Average funds versus average dollars: Implications for mutual fund research

Journal of Empirical Finance 28 (2014) 249–260

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Average funds versus average dollars: Implications for mutual fund research☆ Christopher P. Clifford ⁎, Bradford D. Jordan, Timothy B. Riley Gatton College of Business and Economics, University of Kentucky, United States

a r t i c l e

i n f o

Article history: Received 26 July 2013 Received in revised form 26 June 2014 Accepted 21 July 2014 Available online 25 July 2014 JEL classification: G11 G23

a b s t r a c t The top 5% of actively managed U.S. equity mutual funds in 2012 had greater aggregate TNA than the remaining 95% of funds combined. This skewness in size has implications for mutual fund research: What is true of the average fund is not necessarily true of the average dollar. We explore several key findings in the literature with an eye on this distinction. Our results indicate that if the goal of mutual fund research is to understand the importance of the industry to investors, then researchers should consider the experience of the average dollar, rather than the average fund. © 2014 Elsevier B.V. All rights reserved.

Keywords: Mutual funds Flow convexity Smart money

1. Introduction U.S. equity mutual funds vary tremendously in size. As of the end of 2012, in our sample of 1685 actively managed funds alive at that time, the total net assets (TNA) of the 70 largest funds exceeded the combined TNA of all the remaining 1615 funds.1 The top two funds, the American Funds Growth Fund of America and the Fidelity Contrafund, had a combined TNA of $197 billion, which was greater than the combined TNA of all 1011 funds at or below the 60th percentile (in terms of size). The variation and skewness in fund size have important implications for mutual fund research. Crucially, what is true for the average fund may not be true for the average fund investor. For example, over the period 1991 to 2012, the average equity fund in our sample is 9.5 years old, charges a total expense ratio of 1.4%, and has a turnover ratio of 106%. However, over this same period, the average invested dollar owns a fund that is 28.2 years old, charges an expense ratio of 1.0%, and has a turnover ratio of only 64%. Thus, looking at the typical fund's attributes paints a potentially misleading picture of what investors actually experience. Clearly, there are interesting questions that pertain to the average fund, rather than the average fund-dollar. The answers to these questions, however, are often difficult to extrapolate to fund-dollars. For example, a line of studies beginning with Jensen's (1968) seminal contribution shows that the average fund manager does not have the ability to consistently generate positive abnormal returns, or “alpha”. The conclusion frequently drawn is that investors would be better off in low-cost, passively managed index funds, but this conclusion does not necessarily follow. Recent work by Berk and van Binsbergen (2013) documents that managerial ☆ We thank Sam Ault, Xin Hong, Di Kang, Tim Kerdloff, and Jacob Prewitt for research assistance and seminar participants at the University of Kentucky for comments and suggestions. ⁎ Corresponding author. E-mail address: [email protected] (C.P. Clifford). 1 Our sample is the universe of actively managed equity funds (as defined by us) in the CRSP Survivor-Bias-Free U.S. Mutual Fund Database. We collapse multiple share classes to form each fund-month observation. A detailed description of the sample follows in the next section.

http://dx.doi.org/10.1016/j.jempfin.2014.07.005 0927-5398/© 2014 Elsevier B.V. All rights reserved.

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skill should be measured as the product of the managers' gross alpha and the size of the fund they manage. If a small percentage of fund managers have skill, and they are concentrated at large funds (as one might guess they would be), then investors, on average, could benefit from active management even though the average fund manager lacks skill. With this in mind, our broad goal is to explore several key results in the mutual fund literature that are not directly related to managerial skill.2 We focus on the role of fund size and the difference between the average fund and the average fund-dollar. In particular, we consider two questions, both of which have figured prominently in the mutual fund literature: 1. Is the mutual fund flow/performance relation convex? 2. Is there a “smart money” effect in fund flows? Beginning with the convexity issue, we first verify that funds, on average, appear to face a convex flow/performance relation, even after controlling for the funds' size (Chevalier and Ellison, 1997; Ippolito, 1992; Sirri and Tufano, 1998). The conventional interpretation of this relation is that investors reward successful funds, but don't punish unsuccessful ones (at least not to the same degree). Further, it is argued that this behavior by investors leads to call option-like payoffs for fund managers and may induce “tournament” behavior among fund managers (e.g., Brown et al., 1996). However, in contemporaneous research, Spiegel and Zhang (2013) show that the apparent convex flow/performance relation is due solely to misspecification in the standard empirical model. Likewise, when we examine the convexity issue from the standpoint of the average fund-dollar, we provide clear evidence that the majority of flows are not convex. We find that the convex relation is primarily due to a large number of funds that collectively manage less than 30% of the total assets in our sample. For the remaining 70% of the assets, we find that investors reward and punish top and bottom performing funds with about equal regard. Thus, consistent with the previous literature, we find that the average mutual fund manager does appear to face incentives to increase risk and take advantage of the convex flow relation under the standard model, but we show that this result cannot be extrapolated to the average investor, or fund-dollar. Investors do not, in general, asymmetrically reward fund managers. Rather, they appear to both reward and punish top and bottom performers with equal vigor. One natural critique of our work is that researchers have long been aware of the effect of fund size and have made several attempts at controlling the issue. For example, the literature often includes fund size or some transformation of fund size, e.g., log size, as a control in empirical specifications or alternatively removes the smallest funds from samples for robustness. With regard to controlling for size in a linear regression format, such approaches assume that fund size is linear in effect on the dependent variable. We demonstrate that this is not necessarily the case. As for removing the smallest funds from the sample, we find that procedure makes a non-meaningful change in the distribution of fund size. For example, the median TNA in our sample is $214MM. When we remove the smallest 10% of funds each month, the median TNA only raises to $275MM. In other words, eliminating the smallest funds from the sample still leaves a large number of relatively small funds remaining. In an effort to provide a tractable alternative, we provide a method to enable researchers to instead respecify their models to focus on the largest funds, rather than eliminating the smallest. We then follow previous studies and document a “smart money” effect (e.g., Gruber, 1996; Keswani and Stolin, 2008; Zheng, 1999). Following the previous literature, we find that funds with above median net flows (as a percentage of TNA) subsequently outperform funds with below median net flows by an economically and statistically significant 5.5 basis points per month. However, as with our convexity result, the smart money effect is driven by smaller funds. Thus, the typical dollar in net flow (or, equivalently, the typical investor's net flow) is not “smart.” Taken together, once we focus on fund-dollars rather than funds, we see that the stylized facts from mutual fund research are often based on an economically small portion of the industry. We show that flows respond linearly to past performance and do not exhibit the ability to successfully anticipate future performance among over 70% of industry's assets. And in general, we find that the choice to focus on funds or fund-dollars can lead to very different conclusions. The remainder of this paper proceeds as follows. Section 2 discusses our sample and issues that arise in the mutual fund literature. Section 3 characterizes the average fund against the average fund-dollar. We consider flow/performance convexity and smart money in Sections 4 and 5, respectively. Sections 6 and 7 contain suggestions for future research and conclusions. 2. Sample selection Our sample contains actively managed U.S. equity mutual funds from the CRSP Survivor-Bias-Free U.S. Mutual Fund Database over the 1991–2012 period. We start in 1991 because that is when TNA data (which we must have) become available at a monthly frequency.3 Extracting only actively managed equity funds from the CRSP universe requires us to make a number of decisions regarding such things as how to deal with blended funds, sector funds, and newly launched funds. We also must decide whether to examine funds at the share-class level or aggregate portfolio level. How researchers handle these choices leads to very large differences in sample size (and composition) in the literature. Thus, our goal in this section is to carefully describe how we arrive at our final sample and to highlight some issues that arise. 2 Numerous studies that directly address managerial skill, e.g., Fama and French (2010), typically test both equal and TNA-weighted portfolios to control for the effect of size. 3 Though our final sample begins in 1991, the earliest our tests can begin is 1992 because of the need to lag certain variables.

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We begin by merging the CRSP fund summary and monthly return/TNA databases. This initial sample contains 4,339,218 months of data for 50,979 unique fund share classes. We delete ETFs, variable annuities, and index funds; we also remove monthly observations if return and/or fund size is missing.4 To remove bond funds from our sample, we drop all funds with a Lipper code of “TX” or “MB.” We use CRSP objective codes to identify equity funds to retain in our sample. By doing so, we eliminate specialized funds such as foreign funds, sector funds, and real estate funds, along with any remaining bond funds.5 We then use text searches of fund names to remove lifecycle funds, tax-managed funds, and asset allocation funds, among others.6 An important issue arises when we look at the percentage of a fund's assets that is invested in equities (CRSP field per_com) because essentially no funds are 100%. Our goal (and that of other researchers) is to include funds that are “mostly” equity. Different approaches are used in the literature. Typically, an arbitrary cutoff (e.g., 80% equity) is chosen. Some researchers include all fund-months above the cutoff, but this method introduces a bias. Funds that seek to maintain equity holdings around the cutoff will enter and exit the sample based on their performance. When such a fund's equity holdings perform well (poorly) and cross the cutoff from below (above), the fund-month is included (excluded). Thus, the average fund-month's performance is biased upwards. Variations on this approach appear. For example, some studies include a fund's entire history if, in any month, the equity percentage is above a threshold. This approach has a clear look-ahead bias that again favors better performers. In our case, we also employ an 80% equity cutoff. However, to avoid inducing performance, a fund is admitted to our sample the year after it first passes the 80% threshold. Once in the sample, a fund remains regardless of its equity percentage. To mitigate the effect of asset shocks resulting from fund mergers, we omit months t (the merger month) to t + 2 following any fund mergers. Our sample at this point contains 1,012,097 share class-months representing 11,952 unique share classes. We estimate rolling twelve-month alpha regressions using the Carhart (1997) four-factor model for each share class (because of differing expenses, the alphas based on net returns will differ). We require a fund or fund-class to have all twelve monthly returns available to estimate an alpha. In much of our analyses, we need data at the fund level (as opposed to the share-class level). We therefore collapse multiclass funds to a single fund using the CRSP class group identifier. This variable is unavailable before 1998, so we backfill the CRSP class group variable for funds that continued operations following 1998. We construct fund level measures for items such as expense ratios for the collapsed funds on a TNA-weighted basis. After collapsing the share classes (and requiring an alpha for at least one share class), our sample contains 343,431 fund-months representing 3783 unique funds. Moving from the share-class level to the fund level reduces the number of funds by 68.3%, so the average fund has just over three unique share classes. Finally, we follow Coval and Stafford (2007) and remove fund‐months with changes in TNA N 200% and b−50% to reduce outliers in our fund flow estimates. We reduce the effects of incubation bias (Evans, 2010) by removing funds for which the oldest share class is less than two years old. We are left with 331,386 observations for 3542 unique funds, which is our final fund-level sample, but our tests often have fewer observations because of other data requirements, e.g., control variables.7

3. The average fund versus the average dollar As shown in Table 1, we summarize our sample in two ways. As in many other studies, Panel A presents univariate statistics at the fund level. Here, we equally weight by fund, so we first calculate average values for each fund and then average across our 3542 funds. As shown, the mean fund TNA is $712 million, but the median is only $123 million, a reflection of the skewness in fund size. The magnitude and persistence of this skewness are illustrated in Fig. 1, which shows the percentage of industry assets (in our sample) held by the top ten percent of funds (in terms of size). As shown, from 1992 to 1999, this percentage rose from a little under 57% to over 75%. From 2000 to 2012, the percentage then slowly decreased to about 69%. Continuing with Panel A, the average implied net flow is .4% (of beginning of month TNA) per month.8 The average fund earned .60 (.71) percent per month net (gross) of fees. The average monthly gross alpha is about zero, and the average monthly net alpha is − .12%. The average expense ratio is 1.4% per year. So, overall, the average fund created no value at the gross level and had a net alpha essentially equal to its expense ratio. The average fund is only 9.5 years old in our sample, with a median of 6.4 years.

4 The indicator variables for ETFs, variable annuities, and index funds are not available for the early part of our sample. We therefore delete a fund's entire history if the CRSP variables index_fund_flag, et_flag, or vau_fund are ever equal to one. There is no look-ahead bias induced by doing so because funds in these categories do not change categories. 5 Specifically, we retain all funds whose CRSP objective codes start with “EDC” or “EDY”. 6 We examined a large number of funds to develop a script that identifies funds that, based on their names, are probably not actively managed or are otherwise not ordinary equity funds. In all, we search for 48 separate strings, some of which are similar (e.g., “principal protected” versus “protected principal.”) This code is available upon request. 7 A tabulated “mortality” analysis from this sample selection process is available upon request. 8 As in many other studies, we compute the implied net flow for fund i in period t as:

Implied net flowi;t ¼

TNAi;tþ1 −TNAi;t 1 þ r i;t TNAi;t




where ri,t is the fund's CRSP-reported net return for the month.

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Table 1 The characteristics of the average fund versus average dollar. This table provides summary statistics for the sample of actively managed, domestic equity funds used in this study. The time period covers January 1992–December 2012. We aggregate (TNA-weighted) multiple share classes to form one fund observation. We define Fund TNA as the total net assets managed by the fund (in millions). Implied net flow is the implied monthly net flow of capital to the fund. Our performance measures are calculated monthly. Net return is the fund's after-fee return from CRSP. Gross return is the fund's monthly return gross of fees (net return + 1/12(expense ratio)). Net (Gross) FF4 alpha is the intercept (Jensen's alpha) from a 12 month regression of a funds' net (gross) returns on the Carhart (1997) 4-factor model. Expense ratio and turnover ratio are from CRSP. Age is the length of time (in years) that the fund's oldest share class is listed in CRSP. In Panel A, we capture the effect of the average fund by equally-weighting each fund. In Panel B, we capture the effect of the average dollar invested in a mutual fund by taking the average of the TNA-weighted cross-sectional average for each month in our study. Variable

N

Mean

Median

10%

90%

Standard deviation

Panel A: Average fund per month Fund TNA ($MM) Implied net flow (%) Net return (%) — monthly Gross return (%) — monthly Net FF4 alpha (%) — monthly Gross FF4 alpha (%) — monthly Expense ratio (%) Age (years) Turnover ratio (%)

3542 3542 3542 3542 3542 3542 3542 3542 3542

712 0.4% 0.60% 0.71% −0.12% 0.00% 1.4% 9.5 105.5%

123 0.1% 0.64% 0.75% −0.09% 0.01% 1.3% 6.4 75.8%

8 −1.7% −0.24% −0.10% −0.49% −0.37% 0.8% 2.7 26.5%

1412 2.8% 1.37% 1.48% 0.23% 0.35% 1.9% 18.4 184.0%

2716 2.6% 1.28% 1.27% 0.43% 0.41% 1.0% 10.4 191.1%

Panel B: Average dollar per month Fund TNA ($MM) Implied net flow (%) Net return (%) — monthly Gross return (%) — monthly Net FF4 alpha (%) — monthly Gross FF4 alpha (%) — monthly Expense ratio (%) Age (years) Turnover ratio (%)

252 252 252 252 252 252 252 252 252

1213 0.2% 0.69% 0.77% −0.05% 0.03% 1.0% 28.2 64.0%

1230 0.2% 1.20% 1.28% −0.07% 0.01% 1.0% 28.2 65.7%

800 −0.6% −4.60% −4.53% −0.29% −0.21% 0.9% 25.3 51.7%

1551 1.1% 5.70% 5.78% 0.14% 0.22% 1.0% 31.3 79.3%

277 0.7% 4.40% 4.40% 0.22% 0.22% 0.1% 2.8 11.2%

80.0 70.0

Industry Assets %

60.0 50.0 40.0 30.0 20.0 10.0

2012

2011

2010

2009

2008

2007

2006

2004

2005

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

0.0

Year Fig. 1. The market share of large mutual funds over time. This figure presents the market share of industry assets for the top 10% of mutual funds ranked by fund size from 1992 to 2012.

In Panel B, we explore the typical investor-month. In each month, we compute TNA-weighted averages for each item (other than size). We then average across the months. The values in Panel B can be interpreted as what the typical dollar in assets (or equivalently, the average investor) experienced in an average month.9 Note that the quantiles in Panel B are not comparable to those in Panel A because they are based on 252 fund-months rather than 3542 funds. Comparing Panels A and B, the mean TNA is just over $1.2 billion in Panel B, or slightly less than twice as large as the mean in Panel A. Further, compared to the typical fund in Panel A, the typical dollar is in a fund that (1) is much older (28.2 versus 9.5 years), (2) has lower turnover (64.0 versus 105.5%), (3) has a smaller net flow (.2 versus .4%), and (4) has significantly lower expenses (1.0 versus 1.4%). In terms of performance, the typical dollar has a superior net return (.69 versus .60% per month) and net alpha (−.05 versus 9 As an alternative to Panel B, we could examine the dollar-weighted average fund-month observation; however, the resulting statistics are similar in most regards to those in Panel B and are thus not reported to save space. They are available on request.

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−.12% per month). The higher net alpha is due to the combined effect of lower expenses of about .03% per month and a higher gross alpha of .03% per month. As Table 1 shows, there are significant differences economically between the typical fund and the typical fund-dollar. Most previous studies of mutual funds focus on the typical fund. There is nothing wrong in doing so; whether funds or fund-dollars should be studied depends on the research question. However, as we discussed in our Introduction, the equity mutual fund universe is characterized by a relatively small number of very large funds and large numbers of very small funds. As a result, as we begin to explore in the next section, there is the danger that findings in studies focusing on funds are driven by a large number of small funds with a tiny aggregate market share, whereas the experience of the typical investor is driven mostly by a small number of large funds with a large aggregate market share. In other words, a result that appears statistically significant for mutual funds collectively may lack economic significance for fund investors. 4. Is there a convex flow/performance relation? Beginning with Ippolito (1992), Chevalier and Ellison (1997), and Sirri and Tufano (1998), the mutual fund literature has documented a convex relation between flows and fund performance. This convexity is widely interpreted to mean that investors reward top performers but do not punish poor performers, at least not to the same degree. This important stream of literature spawned an entire sub-field that studies fund manager behavior. It is argued that the convex flow/performance relation creates call option-like payoffs for fund managers, with the implication that managers may be incented to take on excess risk at times. In an early work, Brown et al. (1996) study changes in portfolio risk based on a fund's relative performance at the mid-year point. They document a tournament-like response on the part of fund managers. Funds that are relative losers in the first part of the year increase their riskiness, hoping to increase performance in the second half of the year. However, research contemporaneous with this paper by Spiegel and Zhang (2013) suggests that the apparent convexity is due to misspecification in the standard empirical model. They use changes in fund market shares instead of TNA-scaled fund flows as their dependent variable and find no evidence of convexity. In this section, we take another look at whether fund flows are convex, but instead of changing the dependent variable, we change the question of interest. Specifically, given the considerable variation in fund size, is it really the case that the average dollar in the industry displays non-linear flow/performance characteristics? In Fig. 2, we plot the average net flow (as a percentage of beginning-of-month TNA) for each of 20 performance ranks based on lagged raw returns (calculated over the t − 13 to t − 1 period). We show the results for all funds in our sample, as well as separately for the smallest and largest fund size deciles.10 From the plot of all funds, we confirm the traditional findings from the literature. For example, a fund whose return moves from the 10th ventile to the 20th ventile will see net flow increase from 0.05% to 4.66%, whereas a fund moving from the 10th ventile to the 1st ventile will see net flow fall from 0.05% to only −1.71%. Thus, the average fund does appear to face incentives consistent with the tournament literature. When we turn to the results for the small and large funds, our conclusions change. For example, when we look at small funds, net flow increases from 0.49% to 8.09% as a fund moves from the 10th ventile to the 20th ventile. Net flow decreases from 0.49% to −0.73% as a fund moves from the 10th ventile to the 1st ventile. This implies that the tournament incentives are particularly strong for small funds. However, in the case of the large funds we see an almost linear change as a fund moves between ventiles. A large fund moving from the 10th ventile to the 20th ventile has a net flow that increases from −0.26% to 1.65%. Net flow decreases from −0.26% to −2.06% as a fund moves from the 10th ventile to the 1st ventile. Thus, for large funds, it is unclear if they face tournament incentives. The punishment for losing and the reward for winning are nearly equivalent. As a point of reference, at the end of 2012, the smallest decile of funds managed less than 0.1% of the total TNA in our sample, while the largest decile managed about 69%. To explore this question more fully, we repeat the analysis in a multivariate setting. The dependent variable is the monthly implied net flow for each fund. As in Sirri and Tufano (1998) and other studies, a fund's performance rank (PERFi,t) is defined over the range of zero to one based on the fund's performance in the prior 12 months. Performance is measured by raw returns. The performance of fund i in month t in the bottom quintile is LOWi,t = Min(PERFi,t, 0.2), in the three medium quintiles is MIDi,t = Min(0.6, PERFi,t − LOWi,t), and in the top quintile is HIGHi,t = PERFi,t − MIDi,t − LOWi,t.11 Our panel model takes the general form: Net flowi;t ¼ LOW i;t−1 þ MIDi;t−1 þ HIGHi;t−1 þ Controlsi;t−1 þ Timet þ ϵ i;t :

ð1Þ

Our controls consist of variables widely used in previous research: 1. Log age, log of age (as of the beginning of the month), 2 Log size, log of TNA (as of month t − 13),12 3. Log family size, log of family TNA (as of the beginning of the month),13 10

We use deciles throughout the paper to separate funds into different size groups. The results are qualitatively similar in each instance if we use quintiles instead. We also estimated Eq. (1) using a simple quadratic specification, and we evaluated relative performance using Carhart (1997) alphas instead of raw returns. We find similar results (unreported). 12 Because we calculate performance from the previous 12 months, we look back 13 months to form our size deciles to avoid inducing performance. If we form deciles based on size following our measurement of performance (in month t − 1, for example), we induce performance because the best performers in terms of returns will tend to be larger. 13 Our family size is based only on family equity funds in our sample. We exclude the fund itself from the calculation of fund family TNA and exclude any funds that are the only fund in their family in the sample (about .6% of total observations). If we use log family size as of month t − 13, our results are unchanged. 11

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10.00%

Monthly net flow (%)

8.00% 6.00% 4.00% 2.00% 0.00% 0

2

4

6

8

10

12

14

16

18

20

-2.00% -4.00%

Lag performance rank All funds

Small funds

Large funds

Fig. 2. The interaction of net flows and fund size. This figure presents the average percent net flow by past performance ranking for the overall sample, the smallest size decile, and the largest size decile. Each month, we rank funds into size deciles based on assets under management in month t − 13. Within each size decile and for the full sample, we construct 20 groups based on total returns over the period t − 1 to t − 12.

Table 2 Convexity of fund flows by size decile. This table presents results of panel regressions of mutual fund net flows using Eq. (1) in the paper:

Net flowi;t ¼ LOW i;t−1 þ MIDi;t−1 þ HIGH i;t−1 þ Controlsi;t−1 þ Timet þ ϵ i;t :

The dependent variable is the monthly implied net flow calculated for each fund. Performance rank (PERFi,t) is defined over the range of zero to one based on the fund's performance in the prior 12 months. Performance is measured by raw returns. The performance of fund i in month t in the bottom quintile is LOWi,t = Min(PERFi,t, 0.2), in the three medium quintiles is MIDi,t = Min(0.6, PERFi,t − LOWi,t), and in the top quintile is HIGHi,t = PERFi,t − MIDi,t − LOWi,t. We also include (but do not present for brevity) log aget − 1, log fund sizet − 13, log family sizet − 1, turnover ratiot − 1, expense ratiot − 1, and front/back load dummy variables. We winsorize all non-log continuous variables in the model at the 2.5% level. We estimate the model using time fixed effects. Our standard errors are clustered at the fund level and robust to heteroskedasticity. p-values are reported below the coefficients in brackets. We do not use *s to indicate statistical significance in this table because nearly all the coefficients are significant at the 1% level. We perform a Wald test to determine whether the coefficients on LOWt − 1 and HIGHt − 1 are different and report the p-value from that test at the bottom of the table. All

Low Mid High Controls Time FE Observations r2 Low = High

4. 5. 6. 7.

0.044 [0.000] 0.021 [0.000] 0.100 [0.000] Yes Yes 236,929 0.14 0.000

Size decile Small

2

3

4

5

6

7

8

9

Large

−0.013 [0.396] 0.030 [0.000] 0.185 [0.000] Yes Yes 23,912 0.10 0.000

0.047 [0.000] 0.026 [0.000] 0.151 [0.000] Yes Yes 22,925 0.13 0.000

0.035 [0.000] 0.028 [0.000] 0.125 [0.000] Yes Yes 23,023 0.14 0.000

0.051 [0.000] 0.021 [0.000] 0.126 [0.000] Yes Yes 23,337 0.15 0.000

0.045 [0.000] 0.022 [0.000] 0.094 [0.000] Yes Yes 23,588 0.14 0.000

0.050 [0.000] 0.021 [0.000] 0.078 [0.000] Yes Yes 23,861 0.15 0.017

0.047 [0.000] 0.020 [0.000] 0.082 [0.000] Yes Yes 24,105 0.17 0.001

0.053 [0.000] 0.015 [0.000] 0.053 [0.000] Yes Yes 24,093 0.15 0.985

0.049 [0.000] 0.018 [0.000] 0.056 [0.000] Yes Yes 23,914 0.19 0.464

0.045 [0.000] 0.015 [0.000] 0.042 [0.000] Yes Yes 24,171 0.25 0.639

Front load, equal to one if the fund has a front-load (as of the beginning of the month), Back load, equal to one if the fund has a back-load (as of the beginning of the month), Turnover ratio, turnover (as of the end of the most recent fiscal year), and Expense ratio, expense ratio (as of the end of the most recent fiscal year).14

We also include time fixed effects in the model.15 In the first column of Table 2 (labeled “All”), we estimate Eq. (1) for our entire sample.16 We confirm the previous literature and find a convex relation between flows and past performance. The flow sensitivity for the top performing (HIGH) funds is over twice that of the sensitivity for the bottom performing (LOW) funds. 14 15 16

We winsorize all non-log continuous variables in the model at the 2.5% level. We reach similar conclusions throughout this section if we also include fund fixed effects. Our time period is reduced to January 1998 through December 2012 for our multivariate convexity tests because of the data required.

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We next repeat the panel regressions with one modification. We estimate separate panel regressions for each size decile, thereby allowing all the coefficients in Eq. (1) to vary by size decile. Scanning across the columns in Table 2, the coefficients of the performance measures differ significantly between large and small funds. For large funds, the flow sensitivity coefficients for the top and bottom performing funds are very similar. For example, in the largest fund size decile, the coefficient for LOW funds is 0.045, while the coefficient for HIGH funds is 0.042. A Wald test fails to reject the null hypothesis that those effects are equal. For small funds, however, the results are quite different. The coefficient on the HIGH funds shows much larger sensitivity to past performance than the coefficient on LOW, perhaps giving the managers of these funds significant tournament incentives. Common methods to control for fund size discussed previously will not indicate this difference between large and small funds. In Table 3, we demonstrate this point by showing the effect of different size controls on the full sample result. Column 1 repeats the “All” column of Table 2 without any control variables. The coefficient on LOW is about half that of HIGH. Column 2 returns the control variables, including Log size, to the model, but the coefficients on LOW and HIGH remain about the same. We drop the smallest decile of funds from the sample in column 3, and we find that adjustment also has little effect on the coefficients on LOW and HIGH. Thus,

Table 3 Measuring the difference in convexity between large and small funds. This table presents results of panel regressions of mutual fund net flows using Eq. (1) in the paper:

Net flowi;t ¼ LOW i;t−1 þ MIDi;t−1 þ HIGH i;t−1 þ Controlsi;t−1 þ Timet þ ϵ i;t :

The model is the same as described in Table 2 except we introduce a new variable, Largei,t −13, which is equal to one if the fund is among the largest 10% funds by total net assets, zero otherwise. We include Largei,t −13 in some models and interact it with each of our performance measures (LOWt −1, MIDt −1, HIGHt −1). As with log fund size, we measure this dummy variable as of month t − 13 to avoid inducing performance. In column 3, we exclude the smallest 10% of funds by total net assets. In columns 5 and 6, we divide our time period into two equal halves, January 1998 through June 2005 and July 2005 through December 2012. Our standard errors are clustered at the fund level and robust to heteroskedasticity. p-values are reported below the coefficients in brackets. We also perform Wald tests to determine (1) whether the coefficients on LOWi,t − 1 and HIGHi,t −1 are different and (2) whether the sum of LOWi,t −1 and LOWi,t −1 ∗ Largei,t −13 is different from the sum of HIGHi,t −1 and HIGHi,t − 1 ∗ Largei,t − 13. We report the p-values from those tests at the bottom of the table. Sample

Low Mid High

1

2

3

4

5

6

All

All

Omit small

All

First half

Second half

0.050⁎⁎⁎ [0.000] 0.021⁎⁎⁎ [0.000] 0.105⁎⁎⁎ [0.000]

0.045⁎⁎⁎ [0.000] 0.020⁎⁎⁎ [0.000] 0.102⁎⁎⁎ [0.000]

0.048⁎⁎⁎ [0.000] 0.020⁎⁎⁎ [0.000] 0.093⁎⁎⁎ [0.000]

Yes 222,433 0.12 0.000⁎⁎⁎

−0.002⁎⁎⁎ [0.000] 0.001⁎⁎⁎ [0.000] −0.004⁎⁎⁎ [0.000] −0.001⁎⁎ [0.016] 0.002⁎⁎⁎ [0.001] −0.407⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.000] Yes 222,392 0.14 0.000⁎⁎⁎

−0.001⁎⁎⁎ [0.000] 0.001⁎⁎⁎ [0.000] −0.003⁎⁎⁎ [0.000] −0.001⁎⁎ [0.027] 0.001⁎⁎⁎ [0.008] −0.434⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.000] Yes 200,029 0.15 0.000⁎⁎⁎

0.045⁎⁎⁎ [0.000] 0.021⁎⁎⁎ [0.000] 0.105⁎⁎⁎ [0.000] 0.005⁎⁎⁎ [0.000] 0.004 [0.596] −0.002 [0.227] −0.057⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.000] 0.001⁎⁎⁎ [0.000] −0.004⁎⁎⁎ [0.000] −0.001⁎⁎ [0.042] 0.002⁎⁎⁎ [0.001] −0.415⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.000] Yes 222,392 0.14 0.000⁎⁎⁎ 0.995

0.041⁎⁎⁎ [0.000] 0.025⁎⁎⁎ [0.000] 0.116⁎⁎⁎ [0.000] 0.010⁎⁎⁎ [0.000] −0.014 [0.220] −0.000 [0.922] −0.056⁎⁎⁎ [0.000] −0.003⁎⁎⁎ [0.000] 0.001⁎⁎⁎ [0.000] −0.003⁎⁎⁎ [0.000] 0.001 [0.349] 0.001 [0.103] −0.236⁎⁎⁎ [0.008] −0.002⁎⁎⁎ [0.000] Yes 98,095 0.17 0.000⁎⁎⁎ 0.053⁎

0.047⁎⁎⁎ [0.000] 0.017⁎⁎⁎ [0.000] 0.098⁎⁎⁎ [0.000] 0.002 [0.253] 0.017⁎ [0.087] −0.003 [0.103] −0.052⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.000] 0.001⁎⁎⁎ [0.000] −0.004⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.002] 0.002⁎⁎ [0.012] −0.646⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.000] Yes 124,297 0.12 0.000⁎⁎⁎ 0.135

Large Low ∗ Large Mid ∗ Large High ∗ Large ln(Size) ln(Fam size) ln(Age) Front load Rear load Expense Turnover Time FE Observations r2 Low = High Low + Low ∗ Large = High + High ∗ Large

⁎ Represent statistical significance at the 10% level. ⁎⁎ Represent statistical significance at the 5% level. ⁎⁎⁎ Represent statistical significance at the 1% level.

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Table 4 Do participation costs explain the flow/performance relation of large funds? This table presents results of panel regressions of mutual fund net flows using Eq. (1) in the paper:

Net flowi;t ¼ LOW i;t−1 þ MIDi;t−1 þ HIGH i;t−1 þ Controlsi;t−1 þ Timet þ ϵ i;t :

The model is the same as described in Table 3 except we also interact log family sizet −1 with each of our performance measures (LOWt −1, MIDt −1, HIGHt −1) in some models. We include the control variables presented in Table 3 in every model, but do not present all for brevity. In columns 5 and 6, we divide our time period into two equal halves, January 1998 through June 2005 and July 2005 through December 2012. Our standard errors are clustered at the fund level and robust to heteroskedasticity. p-values are reported below the coefficients in brackets. Sample

Low Mid High ln(Size)

1

2

3

4

5

6

All

All

All

All

First half

Second half

0.011 [0.463] 0.016⁎⁎⁎ [0.000] 0.117⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.000] 0.008⁎⁎⁎ [0.000] −0.007 [0.442] −0.003⁎ [0.066] −0.053⁎⁎⁎ [0.000] −0.000 [0.873] 0.005⁎⁎ [0.012] 0.001⁎ [0.084] −0.001 [0.455] Yes Yes 222,392 0.14

0.016 [0.338] 0.014⁎⁎⁎ [0.001] 0.101⁎⁎⁎ [0.000] −0.003⁎⁎⁎ [0.000] 0.013⁎⁎⁎ [0.000] −0.026⁎⁎ [0.041] −0.004 [0.178] −0.062⁎⁎⁎ [0.000] 0.000 [0.498] 0.004⁎ [0.064] 0.001⁎⁎⁎ [0.008] 0.002 [0.494] Yes Yes 98,095 0.17

0.011 [0.547] 0.013⁎⁎⁎ [0.000] 0.126⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.000] 0.004⁎⁎ [0.048] 0.008 [0.460] −0.004⁎ [0.059] −0.044⁎⁎⁎ [0.000] −0.000 [0.380] 0.005⁎⁎ [0.035] 0.000 [0.300] −0.003 [0.151] Yes Yes 124,297 0.12

0.045⁎⁎⁎ [0.000] 0.020⁎⁎⁎ [0.000] 0.102⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.000]

0.045⁎⁎⁎ [0.000] 0.021⁎⁎⁎ [0.000] 0.105⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.000] 0.005⁎⁎⁎ [0.000] 0.004 [0.596] −0.002 [0.227] −0.057⁎⁎⁎ [0.000] 0.001⁎⁎⁎ [0.000]

Large Low ∗ Large Mid ∗ Large High ∗ Large ln(Fam size)

0.001⁎⁎⁎ [0.000]

Low ∗ ln(fam size) Mid ∗ ln(fam size) High ∗ ln(fam size) Other controls Time FE Observations r2

Yes Yes 222,392 0.14

Yes Yes 222,392 0.14

0.007 [0.637] 0.017⁎⁎⁎ [0.000] 0.127⁎⁎⁎ [0.000] −0.002⁎⁎⁎ [0.000]

0.000 [0.930] 0.005⁎⁎⁎ [0.005] 0.000 [0.253] −0.003* [0.089] Yes Yes 222,392 0.14

⁎ Represent statistical significance at the 10% level. ⁎⁎ Represent statistical significance at the 5% level. ⁎⁎⁎ Represent statistical significance at the 1% level.

neither a control variable for size nor dropping the smallest funds gives any indication of the difference in the convex relation between large and small funds. We find that the difference between large and small funds can be demonstrated by focusing the regression on the largest funds. To make that adjustment, we include a dummy variable, Large, in the regression and interact it with our performance measures. Large is equal to one if the fund is among the largest 10% of funds by total net assets, zero otherwise. Column 4 shows that the main effects of LOW and HIGH are similar to previous models, but the full effects of LOW and HIGH for large funds are nearly identical. The slope for LOW funds is 0.049 (.045 + .004), while the slope in the HIGH funds is 0.048 (.105 – .057). We fail to reject the null hypothesis that these effects are the same (p-value = .995). In columns 5 and 6, we divide our time period into two equal halves because Kim (2011) indicates that the convex relation has changed over time. We find that the flow/performance relation is significantly less convex for large funds in both time periods. We also verify that our result is not simply re-documenting previous results. Huang et al. (2007) show that funds with lower participation costs have a less convex flow/performance relation. Among the proxies they use for participation costs is fund family size.17 Log size and Log family size have a correlation of 0.54 in our sample, so it is possible that fund size is just proxying for participation costs. We test this possibility in Table 4. We repeat our initial tests using the large fund dummy in columns 1 and 2 to reestablish our baseline result. We then interact our performance measures with family size in column 3 and find similar results to Huang et al.

17 Huang et al. (2007) also use marketing expense, affiliation with a star family, and family diversity as proxies for participation costs. If we use those measures, our conclusions are unchanged.

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Table 5 Is money “smart” for both large and small funds? This table presents the performance for mutual funds that receive high and low implied net flows. Following Keswani and Stolin (2008), we define high (low) flow funds as those ranked in the top (bottom) half of all funds each month. Our flow ranks are obtained at month t − 1. We use the “fund” approach for our performance measure. For each fund-month, we run the Carhart (1997) model over the preceding 12 months to estimate factor loadings. We require all 12 months for the fund to be included. The fund alpha is obtained as the difference between the fund's excess return in month t and the product of the fund's factor loadings and the factor realizations for month t. We separately present the results for the high flow, low flow, and the difference between the high and the low flow group. We repeat this analysis for our entire sample, as well as for ten size deciles. We form the size deciles based on fund size at month t − 13. Conditional on the size decile, we place funds into high and low net flow groups based on the implied net flow in month t − 1 (above or below median). All reported alphas are in basis points per month. p-values are reported below the coefficients in brackets. All

High flow Low flow High–Low

−3.07 [0.560] −8.61⁎ [0.080] 5.54⁎⁎ [0.015]

Size decile Small

2

3

4

5

6

7

8

9

Large

0.01 [0.999] −9.51⁎ [0.076] 9.52⁎⁎ [0.043]

4.04 [0.477] −11.79⁎⁎ [0.035] 15.83⁎⁎⁎ [0.000]

3.84 [0.475] −7.01 [0.216] 10.85⁎⁎⁎ [0.003]

−2.12 [0.696] −8.81⁎ [0.069] 6.68⁎ [0.094]

−1.03 [0.860] −7.06 [0.187] 6.03⁎⁎ [0.046]

−6.20 [0.331] −8.51 [0.165] 2.31 [0.553]

−8.11 [0.164] −10.48⁎ [0.055] 2.37 [0.506]

−3.36 [0.564] −13.54⁎⁎ [0.015] 10.18⁎⁎⁎ [0.002]

−5.94 [0.293] −5.39 [0.306] −0.55 [0.875]

−8.57 [0.116] −6.66 [0.184] −1.91 [0.601]

⁎ Represent statistical significance at the 10% level. ⁎⁎ Represent statistical significance at the 5% level. ⁎⁎⁎ Represent statistical significance at the 1% level.

(2007). As fund family size increases, fund flows become more sensitive to fund performance in the LOW tier and less sensitive to performance in the HIGH tier. We test whether this effect subsumes the fund size effect in column 4 by interacting our performance rankings with both our large fund dummy and fund family size. Large funds still have a significantly less convex flow/performance relation after controlling for fund family size. As in Table 3, we repeat the test in column 4 for the first and second halves of our time period in columns 5 and 6. We find that our conclusions hold in both time periods. Thus, it does not appear that the difference in the flow/performance relation for large and small funds can be explained by participation costs. Overall, we find that the convex flow/performance relation documented in the literature is driven entirely by smaller funds. The average mutual fund-dollar is not invested with a manager facing call option-like payoffs based on his performance. Perhaps managers of small funds do engage in tournament-type behavior in response to convexity, but, if so, the aggregate impact on investors collectively is not large. Our results here bridge the gap between the standard convexity results and the counterargument of Spiegel and Zhang (2013). Without modifying the dependent variable, we demonstrate that the convex flow/performance relation is not meaningful for the average investor.

5. Are investor net flows “smart”? Gruber (1996) and Zheng (1999) address an important puzzle in the mutual fund literature: If actively managed mutual funds do not consistently outperform their benchmarks, why do investors buy them? Gruber documents that mutual fund flows appear to be “smart,” meaning that investors buy funds that subsequently outperform, while selling funds that subsequently underperform. Sapp and Tiwari (2004), on the other hand, find no evidence of smart money. Rather, they document that momentum in fund returns can be used to explain the smart money effect. More recently, Keswani and Stolin (2008) find evidence of “smartness” when studying flows of both U.K. and U.S. investors, even in the presence of momentum. Thus, the evidence is mixed, and we attempt to shed further light on the issue by exploring the role of fund size. We follow Keswani and Stolin (2008) in Table 5 and classify all funds each month as either high net flow or low net flow based on whether their net flow was above or below the median. In the month immediately following, we go long (short) the high flow (low flow) funds. We estimate the performance of these portfolios using what Zheng (1999) calls the “fund” approach. To do this, we create an equally-weighted average of the fund-level Carhart (1997) four-factor alphas in each portfolio. The monthly fund alphas are derived from factor exposures from rolling 12 month regressions. In the column labeled “All,” the long-short portfolio has an alpha of 5.5 bps/month (p-value = .015). Thus, consistent with Keswani and Stolin (2008), we find evidence of “smartness,” even after controlling for the momentum factor.18 In the final ten columns of Table 5, we repeat this analysis after first sorting funds into deciles based on size. As in our previous section, we use size as of month t − 13 to avoid inducing performance. Under this approach, smartness is significantly different than zero for the first (smallest) through fifth deciles and the eighth. In the largest size decile, which contains about 70% of the aggregate TNA in a typical month, the smartness is −1.91 bps/month (p-value = .601). Thus, we see little or no evidence of an economically significant smart money effect.

18 Over the period 1991–2004, Keswani and Stolin (2008) find an alpha of 9.3 bps/month. Our estimate is slightly lower which reflects an alpha of only 2.7 bps/month over the period 2005–2012.

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Table 6 Measuring the difference in “smartness” between large and small funds. This table presents results of panel regressions of mutual fund net alphas using Eq. (2) in the paper:

Alphai;t ¼ Net flowi;t−1 þ Timet þ ϵ i;t :

The dependent variable is the net alpha (in basis points) for fund i in month t. The fund alpha is obtained as the difference between the fund's excess return in month t and the product of the fund's factor loadings and the factor realizations for month t. We run the Carhart (1997) model over the preceding 12 months (requiring all 12 months) to estimate the loadings. We include time fixed effects in all models. We z-score net flow each month, i.e., demean then divide by the standard deviation, to rank flows and ease interpretability. In columns 2 through 4, we include the z-score of natural log of fund total net assets as a control variable. In column 3, we exclude the smallest 10% of funds by total net assets as of month t − 13. In column 4, we include the variable Largei,t −13, which is equal to one if the fund is among the largest 10% funds by total net assets in month t − 13, zero otherwise. We interact Largei,t −13 with our measure of net flow. We winsorize all continuous non-log variables in the model at the 2.5% level. Our standard errors are clustered at the fund level and robust to heteroskedasticity. p-values are reported below the coefficients in brackets. We perform a Wald test to see whether the sum of the coefficients on Net flow and Net flow ∗ Large is different from zero and report the p-value from that test at the bottom of the table. Sample

1

2

3

Net flow

All

All

Omit small

All

3.506⁎⁎⁎ [0.000]

3.470⁎⁎⁎ [0.000] −0.338 [0.512]

3.508⁎⁎⁎ [0.000] −0.558 [0.204]

Yes 287,817 0.09

Yes 258,866 0.10

3.610⁎⁎⁎ [0.000] −0.401 [0.542] −0.029 [0.987] −4.201⁎⁎ [0.042] Yes 287,817 0.09 0.770

Yes 287,817 0.09

ln(Size) Large Net flow ∗ Large Time dummies Observations r2 Net flow + Net flow ∗ Large = 0

4

⁎ Represent statistical significance at the 10% level. ⁎⁎ Represent statistical significance at the 5% level. ⁎⁎⁎ Represent statistical significance at the 1% level.

We next repeat this analysis in a multivariate setting to demonstrate how common methods to control for fund size will not indicate this difference between large and small funds. The dependent variable in our model is the net Carhart (1997) alpha for fund i in month t measured in basis points using the “fund” approach. Our variable of interest on the right-hand side is the fund flow in the prior month.19 Our model takes the general form: Alphai;t ¼ Net flowi;t−1 þ Timet þ ϵ i;t :

ð2Þ

We include time fixed effects in the model and z-score, i.e., demean then divide by the standard deviation, net flow each month.20 Performing the z-score process each month gives the flows a within month ranking and allows the coefficient to be easily interpreted. The coefficient indicates the change in alpha in the next month from being one standard deviation above the mean net flow in the prior month.21 We estimate Eq. (2) in column 1 of Table 6. We find that having a net flow one standard deviation above the mean in the prior month predicts an alpha 3.5 bps higher in the subsequent month, i.e., money is “smart.” We next try common methods of controlling for fund size in columns 2 and 3. First, we add the natural log of fund size to model, but it has little effect on our results. Next, we drop the smallest decile of funds, but that too has little effect on our results. If large and small funds do have different levels of “smartness,” these methods do not indicate it. As in the previous section, we now focus the regression on the largest funds instead. We again add a dummy variable, Large, equal to one if a fund is in the largest size decile, zero otherwise, to the model. When we interact Large with net flow, we find a significant difference in “smartness” for large and small funds.22 Column 4 shows that while the main effect is still about 3.6 bps, the full effect for the largest funds is about −0.59 bps (3.610 – 4.201). A Wald test suggests that this value is not significantly different from zero, so money does not appear to be “smart” or “dumb” among large funds. The evidence in this section indicates that if there is a smart money effect, then it is of limited economic importance. While Table 5 found evidence of smart money among the bottom five deciles of funds, those funds combined managed only about 3.4% of the assets in our sample at the end of 2012. The largest decile of funds, which manages about 69% of the assets at that same time, shows no 19

We winsorize both net flow and alpha at the 2.5% level. If we substitute the median net flow for the mean net flow in the z-score process, our conclusions are unchanged. We avoid using other variables in our model because our goal is to demonstrate how size affects “smart money”, not to determine whether the existence of “smart money” is actually driven by other variables. 22 In unpresented results, we ran separate regressions for all ten size deciles. Consistent with the presented findings, we found that flows only predicted future performance among funds below the 80th percentile (in terms of size). These results are available upon request. 20 21

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evidence of smart money. This difference would be obscured by typical methods to control for fund size in our regression specification. However, by instead focusing tests on the largest funds, we can show that difference in a multivariate setting. 6. Why are the largest mutual funds different? While it is clear empirically that the convex flow/performance relation and the “smart money” effect are driven by the large number of small funds, the underlying economic reason is not as apparent. To at least begin to explore this question, we draw on prior studies and examine two potential explanations in this section.23 The first possibility is a relationship between size and participation costs. Huang et al. (2007) show that mutual funds with lower participation costs have a less convex flow/performance relation. Larger funds should have lower participation costs with respect to both information costs and transaction costs. Information costs are lower for larger funds because information on and analyses of larger funds are more readily available. Transaction costs are lower because larger funds have significantly lower fees. Because lower participation costs lessen the convex flow/performance relation, we may not observe the convex relation among larger funds. The lower participation costs of larger funds may also cause flows to those funds to be less “smart” by attracting less informed investors. Following Huang et al. (2007), we considered participation costs and fund size together in Table 4. Consistent with their results, we found that funds with lower participation costs have a less convex flow/performance relation. However, accounting for participation costs using their measures did not change the impact of fund size. While fund size could just be a more effective proxy for participation costs, it may also have an independent effect. For example, the effect could be related to diseconomies of scale. Chen et al. (2004) find that mutual fund performance is decreasing in fund size. Berk and Green (2004) argue that result occurs because a manager's ability to produce abnormal returns is decreasing in fund size. If investors understand that relationship, they would respond to the performance of large and small funds differently. They would not disproportionally reward large funds that perform well as large fund performance is not likely to persist. That same difference in performance persistence would also prevent flows to large funds from appearing “smart.” We have no direct means of testing this explanation, but all of our results are consistent with diseconomies of scale in fund management. 7. Conclusion Because U.S. equity mutual funds vary so much in size, it is difficult to extrapolate from the average fund to the average dollar. For example, the average fund charges about 1.4% per year, but the average investor pays about 1.0%, an economically large difference. Thus, looking at the average fund could lead one to substantially overestimate the aggregate cost to investors of actively-managed equity funds. We explore some of the better known issues in mutual fund research with a focus on the impact of fund size. The variation in size across funds would be of limited importance if large and small funds had similar economic characteristics, but we show that they do not. For example, it is widely thought that mutual funds face a convex flow/performance relation. We confirm that this relation exists for the average fund, but then show that the effect is entirely due to very small funds. Among the largest 10% of funds, which together manage over 70% of aggregate industry assets in a typical year, we find a linear relation. Similarly, we examine whether investor fund flows are “smart,” meaning that they anticipate future performance. We verify that high net flow funds do experience subsequently better performance than low net flow funds, but the effect is again confined to a large number of very small funds. We find no evidence that the net flows of large funds predict future performance. Overall, we show that the impact of variation in mutual fund size is profound. Smaller funds play an economically outsized role in the cases we examine. Research that is limited in the number of funds, but not in percentage of assets, e.g., Adam and Guettler (2013), will still provide insights of significant economic relevance. However, our findings also raise a broader question concerning research in financial economics, particularly corporate finance. Like equity mutual funds, corporations vary enormously in size. In key areas, such as capital structure, is it the case that size plays a role? In other words, perhaps the capital structures of the relatively small number of giant firms matter more in economic terms than the capital structure of the thousands of smaller firms. This too is a question for future research. References Adam, Tim, Guettler, Andre, 2013. Pitfalls and perils of financial innovation: the use of CDS by corporate bond funds. Working Paper. Berk, Jonathan B., Green, Richard C., 2004. Mutual fund flows and performance in rational markets. J. Polit. Econ. 112, 1269–1295. Berk, Jonathan B., van Binsbergen, Jules H., 2013. Measuring skill in the mutual fund industry. Working Paper. Brown, Keith C., Harlow, W.V., Starks, Laura T., 1996. Of tournaments and temptations: an analysis of managerial incentives in the mutual fund industry. J. Financ. 51, 85–109. Carhart, Mark M., 1997. On persistence in mutual fund performance. J. Financ. 52, 57–82. Chen, Joseph, Hong, Harrison, Huang, Ming, Kubik, Jeffrey D., 2004. Does fund size erode mutual fund performance? The role of liquidity and organization. Am. Econ. Rev. 94, 1276–1302. Chevalier, Judith, Ellison, Glenn, 1997. Risk taking by mutual funds as a response to incentives. J. Polit. Econ. 105, 1167–1200. Coval, Joshua, Stafford, Erik, 2007. Asset fire sales (and purchases) in equity markets. J. Financ. Econ. 86, 479–512. Evans, Richard B., 2010. Mutual fund incubation. J. Financ. 65, 1581–1611. Fama, Eugene, French, Kenneth R., 2010. Luck versus skill in the cross section of mutual fund returns. J. Financ. 65, 1915–1947. Gruber, Martin J., 1996. Another puzzle: the growth in actively managed mutual funds. J. Financ. 51, 783–810. Huang, Jennifer, Wei, Kelsey D., Yan, Hong, 2007. Participation costs and the sensitivity of fund flows to past performance. J. Financ. 62, 1273–1311.

260

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Ippolito, Roger A., 1992. Consumer reaction to measures of poor quality: evidence from the mutual fund industry. J. Law Econ. 35, 45–70. Jensen, Michael C., 1968. The performance of mutual funds in the period 1945–1964. J. Financ. 23, 389–416. Keswani, Aneel, Stolin, David, 2008. Which money is smart? Mutual fund buys and sells of individual and institutional investors. J. Financ. 63, 85–118. Kim, Min S., 2011. Changes in mutual fund flows and managerial incentives. Working Paper. Sapp, Travis, Tiwari, Ashish, 2004. Does stock return momentum explain the “smart money” effect? J. Financ. 59, 2605–2622. Sirri, Erik R., Tufano, Peter, 1998. Costly search and mutual fund flows. J. Financ. 53, 1589–1622. Spiegel, Matthew, Zhang, Hong, 2013. Mutual fund risk and market share adjusted fund flows. J. Financ. Econ. 108, 506–528. Zheng, Lu, 1999. Is money smart? A study of mutual fund investors' fund selection ability. J. Financ. 54, 901–933.