The Mismatch Between Mutual Fund Scale and Skill

• Date: 01 October 2020
• Author: YANG SONG
• Published date: 01 October 2020
• DOI: http://doi.org/10.1111/jofi.12950

THE JOURNAL OF FINANCE •VOL. LXXV, NO. 5 •OCTOBER 2020

The Mismatch Between Mutual Fund Scale

and Skill

YANG SONG∗

ABSTRACT

I demonstrate that skill and scale are mismatched among actively managed equity

mutual funds. Many mutual fund investors confuse the effects of fund exposures

to common systematic factors with managerial skill when allocating capital among

funds. Active mutual funds with positive factor-related past returns thus accumulate

assets to the point that they significantly underperform. I also show that the negative

aggregate benchmark-adjusted performance of active equity mutual funds is driven

mainly by these oversized funds.

THE EXTENT TO WHICH AN actively managed mutual fund can add value for

investors depends not only on the portfolio manager’s skill in discovering su-

perior investment opportunities but also on the scale of the fund. Academic

research over the past several decades shows that the aggregate active equity

mutual fund portfolio has significantly negative benchmark-adjusted returns

(alphas) after fees1and that the performance of an average fund is not persis-

tent over time. The seminal work of Berk and Green (2004) (BG) points out that

the lack of return persistence is consistent with a model of rational investors

competing for scarce skill and active funds subject to decreasing returns to

∗Yang Song is at University of Washington. I am grateful for comments from the referees

and the Editor (Stefan Nagel), as well as Svetlana Bryzgalova, Hendrik Bessembinder, Itzhak

Ben-David, Jonathan Berk, John Cochrane, Darrell Duffie, Roger Edelen, Karim Farroukh, Ken

French, Will Gornall, David Hirshleifer,Ben Hébert, Shiyang Huang, Xing Huang, Ron Kaniel, An-

drew Karolyi, Peter Koudijs, Arvind Krishnamurthy, Charles Lee, Ryan Lewis, Jiacui Li, Hanno

Lustig, Terrance Odean, Ľuboš Pástor, Monika Piazzesi, Ken Singleton, Jonathan Wallen, Martin

Schmalz, Mike Schwert, Amit Seru, Yao Zeng, Hong Xiang, Qingyuan Zhao, and Jeffrey Zwiebel.

In addition, I benefited from comments from conference and seminar participants at Stanford

University, University of Washington, Dartmouth Tuck, University of British Columbia, Univer-

sity of North Carolina, Cornell University, Rice University, Chicago Booth School, University of

Rochester, Ohio State University, Hong Kong University of Science and Technology, The Univer-

sity of Hong Kong, the 2017 Financial Research Association Conference, the 2017 Colorado Fi-

nance Summit, and the 2017 Olin Business School Corporate Finance Conference at Washington

University. I have read The Journal of Finance disclosure policy and have no conflicts of interest

to disclose.

Correspondence: Yang Song, University of Washington, Foster School of Business, Seattle, WA

98195; email: songy18@uw.edu.

1See, for example, Malkiel (1995), Gruber (1996), Carhart (1997), Wermers (2000), and Fama

and French (2010).

DOI: 10.1111/jofi.12950

© 2020 the American Finance Association

2555

2556 The Journal of Finance®

scale. However, the BG theory also predicts that managerial skill is matched

with fund scale so that mutual funds earn zero expected alpha net of fees,

which is hard to reconcile with the negative aggregate after-fee performance.

An important assumption of BG is that mutual fund investors rationally

evaluate managerial skill and allocate capital accordingly. However, this as-

sumption seems to be at odds with the characteristics of mutual fund investors

and with previous evidence about their behavior.2Accordingto the 2011 Invest-

ment Company Institute (ICI) Fact Book, for example, 93.7% of mutual fund

assets in the United States were held by households. If mutual fund investors

are not as sophisticated in assessing skill as modeled by BG, then certain funds

would receive more assets than justified by their portfolio managers’ skill, and

as a result observe negative performance due to diminishing returns to scale,3

whereas other funds might become too small. That is, in a market in which in-

vestors do not correctly evaluate managerial skill, the deviation of actual fund

size from fund capacity (the equilibrium size conjectured by BG) would be a

key predictor of future performance.

In this paper, I demonstrate that skill and scale are indeed significantly

mismatched among actively managed equity mutual funds. In particular, be-

cause many mutual fund investors do not adjust for common factors such as

the Fama–French size and value factors when allocating capital among funds,

actively managed funds with positive prior factor-related returns (FRRs) accu-

mulate assets to the point that they significantly underperform various bench-

marks in the future. In this sense, fund flows associated with FRRs are ex-

cessive and cannot be justified by managerial skill. I further show that ex-

cess fund size, rather than total fund size, significantly predicts future per-

formance: controlling for fund size, mutual funds that have attracted flows

through factor exposures significantly underperform benchmarks and other

funds of the same size.

My analysis builds on the observation of Berk and van Binsbergen (2016)

and Barber, Huang, and Odean (2016) that mutual fund flows respond pos-

itively to fund past returns arising from exposures to common factors other

than the market factor.4In a fully rational world, mutual fund investors would

2A large literature shows that mutual fund investors exhibit behavior that is generally con-

sidered unsophisticated. For example, mutual fund investors prefer funds that report holdings

of recent winners and lottery stocks (Solomon, Soltes, and Sosyura (2014)), invest in funds that

advertise a lot (Jain and Wu (2000)) or appear in the media (Kaniel and Parham (2017)), prefer

funds that recently experienced an extremely positive monthly return (Akbas and Genc (2020)),

and time the market poorly (Frazzini and Lamont (2008)).

3For supporting evidence of diminishing returns to scale, see Chen et al. (2004), Pollet and

Wilson (2008), Edelen, Evans, and Kadlec (2013), Harvey and Liu (2017), and Pástor,Stambaugh,

and Taylor (2018).

4In other words, many mutual fund investors appear to attribute the returns associated with

fund exposures to these common factors with managerial skill. Several papers try to explain this

investor behavior. For example, Chakraborty et al. (2018) argue that the results of Berk and van

Binsbergen (2016) and Barber, Huang, and Odean (2016) could be driven by investors’ limited at-

tention. Evans and Sun (2018) and Ben-David et al. (2019) argue that the results can be explained

in part by the fact that investors use Morningstar ratings as their main signal for investment.

The Mismatch Between Mutual Fund Scale and Skill 2557

distinguish return components due to managerial skill, such as processing pri-

vate information and discovering mispriced stocks, from components due to

factor exposures (Grinblatt and Titman (1989) and Pástor and Stambaugh

(2002a)). Due to actual investor behavior, however, actively managed funds

with positive prior FRRs accumulate so many assets that they have negative

expected alphas in the future. I also show that the negative net alphas of the

aggregate mutual fund portfolio documented by,for example, Fama and French

(2010), are driven mainly by the poor performance of the small set of oversized

funds that have significantly positive prior FRRs.

My empirical study relies on the CRSP mutual fund database. I focus on

actively managed equity mutual funds. To estimate a fund’s FRR, I follow Bar-

ber, Huang, and Odean (2016) and use a seven-factor model that augments

the Fama–French–Carhart (FFC) four-factor model with the three industry

factors5of Pástor and Stambaugh (2002b) as the baseline model. The FRR is

calculated as the sum of the return components that are traced to size, value,

momentum, and the three industry factors. For robustness, in Appendix AI

use the FFC four-factor model to estimate factor-related returns and I obtain

similar results.

I start by showing that fund flows respond positively to FRRs. Controlling for

factor-adjusted expected returns (the seven-factor alpha), I find that fund flows

are positively correlated with FRRs, regardless of whether flows are measured

in absolute dollars or as a proportion of fund’s total assets under management

(AUM). For example, funds whose average FRR over the previous four years

is in the top tercile of the sample distribution receive three times as much

flows per quarter, on average, as other funds with the same factor-adjusted

expected returns. This evidence is consistent with the findings of Berk and

van Binsbergen (2016) and Barber, Huang, and Odean (2016).

I next demonstrate that fund flows associated with positive FRRs lead to

negative fund future performance. To this end, I first control for fund AUM.

I find that funds that reach the current size because of positive prior FRRs

significantly underperform various benchmarks and other funds, despite hav-

ing similar AUM. For example, within each AUM quintile group, funds with

top-tercile past FRRs significantly underperform bottom-tercile-FRR funds by

around 300 to 400 bps over the next year, depending on the benchmark. Across

the five AUM quintiles, funds with top-tercile past FRRs have average neg-

ative future alphas of −230 to −250 bps per year. Funds with middle-tercile

FRRs have net alphas of about −20 bps, while funds with bottom-tercile FRRs

have net average alphas of around 70 to 80 bps. These results indicate that

how a fund grows its AUM, rather than fund AUM alone, determines fund

future performance.

I further show that this sharp performance difference is not due to the dif-

ference in prior “real” alphas. Specifically, I find that controlling for the prior

seven-factor alpha, funds that attract additional flows through positive FRRs

5The industry factors are the first three principal components of the residuals in multiple re-

gressions of the industry returns on the FFC factors. See Section Ifor more details.