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Too Many Mutual Funds?1

— Financial Product Differentiation Over The State Space

Shujing Li

Department of Economics

Stanford University

Email: ecli@stanford.edu

First Draft, December 2001

This Draft, January 2003

Comments are welcome.

Abstract: This paper identifies in the mutual fund industry a novel form of

product differentiation — financial product differentiation over the state space. On

the one hand, it is a well-documented fact that investors chase past performances

of the mutual funds. On the other hand, the mutual funds’ performances are

determined not only by fund managers’ abilities, but also by stochastic noise

factors. In such a context, to avoid head-to-head competition created by holding

the same portfolio, the mutual fund managers could gain higher profits by holding

different portfolios which yield distinct returns at varying states. In other words,

different funds win and attract cash in different periods and thus obtain market

power alternatively.

To empirically test this idea, this paper rigorously developed a structural

model — a multinomial IV logit model with random characteristics. Similar to

BLP (1995), this model produces meaningful own-price and cross-price elastici-

1. Introduction

At least 13,000 open-end mutual funds were in the market vying for investors’

money by the end of 2001, among which more than 6,500 held domestic stocks.2

This fact alone could prompt great interest from economists of both finance and

industrial organization. First, the traditional finance models, such as CAPM and

multifactor asset pricing models, predict that a few risk factors can span the

market and account for most of the cross-section return variations of financial

assets. In other words, there should exist only a few mutual funds in the market

representing those few factor-mimicking portfolios. Therefore, it is puzzling to

see that mutual funds numbered in the thousands. In the finance literature, few

attempts have been made to explain the puzzle and no explanation is widely

considered convincing so far.

Second, as the mutual fund industry expands, competition becomes a more and

more significant force in disciplining the fund managers and affecting investors’

wealth. Hence, it is increasingly important to study and understand the demand,

supply and market structure of the industry. However, market structure is not a

usual topic of finance. Many finance theories can only predict the relationships of

prices in the equilibrium but are silent on which equilibrium should prevail in the

market. We can illustrate this point through a simple example. One may argue

that the large number of mutual funds are redundant assets in the market, thus

their existence does not violate the no-arbitrage theory. However, no redundant

assets can exist in the market if we consider competition. Suppose there are only

two mutual funds in the market. If the two funds hold the same portfolio, their

gross returns will be exactly the same. Therefore, investors will invest all their

money in the fund charging lower fees. The no-arbitrage theory predicts that the

two mutual funds can coexist in the market as long as they charge the same fees.

However, if we consider competition, the standard outcome of the Bertrand game

will occur: the two mutual funds can only make zero profits — they cannot charge

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Therefore, this paper partially fills the gap by implementing a structural model

to analyze the demand, supply, and market structure of the mutual fund industry.

In particular, it identifies in the mutual fund industry a novel form of product

differentiation — product differentiation over the state space, as a response to the

performance-chasing behavior of investors. As far as I know, this particular kind

of firm behavior has never been studied in the literature. It is different from other

forms of product differentiation, particularly because the quality of the financial

products are highly stochastic and hard to measure.

In the case of the mutual fund industry, the basic idea is as follows. First,

investors’ demands for the portfolio of a particular mutual fund is positively cor-

related with the mutual fund’s last period performance index, which is a function

of the mutual fund’s return history. In practice, this kind of performance-chasing

behavior is well-documented in the literature.4Second, the performance index

of the mutual funds referred to by investors may not be able to measure fund

managers’ qualities perfectly.5As a result, the performance index depends not

only on the mutual fund manager’s ability (in case we want to assume that there

are indeed hot hands), but also on some noise factors.

As a simple example, consider the case of the oligopoly competition. Suppose

there are two equally capable fund managers in the market. If they apply exactly

the same investment strategy, they are in the Bertrand game situation as we

mentioned before: each fund has one half of the market share and earns zero

profit. However, as long as the investors’ performance index loads in some noise

factors, in order to avoid such a head-to-head competition, the two funds can

“walk away” from each other by holding different portfolios. Hence, in different

market situations (states), one fund’s performance becomes better than the other’s

from time to time. Since consumers invest in the mutual fund that does better

in the last period, the two funds alternatively become the cash attracting one.

4Theoretically, Ippolito(1992) shows that as long as poor-quality funds exist, an investment

algorithm that allocates more money to the latest best performer is a rational investor behavior.

Empirically, Roston (1996), Chevalier and Ellison (1997), Sirri and Tufano (1998) and others

report performance chasing behavior. Carhart (1997), Brown and Goetzmann (1995), Elton,

Gruber and Blake (1996), and Grinblatt and Titman (1994) suggest performance persistence.

Gruber (1996) and Zheng (1999) provide evidence that the return on new cash flows is better

than the average return for all investors in the mutual funds.

5There are two main reasons for the inefficiency of the investors’ indices. First, it is reasonable

to assume that mutual fund managers have an information advantage over investors. Second,

investors may not have enough training in investment and choose mutual funds according to

some simple rule of thumb. They may be confused about the concept of the return and the

risk-adjusted return, the alpha, or even the one realization of the return and the expected return.

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In the period when a fund is winning, the fund possesses market power because

investors can tolerate the higher fees charged by the top fund. Although each

fund still has one half of the market share on average, the demands for mutual

funds become relatively inelastic to fees. As a result, the mutual funds can charge

higher fees and maintain non-zero profits although there is severe competition in

the market. The two portfolios do not make any “real” difference to the investors

because they care about the true quality of the mutual funds, which we assume

are equal in this example. We call this special form of product differentiation

spurious financial product differentiation over the state space.6

Based on the above idea, this paper constructs a structural model to empir-

ically analyze the idea and its implications. First, it proposes a multinomial IV

logit model to estimate the demand system of mutual funds, which accommo-

date stochastic and unobserved quality characteristics. Particularly, it employs

the Fama and French (1993) 3-factor model to decompose mutual funds’ gross

returns, based on which it investigates whether and how investors respond to the

different stochastic components. We find that investors not only chase last period

risk-adjusted returns, the alphas, but also respond to the last period factor re-

turns (instead of expected factor returns), which are irrelevant to fund managers’

abilities. This leaves room for the fund managers to load factor returns differently

and spuriously differentiate their products. Second, the estimated parameters are

used to recover the price-cost margins (PCMs) under Nash-Bertrand competition

without observing actual cost data. Third, the counterfactual PCMs are com-

puted under the assumption that fund managers cannot financially differentiate

their products. Finally, by comparing the estimated versus the counterfactual

PCMs, we estimate that, on average, the growth-oriented equity funds improve

their variable profit levels by about 30% ($2.2 billion in dollar value) through

financial product differentiation.

6The logic can be applied beyond the financial product sector to other products which have

stochastic characteristics and highly volatile market share. For example, it does not make any

sense for two supermarkets to be on sales simultaneously if the total demands are constant.