Mutual Fund Flows and Cross‐Fund Learning within Families

• Published date: 01 February 2016
• Author: DAVID P. BROWN,YOUCHANG WU
• Date: 01 February 2016
• DOI: http://doi.org/10.1111/jofi.12263

THE JOURNAL OF FINANCE •VOL. LXXI, NO. 1 •FEBRUARY 2016

Mutual Fund Flows and Cross-Fund Learning

within Families

DAVID P. BROWN and YOUCHANG WU∗

ABSTRACT

We develop a model of performance evaluation and fund flows for mutual funds in

a family. Family performance has two effects on a member fund’s estimated skill

and inflows: a positive common-skill effect, and a negative correlated-noise effect.

The overall spillover can be either positive or negative, depending on the weight of

common skill and correlation of noise in returns. Its absolute value increases with

family size, and declines over time. The sensitivity of flows to a fund’sown performance

is affected accordingly. Empirical estimates of fund flow sensitivities show patterns

consistent with rational cross-fund learning within families.

WITH A TOTAL OF $26.8 TRILLION assets under management worldwide, mutual

funds are a major player in financial markets, and a primary investment ve-

hicle for households in many countries. In the United States, the $13.0 billion

mutual fund industry attracts 44.4% of households, among which 68% hold

more than half of their financial assets in mutual funds.1As such, mutual

fund investments have a significant impact on the wealth of a large fraction of

the population. They also indirectly affect the efficiencies of stock, bond, and

money markets, by determining the allocation of assets across fund managers

participating in those markets. Not surprisingly, there is strong interest in

understanding investment decisions of mutual fund investors, whether they

are sophisticated, and whether they act rationally. Empirical studies in this

∗Brown is at the Wisconsin School of Business, University of Wisconsin–Madison. Wu is at the

Wisconsin School of Business University of Wisconsin–Madison and Lundquist College of Busi-

ness, University of Oregan. Previous versions of this paper circulated under the title “Mutual

Fund Families and Performance Evaluation.” We thank Kenneth Singleton (Editor) and anony-

mous referees for many thoughtful comments and suggestions, and thank Jonathan Berk, Michael

Brennan, Pierre Collin-Dufresne, Thomas Dangl, Zhiguo He, Bryan Lim, ˇ

Luboˇ

sP

´

astor, Matthew

Spiegel, Neal Stoughton, Luke Taylor, Hong Yan, Tong Yao, Josef Zechner, and seminar partici-

pants at the Utah Winter Finance Conference in 2012, American Finance Association meetings in

2012, Western Finance Association meetings in 2011, Financial Intermediation Research Society

meetings in 2011, China International Conference in Finance in 2011, University of Wisconsin–

Madison, University of Illinois at Urbana-Champaign, University of Illinois at Chicago, University

of TechnologySydney, and Vienna Graduate School of Finance for helpful discussions. The authors

declare that they have no potential conflicts of intrest, as identified in the Journal of Finance

Disclosure Policy, and have received no financial support in the research or writingof the paper.

1These are statistics for the end of 2012, reported in the 2013 Investment Company Fact Book

of the Investment Company Institute (ICI).

DOI: 10.1111/jofi.12263

383

384 The Journal of FinanceR

area produce mixed results. On the one hand, Gruber (1996) and Zheng (1999)

find that investors appear to invest in funds that subsequently perform well.

On the other hand, Sapp and Tiwari (2004) attribute this “smart money” effect

to stock return momentum and investors naively chasing recent performance.

Furthermore, Frazzini and Lamont (2008) and Bailey, Kumar, and Ng (2011)

conclude that fund flows represent “dumb money” that is driven by behavioral

biases instead of rational learning about managerial skill.2

In this paper, we develop a novel test of investor sophistication by extending

the Berk and Green (2004) framework to allow for cross-fund learning within

fund families. Most mutual funds belong to a family.This provides rich possibil-

ities for cross-fund learning that are not available when funds are stand-alone.

We investigate whether investors rationally use information contained in the

performance of all funds in a family to evaluate an individual fund, instead of

evaluating each fund in isolation.

One source of cross-fund learning is common skill or resources shared by

funds in the family. For example, funds in a family may share a common man-

ager or management team, and managers in a family may share information,

opinions, and expertise with each other even if they manage different funds.

Furthermore, funds in a family often have access to the same pool of financial

analysts, trading desks, legal counselors, and outside experts. As a result, a

fund’s performance reflects not only its fund-specific characteristics, such as

its investment strategies, but also the quality of the skill and resources shared

across funds.

Another source of cross-fund learning is correlation in unobservable shocks

to the returns of funds in a family, due in part to the reliance on common skill.

Some aspects of common skill may affect fund alphas without systematically

affecting exposures to risk. Examples include operating efficiency, the quality

of trading desks and supporting staff, and the effectiveness of fund governance

and manager compensation schemes. However, when funds rely on shared

sources of information, they are likely to tilt their portfolios in similar directions

relative to their benchmarks. For example, an idea from one analyst can lead

several funds to simultaneously change their positions in a security. These

funds are then subject to correlated shocks to their performance.

Given the considerations above, how should a rational investor evaluate the

alpha-generating skill of a mutual fund in a family? More specifically, how

does an estimate of skill depend on a fund’s own performance, and how does it

depend on the performance of other funds in the family? Furthermore, how do

the sensitivities of the estimate to fund and family performance change with

fund and family characteristics, including the number of funds in the family?

And, finally, do investors respond to fund and family performance in a manner

that is consistent with optimal learning?

To answer these questions, we develop a continuous-time model in which

a fund’s alpha is driven by a combination of a fund-specific component and a

2See Christoffersen, Musto, and Wermers (2014) for a review of the literature on mutual fund

flows.

Mutual Fund Flows and Cross-Fund Learning within Families 385

common component shared by all funds in the family. We refer to this combi-

nation as composite skill, the fund-specific component as fund skill, and the

common component as family skill. The returns of funds within a family are

subject to correlated idiosyncratic shocks, which are unobservable. Both fund

skill and family skill are unknown constants. A fund’s alpha increases with its

composite skill, and decreases with fund size. Investors estimate funds’ com-

posite skill by observing the returns of all funds in the family, and allocate

wealth across funds, as in Berk and Green (2004).

We derive the sensitivities of the optimal estimate of the composite skill and

fund flows to both fund and family performance, where family performance

for a given fund is defined as the average performance of other funds in its

family.Our model highlights two competing effects of family performance on the

estimated skill and fund flows of a member fund: a positive common-skill effect

and a negative correlated-noise effect. The positive effect arises because family

performance contains information about family skill. The negative effect arises

because family performance is also a signal about unobservable shocks that

affect all funds in the family. The overall spillover effect of family performance

can be either positive or negative, depending on the relative strength of these

two effects. It increases with the weight of family skill, and decreases with

the correlation of noise in fund returns. Its absolute value increases with the

number of funds in the family,and declines over time, as investors become more

certain about the composite skill. The sensitivity to a fund’s own performance

is positive, declines over time, and varies with other fund characteristics in a

direction opposite to that of the cross-sensitivity.

We test our model using a sample of actively managed domestic equity funds

drawn from the CRSP survivor-bias-free mutual fund database, and we find

patterns remarkably consistent with rational cross-fund learning. We measure

the weight of the common component in a fund’s composite skill using the

average manager overlap rate between the fund and the rest of its family, and

measure the correlation of noise between one fund and other member funds

using the average pairwise correlation of idiosyncratic returns. We find that

flows to a member fund respond positively on average to family performance,

suggesting the dominance of the common-skill effect. The sensitivity of fund

flows to family performance is higher when the manager overlap rate is high,

the correlation of idiosyncratic returns is low, and the number of funds in the

family is large. The sensitivity of flows to a fund’s own performance declines

with the manager overlap rate and the number of funds in the family, and

increases with the correlation of idiosyncratic fund returns. Both sensitivities

decline with fund age. These patterns support our model, and suggest that

investors learn rationally from both fund and family performance.

In stark contrast to the positive spillover effect in the full sample, for a

subsample of funds with a below-median family size-adjusted manager over-

lap rate, an above-median family size-adjusted correlation of idiosyncratic re-

turns, and a below-median family size, the response of fund flows to family

performance is significantly negative. This demonstrates the dominance of the

correlated-noise effect in a sizable fraction of funds.