40.69 32.98 31.36 33.84 (2.728) (2.031) (1.819) (1.594) (1.531) (1.631) [0.007] [0.043] [0.070] [0.112] [0.127] [0.104] t−2 9.02 22.23 17.81 17.77 20.51 21.88 (0.470) (0.989) (0.879) (0.882) (0.999) (1.066) [0.638] [0.323] [0.380] [0.378] [0.318] [0.287] t−3 25.86 17.78 19.05 23.69 22.50 23.08 (1.131) (0.866) (0.937) (1.123) (1.091) (1.127) [0.259] [0.387] [0.349] [0.262] [0.276] [0.261] t−4 8.23 8.04 18.31 16.28 17.52 14.60 (0.45) (0.465) (1.014) (0.905) (0.973) (0.813) [0.652] [0.642] [0.311] [0.366] [0.331] [0.417] t−5 4.68 20.71 20.47 22.71 14.03 13.08 (0.276) (1.188) (1.092) (1.249) (0.795) (0.732) [0.782] [0.236] [0.276] [0.213] [0.427] [0.465] t−6 39.67 32.04 28.54 18.07 21.56 15.68 (1.976) (1.625) (1.497) (0.97) (1.142) (0.838) [0.049] [0.105] [0.136] [0.333] [0.255] [0.402]

Panel B: portfolio 9, positive GT weights (GW)

t−1 38.08 35.28 36.70 29.98 27.22 26.24 (2.122) (1.958) (2.071) (1.668) (1.53) (1.464) [0.035] [0.051] [0.039] [0.097] [0.127] [0.144] t−2 29.89 31.05 23.49 20.90 21.79 21.74 (1.694) (1.753) (1.313) (1.186) (1.222) (1.239) [0.091] [0.081] [0.190] [0.237] [0.223] [0.216] t−3 21.93 15.41 15.61 18.52 18.75 19.14 (1.292) (0.891) (0.897) (1.053) (1.103) (1.156) [0.197] [0.373] [0.370] [0.293] [0.271] [0.248] t−4 11.81 13.51 18.02 20.72 20.53 20.29 (0.678) (0.792) (1.025) (1.235) (1.265) (1.267) [0.498] [0.429] [0.306] [0.218] [0.207] [0.206] t−5 18.28 19.50 23.82 23.56 23.55 21.17 (1.054) (1.133) (1.425) (1.433) (1.422) (1.293) [0.292] [0.258] [0.155] [0.153] [0.156] [0.197] t−6 23.21 24.45 23.02 23.61 24.33 25.89 (1.308) (1.398) (1.333) (1.365) (1.443) (1.509) [0.192] [0.163] [0.184] [0.173] [0.150] [0.133]

This table presents Carhart's four-factor risk-adjusted returns for portfolios 5 (Panel A) and 9 (Panel B) for up to six months, weighted by accumulative unexpected flows and accumulative GT weight. The sample in this table consists of top-performing funds whose TNAs are in the lowest 20%. Performance measures are in basis points per month. Rows AL1–AL6 describe the length of the accumulation period, and columns t−1 to t−6 indicate the starting time. For example, the element (t−3, AL4) in Panel A measures the performance of the portfolio with positive unexpected flows and is weighted in proportion to the sum of unexpected flows (Portfolio 5) from t−3 to t−6. The element (t−2, AL3) in Panel B measures the performance of the portfolio with positive GT weights and is weighted by the sum of the GT weight change from t−2 to t−4. The t statistics corrected by the Newey–West covariance matrix are in parentheses, and the p values are in brackets.

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It is important to address a possible concern: Is it possible that these smart investors have both timing ability and fund selection ability? The answer is yes. The two abilities are not mutually exclusive. Reviewing the results inTable 3, the significantly positive risk-adjusted returns can only be observed in portfolios 5 and 9 weighted by unexpected flows under Carhart's four-factor model. However, the equal-weighted portfolios do not produce positive risk-adjusted returns. That is, weighting a portfolio by the unexpected flow produces the risk-adjusted returns, but equal weighting does not. If market-timing ability is the only determinant of positive risk-adjusted returns, we should find that the risk-adjusted return of portfolio 3 is also significant. The comparison between portfolios 3 and 5 implies that smart investors possess not only market-timing ability but also a certain degree of fund selection ability because equal investment in all funds cannot generate risk-adjusted returns.

Note that the finding concerning market-timing ability is not contrary to that ofFriesen and Sapp (2007), who conclude that equity fund investors have poor timing decisions and thereby lead to underperformance. First, whileFriesen and Sapp (2007)

focus on the timing ability of all investors, this paper examines only the timing ability of the investor group that can earn risk-adjusted returns. Second, unlikeFriesen and Sapp (2007)which use the gap between geometric returns and dollar-weighted returns to measure investor timing, this paper adopts multiple regressions to investigate whether the risk-adjusted returns can be explained by the timing factors. Although the timing ability of investors in the aggregate reduces their fund returns inFriesen

and Sapp (2007), there are some smart investors who know when to invest to make significant risk-adjusted returns.

6. Further evidence of the smart money effect

6.1. The measurement offlows

The measurement of flows plays an important role in this paper. However, some may argue that unexpected flows are essentially different from flows used in previous works and regard the empirical pattern documented as due to chance or data snooping. Therefore, I repeat the above analysis using the flow measures ofZheng (1999) and Sapp and Tiwari (2004)to alleviate this concern. In the same manner, the entire sample is double-partitioned into quintiles along the size and excess return dimensions at the beginning of each

Table 7

The timing ability of smart investors.

Portfolio Alpha RMRF Timing SMB timing HML timing PR1YR timing Adj-R2

Panel A: revised Treynor–Mazuy model (TM)

Portfolio 5 positive unexpected flows (CW) 0.002 1.717 0.743

(0.887) (2.490)

[0.377] [0.014]

Portfolio 9 positive GT weights (GW) 0.001 1.318 0.772

(0.631) (2.068)

[0.529] [0.040]

Panel B: revised Henriksson–Merton model (HM)

Portfolio 5 positive unexpected flows (CW) 0.000 0.331 0.741

(−0.113) (2.185)

[0.910] [0.030]

Portfolio 9 positive GT weights (GW) −0.001 0.287 0.772

(−0.377) (2.076)

[0.707] [0.039]

Panel C: Treynor–Mazuy–Carhart factor timing model (TMC)

Portfolio 5 positive unexpected flows (CW) 0.002 1.520 0.309 1.521 −0.528 0.745

(0.848) (2.040) (0.558) (1.488) (−1.413)

[0.398] [0.043] [0.578] [0.139] [0.160]

Portfolio 9 positive GT weights (GW) 0.001 1.115 0.359 1.182 −0.363 0.773

(0.514) (1.610) (0.695) (1.243) (−1.046)

[0.608] [0.109] [0.488] [0.216] [0.297]

Panel D: Henriksson–Merton–Carhart factor timing model (HMC)

Portfolio 5 positive unexpected flows (CW) −0.002 0.302 0.048 0.361 −0.163 0.743

(−0.525) (1.786) (0.284) (1.784) (−1.279)

[0.601] [0.076] [0.777] [0.076] [0.203]

Portfolio 9 positive GT weights (GW) −0.003 0.210 0.014 0.215 0.005 0.771

(−0.777) (1.354) (0.087) (1.153) (0.042)

[0.438] [0.178] [0.931] [0.250] [0.967]

This table shows the alphas and timing ability coefficients for portfolios 5 and 9. The sample in this table consists of top-performing funds whose TNAs are in the lowest 20% from January 1993 to September 2008. Panel A refers to the revised Treynor–Mazuy model, and Panel B refers to the revised Henriksson–Merton model. Panel C is the revised Treynor–Mazuy model plus the squared terms of four factors inCarhart (1997), and Panel D is the revised Henriksson–Merton model plus the squared terms of four factors inCarhart (1997). The four factors include market excess return (RMRF), factor-mimicking portfolios for size (SMB), book-to-market equity (HML) and one-year return momentum (PR1YR). The t statistics corrected by the Newey–West covariance matrix are in parentheses, and the p values are in brackets.

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month. Subsequently, ten portfolios weighted by new cash flow in Eq.(2)or by new cash flow without size adjustment are constructed for each cell.

For brevity,Table 8presents the signs and significance levels of Carhart's four-factor risk-adjusted returns by using new cash flows in Eq.(2)as portfolio weights. The results are similar when new cash flows without size adjustment are used as weights. As

inSapp and Tiwari (2004), there is no smart money effect in all cases when the funds are only sorted by size. However, when I

independently double-sort funds based on size and excess return, the risk-adjusted returns in portfolio 5 are significant when the funds are top-performing and relatively small (size quintiles 1, 2, and 3). To sum up, when new cash flows are used as weights, the smart money effect still exists, but the significance level and the risk-adjusted return are lower. Meanwhile, the dumb money effect also prevails in other cells. In brief, the smart money effect documented in the previous section is ascribed to the partition method rather than the measuring methods of flows.

6.2. Are investors in no-load funds smarter?

Investors in load funds are commonly regarded as uninformed investors because the higher cost of trading in load funds may prevent informed investors from investing (Zheng, 1999). Hence, this section investigates whether the different investment behavior of investors in load and no-load funds influences portfolio performance. I still use funds in the bottom size quintile as the sample, and I rank these funds by their excess returns.

The empirical evidence does not support the view that investors in load funds are not as well informed as investors in no-load funds. Both portfolios 5 and 9 have significantly positive risk-adjusted returns in load and no-load funds. Intuitively, investors are reluctant to buy load funds unless they believe that they will be compensated by a return premium. The positive four-factor risk-adjusted returns in both load and no-load funds indicates that for the investors in the top performance quintile, as long as the

Table 8

The sign and significance of portfolio performance weighed by new cash flow.

P1. average fund 1

(Small)

2 3 4 5

(Big)

P2. weighted by total net asset (VW) 1 (Small) 2 3 4 5 (Big) 1 (Worst) − −− −−− −−− −−− −−− 1 (Worst) −−− −−− −−− −−− −−− 2 −−− −−− −−− −−− −−− 2 −−− −−− −−− −−− −− 3 −−− −−− −−− −−− −−− 3 −−− −−− −−− −−− −−− 4 4 5 (Best) 5 (Best) All −− −−− −−− −−− −−− All −− −−− −−− −−− −−−

P3. positive new cash flows (EW)

1 2 3 4 5 P4. negative new cash

flows (EW) 1 2 3 4 5 1 (Worst) −−− −−− −−− −− −−− 1 (Worst) −−− −−− −−− −−− −−− 2 −−− −−− −− −− − 2 −−− −−− −−− −−− −−− 3 −−− − −− −− 3 −−− −−− −−− −−− −−− 4 4 − −− −− 5 (Best) 5 (Best) All −− − −−− −−− −−− All −− −−− −−− −−− −−−

P5. positive new cash flows (CW)

1 2 3 4 5 P6. negative new cash

flows (CW) 1 2 3 4 5 1 (Worst) −− −−− −− −−− −−− 1 (Worst) −−− −− −−− −−− 2 −− −− −− −− 2 −− −− −− −− −− 3 3 −− −−− − −−− 4 4 −− 5 (Best) ++ ++ ++ 5 (Best) All −− All −−− −− −−− −−−

P7. UPPER 50% of new cash flows (CW)

1 2 3 4 5 P8. lower 50% of new cash

flows (CW) 1 2 3 4 5 1 (Worst) −−− −−− −−− −−− −−− 1 (Worst) −−− −−− −−− −−− −−− 2 −−− −−− −− −−− −− 2 −−− −−− −−− −−− −−− 3 −− − −− −− 3 −−− −−− −−− −−− −−− 4 4 −− 5 (Best) + 5 (Best) All −− −−− −−− −−− All −− −−− −−− −−− −−−

This table presents the signs and significance levels of Carhart's four-factor risk-adjusted returns for the 8 portfolios under the double partition. Each month from January 1993 to September 2008, mutual funds are independently grouped into 25 quintiles according to fund size and past excess returns. The sample in this table consists of top-performing funds whose TNAs are in the lowest 20%. Portfolios 3 to 8 are weighted by new cash flows rather than unexpected flow. The calculation of new cash flow is computed as: flowi, t= [TNAi, t−TNAi, t− 1× (1 + Ri, t)−MGTNAi, t]/TNAi, t− 1, where TNAi, trefers to the total net asset at the

end of month t, Ri, tis the fund's raw return for month t, and MGTNAi, tis the increase in the TNA due to mergers during month t. Carhart's four-factor

risk-adjusted return is calculated as the intercept from the monthly time-series regression of portfolio excess returns on the market excess return (RMRF) and mimicking portfolios for size (SMB), book-to-market (HML) and momentum (PR1YR) factors. +++, ++, and + denote positive returns with significance levels of 1%, 5%, and 10%, respectively, based on t statistics. Conversely,−−−, −−, and − present negative returns with significance levels of 1%, 5%, and 10%, respectively. The t statistics are corrected by the Newey–West covariance matrix.

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return premium compensates for the load fees, load fees are not their major concern with respect to buying or not buying the funds. In other words, load fees do not influence the investment decisions of smart investors.

6.3. Do investors become smarter over time?

To observe whether the results obtained above change over time, the testing period is separated into two sub-periods, 1993/ 01–2000/12 and 2001/01–2008/09, and I find that the results are not influenced by the observation period. The entire testing period is further divided into three sub-periods, and each sub-period covers five years. As expected, portfolios 5 and 9 for the top-performing small funds still produce a significantly positive Carhart's alpha in all sub-periods. Therefore, the finding reveals that investors do not appear smarter over time.

6.4. Supplemental tests

To avoid overweighting extreme observations in the regressions and flow-weighted portfolio construction, I filter out the top and bottom 5% of the new cash flow data and repeat all of the tests. The results are similar to those above. Another potential concern is that the flows of newly established funds are often larger within the first few months than the subsequent average level. Therefore, I recalculate portfolio returns by excluding the flow information in the first three months for all funds following their establishment. Again, the results are not materially altered. Moreover, the unexpected flows may be sensitive to the lagged periods in the Fama–Macbeth regression. Hence, the lagged periods are set to be 3, 6, 9, or 12 months. The results show that the number of lagged periods in the Fama-Macbeth regression does not influence the conclusion significantly. Alternatively, the pooled regression estimated by OLS is also used to compute the unexpected flows in Eq.(3). All major conclusions remain unchanged. To sum up, the results are robust to the classification of load and no-load funds, sample division into sub-periods, the exclusion of outliers, the number of lagged periods, and the estimation methods of unexpected flows.

7. Conclusion

The term smart money in mutual fund literature has come to be associated with the ability of investors to identify future superior performers from a group of comparable funds. Following previous studies, this paper further asks two questions: Where are these smart investors? Why are they smart?

Using all domestic equity funds as a sample, this paper reveals that the smart investors can be identified in top-performing small funds, even after controlling for the momentum factor argued bySapp and Tiwari (2004). This finding demonstrates the importance of using a double partition along the size and performance dimensions in the identification of the smart money effect. Furthermore, this finding implies that smart investors have undiscovered skills with respect to earning significant abnormal returns rather than simply chasing the winner to unwittingly benefit from the momentum profit. The timing models demonstrate that the smart investors possess market-timing ability. The risk-adjusted returns earned by investing in the top-performing small funds become insignificant after including the timing factors. Specifically, both smart investors from momentum-style investors can identify superior funds; however, smart investors purchase and sell these funds in a timely manner. The different trading times distinguish smart investors from pure momentum-style investors.

The findings fuel the debate on whether investors should be protected. Legislators around the world have claimed that investors should be protected from hurting themselves with poor investment decisions. This argument is based on the assumption that investors are not able to make good mutual fund choices. Concurring withKeswani and Stolin (2008), this paper casts doubt on the argument that laws should be established to protect all investors, given that some investors can identify superior funds. However, this paper also shows that the dumb money effect actually prevails in most cases, asFriesen and Sapp (2007)conclude. Undoubtedly, these dumb investors should be protected. Therefore, it will be interesting for future research to identify the investors who fail to be smart from the viewpoint of individual investors’ socioeconomic characteristics. The laws should be established to protect these dumb investors but not to constrain smart investors.

References

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Chen, L.-.W., Adams, A., Taffler, R., 2009. What skills do star fund managers possess? Working Paper. University of Edinburgh. Chevalier, J., Ellison, G., 1997. Risk taking by mutual funds as a response to incentives. J. Polit. Econ. 105, 1167–1200. Coval, J., Stafford, E., 2007. Asset fire sales (and purchases) in equity markets. J. Financ. Econ. 86, 479–512. Fama, E.F., French, K.R., 1993. Common risk factors in the returns on stocks and bonds. J. Financ. Econ. 33, 3–56. Fama, E.F., MacBeth, J.D., 1973. Risk, return and equilibrium: empirical tests. J. Polit. Econ. 81, 607–636.

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Jegadeesh, N., Titman, S., 1993. Returns to buying winners and selling losers: implications for stock market efficiency. J. Finance 48, 65–91. Keswani, A., Stolin, D., 2008. Which money is smart? Mutual fund buys and sells of individual and institutional investors. J. Finance 63, 85–118.

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數據

Table 1 presents descriptive statistics. The average (median) fund size measured by TNA is $466.28 ($37.8) million

Table 1

presents descriptive statistics. The average (median) fund size measured by TNA is $466.28 ($37.8) million p.5
Table 3 presents the results. For brevity, I only report the signs and significance levels here

Table 3

presents the results. For brevity, I only report the signs and significance levels here p.6
Table 6 examines the performance of portfolios 5 and 9 by using the accumulative unexpected flows as weights

Table 6

examines the performance of portfolios 5 and 9 by using the accumulative unexpected flows as weights p.8

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