Financial Product Differentiation and Fee Competitionin the Mutual Fund Industry1

Shujing LiAXA Rosenberg Group

Email: sli@axarosenberg.comThis Version: March 10, 2005

Comments are welcome.

Abstract: This paper studies how and how much the mutual fund in-dustry increases its fees by differentiating products over the state of nature.To avoid head-to-head competition, mutual fund managers hold differentportfolios which yield distinct returns and become star funds alternativelyin different market situations. This enables mutual funds to obtain stochas-tic monopoly power and on average charge higher fees than otherwise. Toemperically test this idea, this paper develops a structural model — a multi-nomial IV logit model with random characteristics. The model is easier toimplement than the random coefficient (mixed logit) model, but yields own-and cross-price elasticities for financial products that are as sensible. Thepaper estimates that, on average, equity mutual funds increase their profitsby roughly 30% ($2.2 bn) through this novel form of financial product differ-entiation. In terms of social welfare, there exists excess entry in the mutualfund industry assuming free-entry with fixed entry costs.

1I am deeply indebted to John Shoven and Tim Bresnahan for their invaluable adviceand encouragement. In addition, I am grateful to Eric Zitzewitz and Patric Bajari fortheir inspiring comments. I have also benefitted from discussions with Takeshi Amemiya,Darrell Duffie, Ming Huang, Xiaowei Li, Jiaping Qiu, Barr Rosenberg, Tom Mead, KennethReid, and Neng Wang. All errors are my own.

1

1 Introduction

Recently, questions on whether mutual fund fees are too high attract tremen-dous attention in both the academic and popular press2. Given the evidencethat active managers cannot outperform passively managed portfolios in mostasset classes,3 the answers tend to be that fund fees for actively managedportfolios are excessive. Considering that there were more than 13,000 mu-tual funds competing in the market at the end of 2001,4 it is puzzling thatprofits seem robust and that rents were not dissipated despite the enormousnumber of competitors in the industry.

Most of the studies on mutual fund fees focus on whether managers cangenerate higher returns than the index funds in order to justify their muchhigher fees. The results are generally negative or mixed at best. Even ifmutual fund managers do create value, we still need to discuss how muchvalue they pass on to investors. This point can be illustrated by a simpleexample. Suppose that there are only two mutual funds in the market. Ifthe two funds hold identical portfolios, their gross returns will be exactly thesame. Therefore, investors will invest all of their money in the fund charginglower fees. No-arbitrage theory is not much help since it predicts that thetwo funds coexist in the market only as long as they charge the same fees,in which case it is undetermined how much value can be passed on to theinvestors. However, if we consider competition, the standard outcome of theBertrand game will occur. The two funds compete in lowering fees untiltheir fees are equal to their marginal costs. They make zero profits and all ofthe value created by the funds is passed on to the investors. Therefore, thecompetition structure affects how much value the investors can receive fromthe mutual funds. However, few studies have been done to investigate themarket structure of the mutual fund industry, despite its vast and growing

2For example, the popular press articles include: Gordon (1998), “Experts call mutual-fund fees too high and warn of investor dissatisfaction,” The Orange County Register, July2, and Singletary (1999), “Are our funds milking us? Who can tell?” The WashingtonPost, April 4. The academic papers are Carhart (1997) and Rubinstein (2001).

3For example, Jensen (1968), Gruber (1996) and Carhart (1997).4Among them, more than 6,500 held domestic stocks. By the end of 2001, the total

number of stocks listed on the NYSE, AMEX, and Nasdaq combined were about 12,000.Normally, multi-class shares are listed as separate mutual funds. The distinct equityportfolios are around 4,000 at the end of 2001. Interested readers can see chapter 3 forthe studying of the nonlinear pricing mechanism in the mutual fund industry.

2

size.5

I propose a new approach to the mutual fund industry called “productdifferentiation over states of nature.” In this special product differentiationmodel, investors treat equally efficient but imperfectly correlated portfoliosas imperfect substitutes because of limitation of investors’ information orknowledge.6 In this study, investors’ information is limited in the sense thatinvestors do not know mutual fund managers’ talent but believe some man-agers may have; thus they allocate investment according to some imperfectposterior statistics on talent based on recent past performance.7

To illustrate the idea, consider again the duopoly competition example.For simplicity, assume the two fund managers are equally capable. Whenthey hold the same portfolio, as I discussed above, each of them earns zeroprofits. However, if investors believe mutual funds’ past performance is pos-itively correlated with fund managers’ talent and “chase past performance”,the two funds can actually avoid head-to-head competition by holding differ-ent portfolios. Depending on the stochastic outcomes of the two portfolios,one of the two funds will appear to be better than the other in differentmarket situations or different states of nature. Since investors “chase perfor-mance”, the fund that appears to be better in the recent period will attractnew investments. More important, the “better” fund can charge higher feesand earn non-zero profits in its reigning period since investors’ demand forthe fund is relatively inelastic. Therefore, even if the two funds have equalprobability of becoming the better fund, the stochastic market power enjoyed

5At the end of 2001, there were approximately 250 million mutual fund accounts and $7trillion of assets managed by mutual funds; The industry employed half a million people.

6There are two main reasons for the inefficiency of the investors’ statistics. First,it is reasonable to assume that mutual fund managers have an information advantageover investors. Second, investors may not have enough training in investment and choosemutual funds according to some simple rule of thumb. They may be confused about theconcept of the return and the risk-adjusted return, the alpha, or even the one realizationof the return and the expected return.

7Theoretically, Ippolito(1992) shows that as long as poor-quality funds exist, an in-vestment algorithm that allocates money according to the latest performance is a rationalinvestor behavior. Empirically, Roston (1996), Chevalier and Ellison (1997), Sirri and Tu-fano (1998) and others report performance chasing behavior. Carhart (1997), Brown andGoetzmann (1995), Elton, Gruber and Blake (1996), and Grinblatt and Titman (1994)suggest weak performance persistence. Gruber (1996) and Zheng (1999) provide evidencethat the return on new cash flows is better than the average return for all investors in themutual funds. However, this study shows that investors put way to much weight in lastperiod returns relative to expenses.

3

by the winning fund makes it possible that overall, both funds make posi-tive profits. In this sense, the two equally efficient mutual funds horizontallydifferentiate their products over states of nature and become imperfect sub-stitutes. This results of extra profits from product differentiation hold evenwhen fees are charged before the random returns are realized.

Based on the above idea, this essay constructs a structural model to em-pirically analyze financial product differentiation of equity mutual funds andits effects on fee competition. First, it proposes a multinomial IV logit modelthat accommodates stochastic characteristics to estimate the demand systemof mutual funds. I employ the Fama and French (1993) 3-factor model todecompose mutual funds’ gross returns.8 I then investigate how investorsrespond to the different stochastic components of the returns. I find thatinvestors not only chase last period’s risk-adjusted returns, but also respondto the last period’s factor returns (instead of expected factor returns). Thisleaves room for the fund managers to load factor returns differently andhorizontally differentiate themselves. Second, the estimated parameters areused to recover the price-cost margins (PCMs) under Nash-Bertrand com-petition without observing actual cost data. Third, counterfactual PCMsare computed under the assumption that fund managers cannot financiallydifferentiate their products. Finally, by comparing the estimated versus thecounterfactual PCMs, I estimate that, on average, growth-oriented equityfunds improve their annual variable profit levels by about 29% ($2.2 billionin dollar value) through this mechanism of financial product differentiation.

As far as I know, this special product differentiation and its effect on feecompetition has not been identified and analyzed in the literature.9 More-over, the logic and the empirical framework of this essay are not confinedto the mutual fund industry. They can be easily applied to other indus-tries where products display stochastic characteristics. One example is thefashion industry. Since fashion trends are stochastic and unpredictable, in-stead of betting on the same style, different fashion companies differentiatethemselves by specializing in different styles. Another example is the movieindustry. Since movie-goers’ tastes are stochastic, instead of investing in a

8Brown and Goetzman (1997) analyze mutual fund styles using clustering method.They find that within the “growth” and “growth and income” categories there are differentstyles such as “small cap”and “value”.

9Laster, Bennett and Geonum (1999) study the strategic behavior of professional fore-casters. They find that the economists make a range of projection that mimics the trueprobability distribution of the forecast variables although they have identical expectations.

4

portfolio of movies, some movie companies specialize in high-budget moviesthat are characterized by high risks and high profits, while other companiesspecialize in low-budget movies with the opposite characteristics.

This essay also contributes to the behavioral finance literature. Since con-sumer demand can be viewed as an implicit contract to discipline the mutualfund managers, consumer information and knowledge are important in de-termining the market structure of the mutual fund industry. This justifiesthe SEC’s decade-long movement to educate investors and to enhance infor-mation disclosure10. This chapter quantitatively measures how consumer’sknowledge and information can affect the competition structure and regula-tion policy of the mutual fund industry.

The remainder of the chapter is organized as follows. Section II reviewsliterature. Section III constructs the multinomial IV logit model to analyzethe spurious financial product differentiation and its implications. Section IVdescribes the data. Section V estimates the demand parameters. Section VIuses the estimated parameters to compute the profits an equity fund can earnby spurious financial product differentiation. Finally, Section VII concludesthe essay.

2 Literature Review

Several papers (e.g. Golec (1992), Tufano and Sevick (1997) and Deli (2002))discuss the advisory contract in the mutual fund industry from a principle-agent perspective. However, considering the large number of investors andmutual funds, it is very costly to write and enforce any contract.11 Instead, it

10Also on December 30th, 2002, in the settlement agreed upon among ten Wall Streetfirms and regulators, the firms will provide $85m to be spent on educating investors. Seethe Economist, January 4th-10th 2003, pp.59.

11Within the framework of federal securities law, mutual fund organizations are perhapsthe most strictly regulated business entities. The major federal regulatory statues forthis industry are the Investment Company Act of 1940 and the Investment CompanyAmendments Act of 1970. In addition, some new regulatory measures were initiatedrecently to tighten governmental and judiciary controls.

Theoretically speaking, the small shareholders can mobilize a challenge to the unde-sirable actions of management. In practice, however, both academic research and recentstudies called by the Congress and the SEC indicated that small shareholders had littleincentive to challenge a fund manager’s decision because of the free-rider problem. Openended nature of mutual funds makes free-riding problem worse. Furthermore, in caseswhere the small investors did challenge, most cases terminated in settlements and the

5

is almost cost-free to transfer money from one fund to another.12 In essence,open-end funds provide a strong form of the “voting with the feet” mech-anism. It is reasonable to believe that market competition is the most im-portant force for disciplining the fund managers. Previous papers that haveinvestigated market demand as an implicit incentive scheme include Boren-stein and Zimmerman (1988), Berkowitz and Kotowitz (1993) and Chevalierand Ellison (1997). However, this study explicitly models and quantifies howthe mutual fund managers’ behavior can affect the market power of the mu-tual funds and how profitable that behavior can be when there is monopolisticcompetition.

There is increasing interest in studying the financial industry from theindustrial organization point of view. As far as I know, there are two theoret-ical models addressing similar questions. Massa (2000) argues that the brandproliferation in mutual fund industry is the marketing strategy used by themanaging companies to exploit investors’ heterogeneity and the reputationof the top performing fund. The closest paper to this study is Mamayskyand Spiegel (2001). They treat mutual funds as financial market intermedi-aries to take orders from their investors. The large number of mutual fundsare necessary to span the different dynamic trading strategies of investors.The chapter differs from those two papers in that I argue that the fundproliferation is a product differentiation strategy used by fund managers tomaintain higher profit-cost margins. On the empirical side, Khorana andServaes (1997, 2001) study the determinants of mutual fund starts and themarket share at the family-of-funds level. However, Khorana and Servaesbasically treat financial products as normal commodities without modelingtheir special properties. Unlike most of the empirical work studying mu-tual fund industry, this essay develops a structural model instead of reducedform regression model. With a structural model, I can not only demonstratethe mechanism of financial product differentiation, but also do comparativestatic welfare analysis, e.g. I can compare PCMs of the two equilibria withor without financial product differentiation.

plaintiffs were almost never successful. For instance, as of 1987, fifty-five litigation caseswere generated under the 1970 Amendments. Among these fifty-five cases, most weresettled, six were decided for dependants and four were decided for plaintiffs. In general,although the two Acts provided the weapons with which the small investors could fight,they were ineffective in actually helping the investors to solve the problems.

12The costs of transferring money among mutual funds include loads, realized capitalgain taxes and other transaction-related fees.

6

The most general goals of this study are related to the large literature(e.g. Lazear and Rosen (1981), Ehrenberg and Bognanno (1990) and Meyerand Vickers (1997)) that studies the effects of relative performance evaluationschemes. One of the by-products of the financial market is that the marketprovides benchmarks to evaluate the performances of the individual firmsor mutual funds (Jensen and Murphy (1990), Gibbons and Murphy (1990)and Antle and Smith (1986)). This essay provides an empirical frameworkto qualitatively and quantitatively study the effect of relative performanceevaluation schemes when there are a large number of contestants. My workdemonstrates that, as long as the measures of quality are not perfect, themutual fund managers can make the benchmark ineffective by differentiatingfrom each other and can collect more rent from investors despite the factthat there are large number of players and severe competition in the market.

3 The Empirical Model

The timing and nature of the decision process is a three-stage game as fol-lows: At the first stage, mutual funds choose their service characteristics andinvestment strategies; at the second stage, mutual funds decide to set theirfee levels;13 at the third stage, the returns of the mutual funds are realizedand investors invest their money in the best mutual fund in terms of servicesand their perception of fund managers’ investment talent. In this model, Iassume investors do not know mutual fund managers’ talent but believe somemanagers may have. They measure fund managers’ talent by some posteriorstatistics on talent based on recent past.performance.

As with most empirical work studying product differentiation, I am inter-ested in the last two stages of the game. I do not model the determination offund characteristics. Interested readers can see Chapter two for the explicitmodelling of the determination of mutual funds’ portfolios. Instead, I treatmutual funds’ characteristics and investment strategies as exogenously givenwhen mutual funds make their decision on fees.

My general estimation strategy goes in the reverse direction from the de-cision process. I study investors’ demand system first and I am especially

13I assume that mutual funds set annal expense fees before the outcome of mutualfunds’ investments. This is because the change of expense fees must be approved by theshareholders. The existing literature documented that mutual fund fees are not sensitiveto recent performances. See Zitzewitz (2003).

7

interested in how investors respond to the stochastic characteristics of mu-tual funds. Then I discuss the possible opportunities for the fund managersto financially differentiate their products and calculate how much the mutualfunds can improve their profit margins through financial product differenti-ation.

3.1 Mutual Fund Returns

The assumption that returns are linear functions of a set of observable orunobservable factors is an important building block in the finance literature.Assume there are a set of K factor-mimicking portfolios (also known as pas-sive benchmark assets) and J actively managed mutual funds available inthe market. Let εFt , a K × 1 vector, denote the factor’s excess returns overthe riskless rate of interest at time t. Rjt, is the gross excess return of ac-tively managed mutual fund j over the riskless rate of interest. Throughoutthis article, I assume that the excess gross returns of the mutual fund j aregenerated by the multi-factor return-generating process of the following form:

Rjt=α0j + βjεFt+εjt. (1)

βj is a 1×K vector of fixed parameters. Its kth elements, βjk, is mutual fundj’s loading on the returns of factor-mimicking portfolio k. In the closely re-lated style analysis (Sharpe (1992)), the factor loading vector βj, determinesthe “style” of mutual fund j. α0j is manager j’s ability to outperform theK factor-mimicking portfolios. εjt, a random variable, is the idiosyncraticrisk of mutual fund j’s portfolio. The volatility of εjt, σ2

εj, measures how

consistently fund manager j outperforms or under-performs the K factor-mimicking portfolios. In this study, I assume α0j and σ2

εjare exogenously

endowed to the fund manager j. The K-factor model is consistent with amodel of market equilibrium with K-risk factors. Alternately, it may be in-terpreted as a performance attribution model, in which the coefficients andpremiums on the factor-mimicking portfolios indicate the proportion of meanreturn attributable to the K elementary passive strategies available in themarket.

8

3.2 A Discrete-Choice Framework to Model a DemandSystem

There are four reasons frequently cited14 for the appeal of mutual funds: cus-tomer services, low transaction costs, diversification and professional man-agement (security selection). When investors are faced with the decision ofchoosing a mutual fund, they need to choose among a large number of closelyrelated products that vary according to the aforementioned attributes. Tocircumvent the dimensionality problem, I employ a discrete-choice frameworkto model the demand system.

3.2.1 Investors’ Subjective Utility Function

Investor i’s subjective utility function of fund j = 0, ..., J at time t =1, 2, ..., T , is:

uijt = Xjtb + Indexjt(ϕ, Rt−1j ) + ξjt + εijt, (2)

where Xjt is an L-dimensional vector of observable characteristics of fundj which are related to mutual fund j’s service and reputation; b is an L-dimensional vector of individual-specific taste parameters on those servicecharacteristics. ξjt is a scalar, which denotes the quality attribute of fundj that is observable to investors but unobservable to econometrician; andεijt is a mean-zero stochastic term. Indexjt(ϕ, Rt−1

j ) is a statistics index con-structed by investors to evaluate fund manager j’s investment talent based onfund j’s return history Rt−1

j ; and ϕ are parameters that need to be estimated

in the investors’ index function Indexjt(ϕ, Rt−1j ).

3.2.2 The Index Function

In my model, Indexjt(ϕ, Rt−1j ) has the flexible function form as below. I as-

sume that investors have commonly applied mean-variance utility functionalform. In addtion, I assume that investors’ subjective conditional expectationof mutual fund j’s return at time t is a linear function of mutual fund j’s lastperiod return and investors’ subjective conditional expectation of fund j’sreturn volatility at time t is a linear function of fund j’s last period returnvolatility. Please check Appendix B.1 for discussion of the micro-foundation

14For example, Gruber (1996) and Chordia (1996).

9

of the index function:

Indexjt(ϕ, Rt−1j ) = ϕ0 · α0j +

K∑k=1

ϕk · (εFkt−1βjk)−

1

2ϕK+1 · V ar(Rjt−1) (3)

where ϕk, k ∈ {0, ..., K + 1} are the parameters need to be estimated. Theymeasure how investors respond to different components of mutual fund pastreturns. εFkt−1

is the return of factor k at time t − 1. Mutual fund j’srisk-adjusted return, α0j and its style βjk∈{1,...,K} are obtained from the de-composition of mutual fund last period gross returns Rjt−1 by equation 1.V ar(Rjt−1) is the volatility of mutual fund j’s last period gross return Rjt−1.

One special property of mutual funds is that the performance data arenoisy across mutual funds and over time. This means it is hard for investorsto know fund managers’ talent. However, investors believe that they canevaluate fund managers’ talent according to the above posterior statisticsindex Indexjt(ϕ, Rt−1

j ) based on mutual fund past performance.15

In my model, I need to estimate parameters ϕk∈{0,...,K+1} to test whetherinvestors’ aforementioned performance chasing behavior is efficient. Ac-cording to classic asset pricing theories (Ross (1976) and Fama and French(1996)), α0j is the risk-adjusted return which I assume to be the true levelof fund manager j’s talent in this model. If investors are rational and under-stand asset pricing theories, they should only respond to α0j but not the firstand second moments of fund j’s last period returns. If ∃ϕk∈{1,...,K+1} 6= 0,investors respond to past factor returns and load some noise in their statisticsindex.

3.2.3 The Ex Post Market Share

Since I have no individual investors’ investment data, I need to integrate outthe heterogeneity of the individual investors and obtain the aggregate marketshare equation. Investors are assumed to invest a fixed amount of money inthe fund that gives the highest utility. In the model, investors pick onemutual fund out of a large pool of candidates instead of diversifying amongmutual funds. It is worthwhile to discuss the realism of this assumption.One of the main reasons that investors buy mutual funds is that they holdwell-diversified portfolios. It is reasonable to assume that investors therefore

15Gruber (1996) and Zheng (1999) document that investors chasing past performancecan earn extra returns.

10

hold a single mutual fund. One reason for this is transaction costs. If it iscostly for investors to follow two mutual funds, investors will sacrifice thebenefit of holding both to save the transaction costs. This model can alsobe viewed as an approximation of the true choice model. Empirical evidenceshows that the median investor holds two funds (Barber, Odean and Zheng(2000)) and one of them is more likely to be a bond fund (Alexander et al.(1997)). Since this article studies the demands within one fund category, itis more likely that investors will want to choose the best fund within thecategory.

The set of unobserved stochastic shocks εijt that lead to the choice offund j is defined by,

Ajt(Xjt, Indexjt, ξjt; b, ϕ) = {εijt|uijt ≥ uilt∀l = 0, 1, ..., J}.

Then, mutual fund j’s aggregate market share at time t is:

sjt =

∫Ajt

dP (εijt).

where P (·) is the probability distribution function of the unobserved stochas-tic shocks εijt.

If we assume the stochastic shocks εijt are distributed i.i.d. with a type Iextreme-value distribution, the short-term market share of mutual fund j isequal to,

sjt =exp(Xjtb + Indexjt(ϕ, Rt−1

j ) + ξjt)∑l exp(Xltb + Indexlt(ϕ, Rt−1

l ) + ξlt)(4)

After observing mutual fund j’s market share, service characteristics at timet and mutual fund last period returns, I can apply the method proposed byBerry (1994) to estimate all the parameters in demand function 4.

3.2.4 The Definition of Financial Product Differentiation

The Equivalent Spatial Competition Model In the Appendix A.1, Iderive that ex post market share equation 4 is equivalent to a spatial com-petition model with quadratic “transportation” costs as follows:

sjt =exp(Xjtb + Ψ(αjt, σεjt

)− 12ϕK+1 · (β∗

t−1 − βj)′Vt−1(β

∗t−1 − βj) + ξjt)∑

l exp(Xltb + Ψ(αlt, σεlt)− 1

2ϕK+1 · (β∗

t−1 − βl)′Vt−1(β∗t−1 − βl) + ξlt)

(5)

11

whereβ∗

t−1 = (Vt−1)−1 (εFt−1 ·

ϕ

ϕK+1

), (6)

Ψ(αjt, σεjt) = ϕ0α0j −

1

2ϕK+1σ

2εjt

(7)

ϕ is the parameter vector (ϕ1, ..., ϕK)′. Vt−1 is the co-variance matrix ofthe K factor returns εF during period t − 1. εFt−1 is the K × 1 vector thatdenotes the K factor’s returns at time t − 1. In Appendix A.1, I show thatβ∗

t−1 is the “hot” mutual fund style given last period factor returns εFt−1 . Inother words, given last period factor returns εFt−1 and other things equal,β∗

t−1 is the vector of factor loadings giving investors the highest value ofIndexjt(ϕ, Rt−1

j ).The term Ψ(αjt, σεjt

) measures how well fund manager j can activelymanage fund j’s portfolio. α0j is manager j’s ability to outperform the Kfactor-mimicking portfolios. The volatility of εjt, σ2

εjt, measures how consis-

tently fund manager j outperforms or underperforms the K factor-mimickingportfolios.

It is interesting to compare the above model to the conventional spatialcompetition model. The hot style β∗

t−1 is similar to the concept of the positionof customers. The loading factor vector βj, or the style of fund j, marksmutual fund j′s position in the state space. 1

2ϕK+1(β

∗t−1−βj)

′Vt−1(β∗t−1−βj)

denote the “transaction costs” between fund j’s portfolio and the hot styleβ∗

t−1. From equation 5, we can see that, at time t, the fund with style β equalto β∗

t−1 has the smallest “transaction costs”.16

Since I assume that it is cost-free for fund managers to choose the style βsof their portfolios, all the managers want to choose the hot style. However,ex ante, the hot style β∗ is stochastic and unpredictable. We can see thisfrom equation 6. ex ante, hot style β∗ is a linear function of factor returnsεF whose outcomes are stochastic and changing from time to time. Thus,if financial firms hold different styles, they become the best hot styles indifferent states of nature depending on the outcomes of factor returns.

The Definition of Financial Product Differentiation In the marketshare equation 5, we can see that mutual funds factor loading βs will not

16In this sense, many of the results of spatial competition models, such as Hotelling(1929), and many of the models discussed in Anderson, De Palma, and Thisse (1992) andGoettler and Shachar (2001), are valid here. The intuition behind the models is similar.

12

affect the ex post market share if either investors do not respond to factorreturns, i.e. ϕk∈{1,...,K+1} are equal to zero, or mutual funds’ styles βs equalcross-sectionally. However, if ∃ϕk∈{1,...,K+1} > 0, there are opportunities forfund managers to differentiate their products by holding different factor-loading βs. Through this, mutual funds can become “hot” in different statesdepending on the realization of factor returns. For example, when the marketis going up, the mutual funds having large positive market-portfolio loadingsdo particularly well and attract more money. However, in a down market, themutual fund having less or even negative market-portfolio loadings performbetter and obtain a higher market share. If mutual funds hold different βs,the performance indices Indexjt, j ∈ {0, ..., J}, look much more differentthan fund manager’s real ability difference in αjt, j ∈ {0, ..., J}. I call thisform of product differentiation financial product differentiation overthe states of nature. I would like to emphasize that mutual funds canhorizontally differentiate their products although investors are homogeneous.In this sense, financial product differentiation over states of nature differsfrom the conventional spatial competition model in a very critical way.

In this model, I assume that the choice of style βj is not correlated withmanagers’ real ability αjt. Hence, the financial product differentiation in thedimensions of factor return loadings is spurious. However, even if for someunknown reason it is useful for investors to chase factor returns, the fundmanagers can still horizontally differentiate their products, but the financialproduct differentiation is not spurious any more. Thus, whether investors’factor returns chasing behavior is rational or not is not a critical assumptionand will not affect the main results of this study.

The Expected Market Share With financial product differentiation, themarket share of fund j is stochastic depending on the realization of factorreturns. Thus, ex ante, mutual fund j can only know its expected marketshare. The expected market share of fund j is:

sejt =

∫exp(Xjtb + Ψ(αjt, σεjt

)− 12ϕK+1 · (β∗

t−1 − βj)′Vt−1(β

∗t−1 − βj) + ξjt)∑

l exp(Xltb + Ψ(αlt, σεlt)− 1

2ϕK+1 · (β∗

t−1 − βl)′Vt−1(β∗t−1 − βl) + ξlt)

dF (εF1 , ..., εFK),

where F (εF1 , ..., εFK) is the probability distribution function (pdf) of factor

returns.

13

Price Elasticities I model the demand system of mutual funds by a multi-nomial IV logit model. However, the above model is in essence a mix-logitmodel (BLP (1995), McFadden & Train (2000)). The average own and cross-price elasticities of fund j are:

ηej =

∂sej/s

ej

∂pk/pk

=

{ pj

sej

∫b0sjt(1− sjt)dF (εF1 , ..., εFK

) ifj = k

−pk

sej

∫b0sjtsktdF (εF1 , ..., εFK

) ifj 6= k,

where b0 is the coefficient on fees in investors’ subjective utility funciton.It is interesting to compare the above results to the BLP (1995) model

with random coefficients. As with the random coefficient model, I find themulti-logit model with random characteristics can produce reasonable own-price elasticity and cross-price elasticities. The own-price and cross-priceelasticities will no longer be determined by a single parameter, b0 and marketshare. In each state, the mutual fund will have a different price sensitivity.The mean price sensitivity will be the average of the different price sensi-tivities in every state. On the other hand, in the BLP (1995) model, themean price sensitivity is the average of the different price sensitivities of het-erogenous investors. My model also allows for flexible substitution patterns.The products with similar factor loadings have higher cross-price elasticitiesbecause their market shares are more highly correlated.

The Demand Curves Become Steeper Scharfstein and Stein (1990)and Zwiebel (1995) present models in which optimal performance evaluationgives managers an incentive to “herd.” However, Mamaysky and Spiegel(2001) shows that fund families have incentive to spread out their offeringsin strategy space. Laster, Bennett and Geonum (1999) and Zitzewitz (2002)have similar results when they studied the strategic behaviors of professionalforecasters. One of the important results of this paper is that mutual funddemand curves become steeper if the mutual funds “walk away” from thecompetition and differentiate themselves from each other.

The Effect Coming from a Random Market Share If mutualfunds differentiate themselves from each other, their market shares sjt arestochastic. Let se

j denote the average market share of mutual fund j. Forcomparison, consider a hypothetical case such that the mutual fund sharesare not stochastic, but fixed at their average level, i.e. sjt = sj =se

j for all t.

14

Then, the price elasticities in this case is:

ηjk =

{b0pj(1− se

j) ifj = k−b0pks

ek ifj 6= k

.

|ηejj| = |∂se

jpk

∂pksej| < |ηjj|

Proof: ∣∣ηejj

∣∣ =

∣∣∣∣∂sejpk

∂pksej

∣∣∣∣=

∣∣∣∣β0pj

sj

∫sjt(1− sjt)ddF (εF1 , ..., εFK

)

∣∣∣∣=

∣∣β0pj(1− sej − V ar(se

j)/sej)

∣∣< β0pj(1− se

j)

= |ηjj|

The intuition of the proof is as follows: By holding different βs, mutualfunds become the hot style funds in different states. Thus, different mutualfunds attract can in different market situations. When a mutual fund has alucky year, it enjoys both a higher market share and higher market powersince the demand curve of mutual fund is a highly nolinear function of pastperformance.17 This means that the year with higher market power has ahigher weight. On average, this strategy can cause the demand curves ofmutual funds to become steeper.

Distortion of the Market Share Furthermore, financial product dif-ferentiation also distorts the distribution of the average market shares whichin turn affects the price elasticities. Because of the monopolistic competi-tion, the market shares are nonlinear functions of product attributes in themodel. If the mutual funds hold different portfolios, the market shares will bestochastic. The average of fund j’s market share is affected not only by thelevel βj but also the cross-sectional distribution of β. The further a mutual

17For example, Ippolito (1992), Chevalier and Ellison (1997), and Sirri and Tufano(1998) have documented that the relationship between flow and performance is nonlinear.In this Chapter, I use logit model to estimate the demand function of mutual funds. Thismay provide a micro-foundation for the nonlinearity of the relationship between flow andperformance.

15

fund differs from the average, the more volatile its market share. However, Ido not have a closed form solution on how the cross-sectional distribution ofβ affects the average market share. I will study the distortion of the marketshare empirically.

3.2.5 Supply

Suppose there are F mutual fund families. Each family comprises somesubset, zf , of the j = 1, ..., J mutual funds. I assume mutual fund familieshave full knowledge of investors’ behavior and the characteristics of all themutual funds in the industry. They are risk neutral and set optimal fee levelto maximize their expected profits.

The Mutual Fund’s problem The mutual fund family f ’s profit maxi-mization problem is as follows:

pjMaxΠf = E[∑j∈zf

Nsj(pj)(pj −mcj)− Cf ]

=∑j∈zf

Nsej(pj)(pj −mcj)− Cf ,

where sej(pj) is the expected market share of mutual fund j; N is the size of

the market, and Cf is the fixed cost of production.As most of the literature does, the characteristics are taken as given.

They are determined in the first-stage game. Assuming the existence of apure-strategy Bertrand-Nash equilibrium in prices, the price, pj, satisfies thefirst-order conditions:

sej(p) +

∑j∈zf

(pr −mcr)∂se

r(p)

∂pj

= 0, j = 1, ..., J.

Define ∆ as a J × J matrix and its (j, r) item

∆jr = {.−∂ser(p)

∂pj

, if(r, j) ⊂ zf0,otherwise.

In vector notation, the first order conditions can then be written as

me = p−mc = ∆−1se(p),

where me is a vector of the markups.

16

3.2.6 Implications

The Incentive Effect Assume α0j is the true quality of mutual fund j. Ifinvestors chase performance index Indexjt(R

t−1j ), mutual fund j with higher

α0j is able to capture a higher market share.

∂sej

∂α0j

=

∫ϕ0sjt(1− sjt)dF (εF1 , ..., εFK

) > 0

This provides the incentives for the fund managers to generate a higheralpha.

The Effect on Mutual Fund Profits As we discussed in the previoussection, if ∃ϕik∈{1,...,K+1} > 0, fund managers can differentiate their prod-ucts over states of nature by holding different factor loading βs. This formof product differentiation has two effects: (1) a decrease in the own-priceelasticity (in absolute value) because of stochastic market shares; (2) thedistortion of average market shares. It is interesting to check how those twoeffects impact mutual fund profits.

Let sej , pe

j and mej denote the Nash-equilibrium expected market share,

price and expected markups of fund j if there is spurious financial productdifferentiation. Consider a hypothetical case in which mutual funds hold thesame βs and do not differentiate their products. In this case, the counter-factual Nash-equilibrium market share, price and markups of fund j are s∗j ,p∗j

18 and m∗j , respectively.

Then, the difference in markups between the case with and without spu-rious financial product differentiation is as follows:

mej −m∗

j = (mej −mj) + (mj −m∗

j)

where mj is the markups of the intermediate case in which mutual fundj maintains its market share and price at the level of se

j and pej without

product differentiation. mj −m∗j is the change in the markup due to random

18According to Berry (1994), there exists p∗j∈{0,1,...,J} s.t.

exp(δj + Ψ(αjt, σεjt;ϕ0, ϕK+1))

1 +∑

j exp(δj + Ψ(αjt, σεjt;ϕ0, ϕK+1))

= s∗jforallj = 0, 1, ..., J

17

market share effect. From the results of Proposition 1., we have, mj −m∗j >

0 for every j because the own-price elasticities become steeper due to therandom market share effect. me

j − mj is the markup change due to marketshare distortion. The sign of the second term me

j − mj is ambiguous. Themain task of this paper is to correctly estimate the demand system andthen calculate whether the whole industry’s profit actually improved withthe spurious financial product differentiation documented in this paper.

4 Data

The sample of funds examined are the open-end diversified equity mutualfunds from 1992 until 1998 at the Center for Research in Security Prices(CRSP) Mutual Fund Database. This dataset is free of survivorship bias19.There are several reasons for examining the 1992-1998 period. First, theindustry experienced rapid growth during this period. Second, the CRSPSupplementary Annual Data File provides relatively complete information atthe individual fund level on the mutual fund family and mutual fund expensesduring this period. Furthermore, I supplement the above information withdata on distribution channels and other detailed fund characteristics fromthe Morningstar Principia CDs, which are available from 1992 onwards.

Table 1 provides the descriptive statistics of the general diversified equityfunds, which includes the funds in the aggressive growth, long-term growthand growth and income categories in the mutual fund industry. The fundinvestment strategy is identified by Source Standard and Poor’s Micropal.My sample design is analogous to that of most of the empirical literatureon mutual funds, e.g. Carhart (1997) and Zheng (1999). I omit sectorfunds, international funds, and balanced funds for testing purposes. Suchfunds contain other factors not covered in these studies. However, all themethodology is easy to implement in other categories. One remarkable aspectis the tremendous increase in the number of the funds. There were around779 funds in 1992, while in 1998 there were 2,943 funds. However, the numberof management companies increased only from 444 to 542. Obviously, themanagement companies adopted a multiple products strategy to compete.

In Table 1, I count the multi-class funds as separate funds. Multi-classfunds are funds which have the same manager and hold the same portfolio,but with different fee structures (or classes of shares). There are typically

19See Elton, Gruber and Blake (2001) for the limitation of the CRSP dataset.

18

three classes of funds. Class A fund has high front-load20 but low annualexpense ratio. Class B fund has no front-load but with high annual expenseand high deferred load21. Class B share normally has conversion figure, whichmeans, after several years, the Class B share will change to a Class A share.Class I is for institutional investors. Class I share has neither front-loadnor end-load, and the expense ratio is low. However, the initial purchaserequirement is high (e.g. $5Million). There are other variants. For example,Class C share has relatively lower annual expense and lower deferred loadthan class B share, but without conversion features. This class share is forthe investors who want to stay in a fund less than 5 years. However, themost popular one is the first three types of classes. The regression part ofthis study covers a total of 1,337 diversified equity funds and 6,132 fundyears. If a fund has multi-class shares, I only consider the Class A sharesbecause of the different fee schedules of different classes of funds may generatemisleading results.22

The individual stock and the factor-mimicking portfolio returns that weused to decompose the mutual fund returns were obtained from the CRSPUS Stock and Indices Data database. The market capitalization data ofindividual stocks came from Standard and Poor’s Compustat database.

5 Estimation

5.1 Return Decomposition

I employ the Fama and French (1993) 3-factor model to decompose the per-formance of mutual funds:

rjs = αj0t+βj1tRMRFs+βj2tSMBs+βj3tHMLs+ejs s = 1, 2, ..., 36

where rjs is the gross return on the portfolio of fund j in excess of the one-month T-bill return; The three factor-mimicking portfolios, RMRF , SMB,

20The front load is a one time charge applied at time of purchase. These sale loads havegradually declined from 8.5% in 1960s to an average of 4% to 5% currently.

21The deferred load is also called back-end load or contingent deferred sales charge(CDSC). The deffered load applies when investors leave funds and is commonly leviedagainst the value of the original investment. The fee is contingent in the sense thatit decrease periodically in steps and usually disappear after several year.

22Interested readers please see Li and Shoven (2003) for the multi-class funds problem.

19

and HML are constructed according to the descriptions in Fama and French(1993). RMRF is the difference between the return on the CRSP value-weighted portfolio of all NYSE, Amex and Nasdaq stocks and one-monthT-bill yields. SMB is meant to mimick the returns of the risk factor relatedto size. It is the returns of a zero-investment portfolio that longs the small-size stocks and shorts the big-size stocks. Similarly, HML are returns onthe value-weighted, zero-investment, factor-mimicking portfolios that longsthe high (top 30%) and shorts the low (bottom 30%) book-to-market equitystocks. We can also treat these three portfolios as three passive investmentstrategies available in the market.

Summary statistics of the factor portfolios are reported in Table 2. The3-factor model can explain considerable variation in returns. First, note therelative low mean returns of the SMB, HML zero-investment portfolios. Thismeans for a buy-and-hold investor through period 1992 -1998, the mean con-tribution coming from this two factors are almost zero. Second, the varianceof the SMB, HML zero-investment portfolios are high. This suggests that the3-factor model can explain sizeable time-series variations. Third, the correla-tions between these two factors and between these two factors and the marketproxie are low. The low cross-correlations imply that mulitcollinearity doesnot substantially affect the estimated 3-factor model loadings.

In year t, I run the monthly gross excess return rjs of mutual fund j inthe past three years on RMRF , SMB and HML to obtain the estimatesαj0t and βjkt. The annual average excess gross return can be decomposedinto alpha and factor return loadings based on,

rjt ' αj0t + βj1tRMRF t + βj2tSMBt + βj3tHMLt.

rjt is the annual average return of fund j. RMRF t, SMBt and HML arethe annual factor returns at year t. We can interpret that rjt consists of

four parts. βj1tRMRF t, βj2tSMBt and βj3tHMLt indicate the proportionsof mean return attributable to the three passive strategies available in themarket. Component αj0t measures fund manager j’s ability to beat thebenchmark passive portfolios. Summary statistics of cross-section mutualfund excess returns rjt, and factor return loadings are reported in Table 3.Each year, alphas and the three factor return loadings account for muchcross-sectional variation in the annual mean return on stock portfolios.

Summary statistics of cross-section mutual fund αj0t and βjkt are reportedin Table 4 Panel A. The equal weighted average cross-section market portfolio

20

loading β1 is almost 1 and slightly declines from 1992 to 1998. The equalweighted average cross-section loadings of size factor is greater than zero,but the loadings of the book-to-market equity factor is smaller than zero.This reflects the fact that mutual funds tended to hold small and growth-oriented stocks during this period. However, we find, for all the three factors,the cross-section standard deviations of the factor loadings are large andwell spread out around the mean levels. This means that the yearly cross-section return variation are attributable to different loadings of the passivebenchmark portfolios.

To provide some evidence that mutual fund managers differentiate theirproducts, we compare the cross-section αj0t and βjkt of mutual fund re-turn processes to those simulated mutual funds that choose stocks randomly.First, we obtain the number of equity holdings of each of the mutual funds inour sample in year 1998. Second, we assume that the fund managers choosepublicly traded stock randomly from the stock universe, i.e. throw a dartat the stock list board to make a choice. Then we calculate the αh

j0t and

βhjkt of the hypothetical mutual fund portfolios. I find that the cross-section

distribution of factor loadings of real mutual fund portfolios are much morefat-tailed than those of the hypothetically simulated mutual funds. In Table4 panel B, the F test shows that both the manager’s ability measure α·0t andthe factor loading β·kt of mutual funds are more spread out than those of therandom strategy funds.

5.2 The Logit and The IV Logit Demand Estimation23

5.2.1 Market Share

I estimate the demand functions within three particular investment objec-tives: aggressive growth, long-term growth, and growth and income as iden-tified by Source Standard and Poor’s Micropal. I define the market share atthe objective level for each fund as the total net assets under management bythe fund divided by all assets under management in its objective category.I implicitly assume that investors make investment decisions every year. Inmutual fund industry, tax and load fees are the transaction costs make thisassumption unrealistic. It is interesting to study the effect of transaction

23A full random coefficient model in the framework of BLP(1995) can also be appliedhere.

21

costs on investors’ demand function. However, more specific individual leveldata are needed in order to conduct this experiment.

5.2.2 Outside Good

As with most of the logit model, I define an outside “good” to invert thesystem of equations. If investors decide not to invest in any actively managedportfolios, but instead allocate all income to the passive portfolios (indexfunds) available in one category, we think investors will invest in mutualfund j = 0, the “outside fund.” The indirect utility from investing in thisoutside fund is:

uijt = ξ0t + Index0t(ϕ, Rjt−1) + X0b0 + εi0t.

As with most empirical work using the discrete-choice model, I normalizeξ0t to zero. X0b0 not identified separately from the intercept in equation.Index0t(ϕ, Rjt−1) is the mean performance index of the index funds.

5.2.3 Regression Equation

We define ζjt+1 as,ζjt+1 = ln(sjt+1)− ln(s0t+1)

where sjt+1 is the market share of total net asset of fund j at year t. s0t+1

is the “outside fund” market share. Hence we obtain the regression func-tion of ζjt+1 on price, service characteristics and mutual funds’ temporaryperformance indices at time t,

ζjt+1 = c + b0pj + ( Indexjt − Index0t) + Xjb6 + ξjt,

where,

Indexjt = b1·αj0t+b2·βj1tRMRFt+b3·βj2tSMBt+b4·βj3tHMLt+b5·V arRetjt

and,

Index0t = b1·αj0t+b2·β01tRMRFt+b3·β02tSMBt+b4·β03tHMLt+b5·V arRet0t.

Table 5 summarizes the statistics of variables included in our demandsystem that are not related to the performance indices. The average fund

22

size is $673.3 million. The standard deviation of the fund size is $2656 million.The average sizes of aggressive growth funds are the smallest. The averagesizes of growth and income funds are the biggest. The average gross cashinflow is $95.32 million per fund. The standard deviation is $316.3 million.The mean expense ration is 1.2%. Aggressive growth funds charge the most— 1.4%, and growth and income funds charge the least – 1.1%. The standarddeviation of the expense ration is 0.45%.

We can use the OLS method to estimate the above logit model. However,the OLS estimation can under-estimate the demand elasticities to fees be-cause of the correlation between the unobservable quality term ξjt and pj. Forexample, a mutual fund providing with better services is more likely to chargehigher fees. The possible correlation between price and the unobserved at-tribute will tend to bias the price coefficient upwards. We need to instrumentfor price in order to obtain consistent estimates for price elasticities.

5.2.4 Instruments

The instrumental variables used are basically the demand-side instrumentalvariables discussed in Berry (1994) and BLP (1995). Let zjk denote thekth characteristic of fund j produced by firm f . The first order optimalinstrumental variables associated with zjk are

zjk,∑

r 6=j,r∈zf

zrk,∑

r 6=j,r /∈zf

zrk

where zf is the set of products produced by firm f . For example, in myregression, α is the characteristic measuring fund manager’s investment abil-ity, which is exogenously endowed to fund manager j. Then the α of fund j,the sum of α across the mutual funds in j’s family and the sum of α acrossrival fund family’s mutual funds are the three first order optimal instrumen-tal variables associated with α. Since I include a constant term as one ofthe characteristics, the number of own-family mutual funds become a nat-ural instruments. If we are sure that I characteristics are exogenous, wehave 3I instrumental variables for each regression. The reason that thosevariables can be used as instrumental variables is because they are not cor-related with the unobservable quality variable ξjt but they affect the feespj charged by mutual fund j through competition. Insterested readers can

23

check BLP(1995) for a detailed description of the estimation method.24

In practice, the instruments may have multicollinearity problem. In myregression, I use

∑r 6=j,r∈zf

αj,∑

r 6=j,r∈zfβj1,

∑r 6=j,r∈zf

βj2 and∑

r 6=j,r∈zfβj3

as the instrumental variables for price additional to the fund characteristics.Using these instrumental variables, I run the above logit regression usingtwo-stage least squares. For comparison, we report both the results basedon the simplest logit without instrumenting for the unobservable componentξjt, and IV logit specification for the utility function.

5.3 Results

5.3.1 The Demand System

The estimated results of the demand system are shown in Table 6. The2nd, 4th and 6th numerical columns report the estimates from the OLS logitmodel of the aggressive growth, long-term growth and growth income cate-gories, respectively. I am are most interested in investors’ sensitivity to theprice (fees) and their response to past performance. The price coefficients arenegative and significantly different from zero. The price coefficient of the ag-gressive growth category is lower than those of the other two categories. The3rd, 5th and 7th columns in Table 6 report the estimates from the two-stageleast square estimation. After we instrument for price, the estimated demandbecomes more elastic. Investors do respond to historic performance. Theynot only respond to gross alphas but also to different factor returns. Thecoefficients of the factor terms are positive and significantly different fromzero. I also find that investors do not like funds with higher return volatility.According to “the rule of thumb,” investors should adjust the factor risksand chase only alphas. In this sense, investors chase noise factors when theyinvest. Investors also avoid funds having a high capital gain distribution be-cause of tax considerations. Load funds in general enjoy higher cash inflowscompared to nonload funds, probably because brokers’ solicitations are effec-tive. However, within the load fund category, a higher load deters new cashinflows. Being part of a multishare-class common portfolio hurts the market

24The instrumental viables are not legitimate if they correlated with the unobservablequality terms. However, this problem is not serious in my study. The cross-section disper-sion of β·k is symmetric around mean, there is no evidence that the lower quality fundswill choose larger or smaller beta. Even if the low quality funds are more likely to chooseextreme β·ks, the correlation between β·k and ξjt is still equal to zero.

24

shares of funds. The overall effect of multishare-class is unclear. The 2SLScoefficients of the attributes other than price remain quantitatively similarto the OLS results.

5.3.2 Robust Check

In previous estimation, we define the market share using stock data. Weimplicitly assume that investors make purchase decision every year. Thetransaction costs, such as sales loads and tax consequences, may put somepotential problem on this assumption. For robust check, we define the marketshare as the market share of the gross cash inflow into the fund.25, However,the gross cash inflow data normally are not available.26 We construct a proxyfor the annual gross cash inflow data by adding all the positive monthly netflows over the year27:

GrossInflow =12∑

s=1

max(Newmoneyjs, 0).

The monthly new money or cash flow is defined as the dollar change in totalnet assets (TNA) minus the appreciation in the fund assets and the increasein total assets due to merger (MGTNA),

Newmoneyjs = TNAjs − TNAjs−1 ∗ (1 + Rst)−MGTNAjs.

Then I calculate market share of gross cash inflow at the objective levelfor each fund as the total gross cash inflow into one fund divided by all assets

25There are three reasons for using gross cash inflows instead of total net assets managedby mutual funds: 1) In typical demand systems, purchases are flows of goods. Newflows into the fund, rather than the asset stock of the fund, are closer to this traditionaldefinition. 2) Survey studies report that fund managers are most concerned about thenew money they make. The fund managers compete for floating money in the market.3) Empirical work, such as Sirri and Tufano (1998), documented that the relationship ofthe relative performance and growth is option-like. The market share function in the logitmodel is a good approximation of the relationship between performance and growth.

26Edelen (1999) studies the indirect cost of providing liquidity by using gross cash inflowand outflow data from N-SAR report.

27Since any within-month redemption will cancel out an equal amount of purchasesin that month, the true gross flows are higher than the value we estimated. However,we observe that each year, the absolute amounts of cash inflow and outflow tend to benegatively correlated. Therefore, our estimations of gross cash inflows are reasonablemeasures of the true value.

25

under management in its objective category. The demand system estimationusing flow data are listed in Table 7. The results are qualitatively the same asthe previous one using stock data. Quantitatively, the price elasticity slightlyhigher in the cash using flow data. The perform chasing behavior are alsostronger if we use flow data.

6 The Effect of Spurious Financial Product

Differentiation

Assume I obtained consistent estimates of the parameters in the demand sys-tem at the previous section. I can study how financial product differentiationover the state space affects the demand elasticities and the profit margins ofthe mutual funds.

6.1 Ex Post Price Elasticities

The ex post own-price and cross-price elasticities of fund j can be calculatedby,

ηj(·) =∂sjtpk

∂pksjt

=

{− pj

sjtb0sjt(1− sjt) ifj = k

− pk

sjtb0sjtskt ifj 6= k

.

The estimated individual fund ex post price elasticities are available uponrequest.

6.2 Ex Ante Expected Price Elasticities

For calculating the expected own-price and cross-price elasticities at ex ante,we need to simulate the results. When we decomposed the fund returns, weobtained the factor loadings of fund j at time t. Then we simulated the Tobservations of the K factor returns by the bootstraping method: we draw12 × T monthly return from empirical distribution;28 then we generate Tobservations of the yearly conditional first and second moments of the Kfactor returns. Then, we can calculate the expected price elasticities of fund

28We can also implement the Monte Carlo method.

26

j at t:

ηej (·) =

{−pj

sejβ01/T

∑Tτ=1 sjτ (1− sjτ ) ifj = k

−pk

sejβ01/T

∑Tτ=1 sjτskτ ifj 6= k

.

The estimated individual fund expected price elasticities are available uponrequest.

6.3 Estimated Variable Profit Margins With SpuriousFinancial Product Differentiation

Assuming that a mutual fund maximizes its own profits, the estimated profitmargins are:

me/pej = ( pe −mc)/pe

j = ∆−1se(p)/pej

= 1/ηej (·). (∗)

The individual fund markup estimations with the product differentiation overthe state space are available upon request.

6.4 Estimated Variable Profit Margins Without Spu-rious Financial Differentiation

Suppose mutual fund managers do not financially differentiate their prod-uct, i.e. the factor loadings β·kt are the same cross-sectionally. Let s∗j andm∗

j denote the equilibrium market share and markups of fund j in this case.I have already estimated the parameters in the demand system. However,we need to know the marginal cost information to calculate the new Nashequilibrium. Since I have no data on the marginal cost, we estimate themarginal cost by assuming that Equations (*) give the correct functions forthe mutual fund managers to make their decisions. I calculate the conter-factual marginal cost from Equations (*). After we obtain the conterfactualmarginal cost, we calculate s∗j , and p∗j through following equations:

p∗ = mccont + ∆−1s∗(p∗).

The estimated profit margins without product differentiation over the statespace are,

m∗/p∗j = 1/η∗j

27

The estimated individual fund profit margins without spurious productdifferentiation are available upon request.

6.5 Industry Profit Margin Improvement through Spu-rious Financial Differentiation

The whole industry’s average profit margins with and without spurious fi-nancial product differentiation,

∑Jj=1 sjm

ej/p

ej and s∗jm

∗j/p

∗j respectively, are

listed in Table 7. I find that the aggressive growth category has the highestprofit margin, on average more than 50%. Every year, the total industryprofit margins with spurious product differentiation are higher than with-out it in each category. On average, we find that the mutual fund industryimproved its profits by 29% through the spurious product differentiation in1998. ∑J

j=1 sjmej/p

ej − s∗jm

∗j/p

∗j∑J

j=1 s∗jm∗j/p

∗j

= 29%.

In dollar value, with spurious financial product differentiation, the diver-sified equity funds can maintain a profit of $9.7billion. However, withoutspurious financial product differentiation, the diversified mutual funds canonly maintain a profit of $7.5billion. The mutual fund managers can seek$2.2billion more rent from investors through spuriously differentiating theirproducts.

7 Conclusion

This study shows that one of the key factors for driving brand proliferation inthe mutual fund industry is a special form of spurious financial product dif-ferentiation over the state space, which is caused by investors’ performance-chasing behavior. Through this kind of financial product differentiation, mu-tual funds can become top funds and obtain market power alternatively indifferent market situations to avoid competing head-to-head (state by state).Since investors can tolerate higher fees charged by top funds, on average, mu-tual funds can lower their own price elasticities (absolute value) and maintainhigher profits.

To measure the market power that the mutual funds can obtain throughspurious financial product differentiation, we propose a multinomial IV logit

28

discrete-choice model, which accommodates both stochastic and unobserv-able quality characteristics, to study the demand system of the growth-oriented equity funds. I estimate the parameters of how investors respondto mutual fund fees. In particular, we find that investors not only chaselast period risk-adjusted returns, the alphas, which we treat as the real qual-ity measures of the mutual funds, but also respond to the last period fac-tor returns (instead of expected factor returns), which are not relevant tothe quality of mutual funds’. This leaves room for the fund managers toload factor returns differently and spuriously differentiate their products. Iestimated the brand-level price elasticities under the assumptions, with orwithout the aforementioned spurious financial product differentiation. Thenthe estimated elasticities are used to compute the price-cost margins underNash-Bertrand price competition. I estimate that the average variable profitmargin of growth-oriented equity funds was 42% in 1998. Nonetheless, thecalculated average variable profit margin without spurious financial productdifferentiation was 32%. The mutual fund industry improves its profit levelby about 30% ($2.2 billion in dollar value) through spuriously differentiatingtheir products.

An immediate application of the result of this study is to analyze thevalues of the mutual fund ranking service companies, e.g. the Morningstar,Inc. From investors’ point of view, better informed investment behavior canimprove the competition of mutual funds and lower the industry expenseratio about 25%. From a social welfare standpoint, first, the investor canavoid the welfare loss because of the fund managers’ deviations from theoptimal style to the investors; second, if we assume free-entry and there arefixed costs to start a new fund, there is excess entry in the mutual fundindustry. However, more sensible tests require more detailed mutual fundcost data.

The structural model and method of this paper can be applied to ana-lyze the welfare effect of the regulation policies, such as the risk disclosurerequirements and the SEC’s decade-long investor education program. Allthese analyses rely on estimates of demand and assumptions about pre- andpost- policy equilibrium to predict the effects of such policies. This paperpointed out a special and important dimension to consider when estimatingthe demand system of financial products, whose quality characteristics arehighly stochastic and difficult to measure.

Although we study fee competition in the mutual fund industry instead ofasset-pricing, we provide suggestive evidence that the state prices discussed

29

by most asset-pricing models are also determined by market competitionstructure. Similar to the spatial competition concept, where the mutualfund companies allocate their assets over the state space affects their marketshare and their ability to charge fees. In summary, better understanding thedemand, supply and price competition in the financial industry is importantand much more work needs to be done.

30

Appendix

The following proof shows that the market share equation in this studyis equivalent to a spatial competition model with quadratic “transportation”cost.

The above claim is first proved in the framework of a single factor model.It is then generalized to a multi-factor model.

Single Factor ModelSuppose the return of mutual fund j Rj is generated by the following one

factor model:

Rj = αj + βjεRM+ εj

In addition, suppose the subjective expected utility function of investor iis:

Et(uij) = b0Pj + l = 1L∑

bjXjt + Et(ϕi0α0j + ϕi1(εRMβj) + εj)−

1

2ϕi2V art(Rj) + εijt

= b0Pj + l = 1L∑

bjXjt + ϕi0α0jt −1

2ϕi2σεjt

+

{ϕi1Et(εRM

βj)−1

2ϕi2V art(βjεRM

)

}+ εijt

= Ψi(Pj, Xjt, αjt, σεjt) + uiM(βj) + εijt.

where Ψi(Pj, Xjt, αjt, σεjt) = b0Pj + l = 1

L∑bjXjt + ϕi0α0jt − 1

2ϕi2σεjt

uiMt(βj) = ϕi1Et(εRMβj)− 1

2ϕi2V art(βjεRM

).I can

interpret Ψi(Pj, Xjt, αjt, σεjt) as the quality of mutual funds related to mu-

tual fund service and fund manager’s ability to beat the market. uiMt(βj)measures how mutual fund j′s style.βj fits investor i.

The best matched style for consumer i is,

β∗it =

(ϕi1

ϕi2

)V −1

mt · µmt

where Vmt = V art(εRM) and µmt = Et(εRM

).

31

The utility coming from the best matched style is,

u∗iM = uiM(β∗i

t ) =1

2ϕi2(

ϕi1

ϕi2

V −1mt · µmt)

′Vmt(

ϕi1

ϕi2

V −1mt · µmt)

=1

2ϕi2 · β∗i′

t Vmtβ∗it

So that,

Et(uij) = Et(uij)− u∗iM + u∗

iM

= Ψi(Pj, Xjt, αjt−1, σεjt−1)− 1

2ϕi2(β

∗it − βjt)

′Vmt(β∗it − βjt) + u∗

iM + εijt

For consumer i, the measure of choosing fund j is,

dη(ϕi) =exp

[Ψi(Pj, Xjt, αjt−1, σεjt−1

)− 12ϕi2(β

∗it − βjt)

′Vmt(β∗it − βjt)

]∑j exp

[Ψi(Pj, Xjt, αjt−1, σεjt−1

)− 12ϕi2(β∗i

t − βjt)′Vmt(β∗it − βjt)

]The ex post market share of fund j is,

sj =

∫dη(ϕi)

=

∫exp

[Ψi(Pj, Xjt, αjt−1, σεjt−1

)− 12ϕi2(β

∗it − βjt)

′Vmt(β∗it − βjt)

]∑j exp

[Ψi(Pj, Xjt, αjt−1, σεjt−1

)− 12ϕi2(β∗i

t − βjt)′Vmt(β∗it − βjt)

]dϕi

The expected market share of fund j is,

sej =

∫dη(ϕi)

=

∫exp

[Ψi(Pj, Xjt, αjt−1, σεjt−1

)− 12ϕi2(β

∗it − βjt)

′Vmt(β∗it − βjt)

]∑j exp

[Ψi(Pj, Xjt, αjt−1, σεjt−1

)− 12ϕi2(β∗i

t − βjt)′Vmt(β∗it − βjt)

]dϕidµmtdVmt

Generalize to Multifactor ModelAssume that the excess gross returns of the mutual funds are generated

by the multi-factor return-generating process of the following form:

Rj= α0 + β′jεF+εj.

32

βj, a fixed K×1 vector, is mutual fund j’s loading on the factor returns. α0j

is manager j’s ability to outperform the K factors. εF is the vector of factorreturns.

The Investor i’s subjective expected utility function is:

Et(uij) = Et(uij)− u∗iM + u∗

iM

= Ψi(Pj, Xjt, αjt−1, σεjt−1)− 1

2(β∗i

t − βjt)′V (β∗i

t − βjt) + u∗iM + εijt

whereβi∗

t = (Vt)−1 (

ϕi · εFt

ϕiK+1

).

Thus, we can obtain the expected market share of fund j as follows,

sejt+1 =

∫exp(δjt+1 + ϕi0α0jt − 1

2ϕiK+1σεjt

− 12ϕiK+1(β

i∗t − βjt)

′Vt(βi∗t − βjt))∑

j exp(δjt+1 + ϕi0α0jt − 12ϕiK+1σεjt

− 12ϕiK+1(βi∗

t − βjt)′Vt(βi∗t − βjt))

dP (ϕi)dF (εFkt, Vt).

ReferencesAlexander, G., Jones, J.D. and Nigro, P. (1998), Mutual Fund Share-

holders: Characteristics, Investor knowledge, and sources of information,Financial Services Review 7, 301-316.

Anderson, S., De Palma, A. and Thisse, J. (1992), Discrete Choice Theoryof Product Differentiation.

Barber, B., Odean, T. and Zheng, L. (2000), Out of Sight, Out of Mind:The Effects of Expenses on Mutual Fund Flows, Working Paper.

Bergstresser, D. and Poterba, J. (2000), Do After-Tax Returns AffectMutual Fund Inflows?, Working Paper.

Berry, S., (1994), Estimating Discrete Choice Models of Product Differ-entiation, RAND Journal of Economics, 25, 242-262.

Berry, S., Levinsohn, J. and Pakes, A. (1995), Automobile Prices in Mar-ket Equilibrium, Econometrica, 63.

Chevalier, J. and Ellison, G., 1997, Risk Taking by Mutual Funds asa Response to Incentives, Journal of Political Economy; 105(6), December,pages 1167-1200.

Christoffersen, S. and Musto, D.K.,2000, Demand Curves and The Pricingof Money Management, forthcoming Review of Financial Studies.

33

Deli, D., 2002, Mutual Fund Advisory Contracts: An Empirical Investi-gation. Journal of Finance, Forthcoming.

Edelen, R., 1999, Investor Flows and the Assessed Performance of Open-end Mutual Funds, Journal of Financial Economics, v53, n3.

Ehrenberg, R. and Bognanno, M., 1990, Do Tournaments Have IncentiveEffects?, Journal of Political Economics, Vol. 98, No. 6.

Elton, E., Gruber, M., 1992, Portfolio Analysis with a Nonnormal Multi-Index Return-Generating Process, Review of Quantitative Finance and Ac-counting, Vol 2.

Elton, E., Gruber, M and Blake, C., 1999, Common Factors In Activeand Passive Portfolios, European Finance Review,Vol 3, No 1.

Fama, E., 1996, Multifactor Portfolio Efficiency and Multifactor AssetPricing, Journal of Financial and Quantitative Analysis, pp. 441-453.

Fama, E. and French, K., 1993, Common Risk Factors in the Returns onStocks and Bonds, Journal of Financial Economics, Vol 33, pp. 3-56.

Fama, E. and French, K., 1996, Multifactor Explanations of Asset PricingAnomalies, Journal of Finance, 51, pp. 55-84.

Goettler, R., and Shachar, R., 2001, Spatial Competition in the NetworkTelevision Industry, Vol. 32, No. 4.

Gruber, M.J., 1996, Another Puzzle: The Growth in Actively ManagedMutual Funds, Journal of Finance, Vol. 51, pp. 783-810.

Ippolito, R., 1992, Consumer Reaction to Measures of Poor Quality: Ev-idence From The Mutual Fund Industry, Journal of Law & Economics, Vol.XXXV.

Khorana, A. and Servaes, H., The Determinants of Mutual Fund Starts,Review of Financial Studies 12, 1043-1074.

Khorana, A. and Servaes, H., What Drives Market Share in the MutualFund Industry?, Working Paper, 2001.

Lazear, E. and Rosen, S., 1981, Rank-Order Tournaments as OptimumLabor Contracts, Journal of Political Economy, Vol. 89, No. 5.

Laster, D., Bennett, P. and Geoum, I., 1999, Rational Bias in Marcroe-conomic Forecasts, Quarterly Journal of Economics, Vol. 114, No.1.

Massa, M., 2000, Why So Many Mutual Funds? Mutual Fund Families,Market Segmentation and Financial Performance, Working Paper.

Mamaysky, H. and Spiegel, M., 2002, A Theory of Mutual Funds: Opti-mal Fund Objectives and Industry Organization, Yale ICF Working Paper.

Merton, R., 1973, An Intertemporal Capital Asset Pricing Model, Econo-metrica, 41, pp. 867-887.

34

Meyer, M., and Vickers, J., 1997, Performance Comparisons and DynamicIncentives, Journal of Political Economy, Vol. 105, no. 3.

Nevo, A., 2001, Measuring Market Power in the Ready-To-Eat CerealIndustry, Econometrica, Vol. 69, No.2, pp. 307-342.

Nanda, V., Wang, J. and Zheng, L., 2004, Family Values and the StarPhenomenon, The Review of Financial Studies, 667-698.

Ross, S., 1976, Arbitrage Theory of Capital Asset Pricing, Journal ofEconomic Theory, V13, pp. 341-60.

Rubinstein, M., 2001, Rational Markets: Yes or No? The AffirmativeCase, June, pp.

Sharpe, W., 1992, Asset Allocation: Management Style and PerformanceMeasurement, Journal of Portfolio Management, Vol. 18, No. 2.

Sirri, E. and Tufano, P., 1998, Costly Search and Mutual Fund Flows,Journal of Finance, Vol. 53, pp. 15891622.

Varian, Hal R., 1980, “A Model OF SALES,” American Economic Re-view, Sep., Vol. 70 No.4.

35

Table 1 Statistics of the Growth-Oriented Funds 1992-1998

Sample includes growth-oriented diversified equity funds in the aggressive growth,long-term growth and growth and income categories reported in CRSP Dataset. The multi-class funds count as separate funds. The mutual fund annual net returns are the annualafter expense return and the market return is the annual CRSP (Center for Research inSecurity Prices) value-weight stock index.

Y ear No. of Mutual Fund Market∗ Average No. of Mgmt. No. of No. ofFunds Net Return Return Size ($M) Company. New Fund Dead Fund

1992 779 0.09 0.09 429.6 444 198 411993 996 0.12 0.10 469.9 464 217 431994 1261 −0.02 0.01 405.8 491 256 461995 1582 0.31 0.32 495.8 496 321 751996 1912 0.19 0.20 560.5 512 330 751997 2431 0.23 0.28 604.7 533 519 901998 2943 0.14 0.25 612.1 542 512 130

*The market returns are the returns on the CRSP value-weighted portfolio of allNYSE, Amex and Nasdaq stocks.

36

Table 2: Performance Measurement Model Summary Statistics,January 1992 to December 1998

RMRF is the difference between CRSP (Center for Research in Security Prices) value-weight stock index and the one-month T-bill return. SMB and HML are Fama and French’s(1993) factor-mimicking portfolios for size and book-to-market equity. All the return dataare monthly.

Factor Excess t-stat for Return CorrelationPortfolio Return Std Mean=0 RMRF SMB HML

RMRF 1.11 3.58 2.82 1.00SMB −.17 2.78 −.55 .368 1.00HML .27 2.81 .88 −.534 −.299 1.00

37

Table 3: Cross-Section Excess Return and Factor loadingSummary Statistics, January 1992 to December 1998

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

performance, rjs = αj0t + βj1tRMRF s + βj2tSMBs + βj3tHMLs. RMRF is theaverage difference between CRSP (Center for Research in Security Prices) value-weightstock index and the one-month T-bill return. SMB and HML are the mean of Famaand French’s (1993) factor-mimicking portfolios for size and book-to-market equity. Allthe data are monthly.

Year rjt RMRF t Alpha3t βj1tRMRF t βj2tSMBt βj3tHMLt

1992MeanStd

.00546

.00891.00553−−

−.00015.00513

.00457

.00110.00139.00232

−.00122.004592

1993MeanStd

.00780

.00893.00606−−

.00044

.00477.00607.00146

.00141

.00230−.00094.00319

1994MeanStd

−.00437.00665

−.00320−−

−.00029.00418

−.00312.00080

.00007

.00021.00005.00023

1995MeanStd

.01853

.00921.02152−−

−.00055.00479

.02070

.00461−.00114.00160

.00028

.00076

1996MeanStd

.01131

.00663.01268−−

−.00039.00497

.01164

.00251−.00007.00022

.00009

.00027

1997MeanStd

.01433

.00915.01922−−

−.00138.00600

.01824

.00377−.00048.00078

−.00048.00268

1998MeanStd

.00971

.01740.01685−−

−.00131.00721

.01559

.00358−.00537.007929

.00012

.00524

38

Table 4:Panel A

Cross-Section Alpha and Betas of Mutual Fund Net Returns

I employ the Fama and French (1993) 3-factor model to decompose mutual funds’ netreturns, rjs = αj0t + βj1tRMRFs + βj2tSMBs + βj3tHMLs + ejs, s=1,2,...,36.RMRF is the difference between CRSP (Center for Research in Security Prices) value-weight stock index and the one-month T-bill return. SMB and HML are Fama and French’s(1993) factor-mimicking portfolios for size and book-to-market equity.

Year α3t Stdα3t Meanβ.1t Stdβ.1t Meanβ.2t Stdβ.2t Meanβ.3t Stdβ.3t

1992 -.00015 .0051 1.00 .24 .23 .37 -.07 .281993 .00045 .0048 .99 .24 .25 .41 -.08 .281994 -.00029 .0042 .99 .23 .27 .39 -.07 .311995 -.00055 .0048 .95 .21 .28 .38 -.12 .311996 -.00066 .0051 .93 .18 .24 .42 -.13 .381997 -.0014 .0050 .96 .20 .27 .41 -.10 .35

39

Panel BCross-Section Alpha and Betas of Simulated Mutual Fund Gross

Returns of 1997

The number of portfolio holdings nj of each mutual fund j in year 1997 are obtainedfrom Morningstar Procinpia Plus. The hypothetical portfolios of mutual fund j consist ofnj equally weighted stocks which are randomly picked from the stocks listed in NYSE,Amex and NASDAQ. Then we decompose the gross returns of the hypothetical portfoliosand calculate the alphas and betas of the hypothetical portfolio.

Year 1997 α∗3t Sdα3t Mnβ.1t Sdβ.1t Mnβ.2t Sdβ.2t Mnβ.3t Sdβ.3t

Hypo- Eql Wgt -.0015 .0047 .86 .14 .85 .16 .14 .23thetical Cap Wgt .0001 .0023 .99 .10 .20 .09 .18 .18

Sector .0003 .0050 .96 .20 .27 .41 -.10 .35Real Agg .0011 .0068 .97 .26 .68 .34 -.24 .47

LongTerm -.0001 .0044 .97 .18 .17 .31 -.11 .30Income .0001 .0033 .93 .15 -.02 .20 .06 .19

F − testofσ2·real > σhypo

2.4 2.5 7.8 3.7

* Note: For real mutual funds, Alpha is the gross alpha before fees.

40

Table 5: Descriptive Statistics

Note: Sample limited to the funds that at least have 12 month return data in CRSPdataset. The sample only includes Class A fund if one fund has multi-class shares.

Market Share Aggressive Gth Long-Term Gth Gth & Income TotalMean Std Mean Std Mean Std Mean Std

TotalNetAsset($M) 380.6 1108 714.6 2881 939.7 3391 673.3 2656GrossInflows ($M) 83.28 245.7 96.30 331.4 107.50 359.33 95.32 316.3Expense (%) 1.37 .47 1.21 .42 1.11 .44 1.23 .45Age 7.52 9.21 11.45 13.89 15.27 20.47 11.2 15.1Max load (%) 1.91 2.44 2.29 2.58 2.21 2.57 2.15 2.54Cap Gains (%) .127 1.06 .089 .465 .121 .974 .109 .825Turnover (%) 101.0 143 80.0 75 58.9 57 80.5 98imshare .306 .461 .313 .463 .309 .462 .310 .463iload .494 .500 .527 .499 .536 .499 .519 .500

N 1847 2670 1615 6132

41

Table 6: Mutual Fund Demand System Estimates ( Stock Data)

Market Share Aggressive Growth Long-Term Growth Growth IncomeLogit IV Logit Logit IV Logit Logit IV Logit

(1) (2) (3) (4) (5) (6) (7)

Constant-3.6∗∗∗

(.13)-2.6∗∗∗

(0.42)-2.3∗∗∗

(.16)-1.4∗∗∗

(.43)-5.1∗∗∗

(.15)-4.5∗∗∗

(.33)

Price-77.5∗∗∗

(3.5)-159.3∗∗∗

(34.4)-136.2∗∗∗

(7.9)-213.4∗∗∗

(32.9)-141.5∗∗∗

(10.1)-203.4∗∗∗

(30.3)

Gross αt−160.9∗∗∗

(5.4)61.3∗∗∗

(5.6)166.8∗∗∗

(10.0)158.1∗∗∗

(10.8)89.7∗∗∗

(14.1)86.7∗∗∗

(14.4)

βj1t−1RMt−158.5∗∗∗

(9.5)49.4∗∗∗

(10.6)222.7∗∗∗

(15.3)204.0∗∗∗

(17.4)144.0∗∗∗

(18.0)124.3∗∗∗

(20.0)

βj2t−1SMBt−1107.8∗∗∗

(12.8)107.5∗∗∗

(13.3)283.3∗∗∗

(37.1)285.7∗∗∗

(38.0)212.1∗∗∗

(44.1)133.4∗∗∗

(45.7)

βj3t−1HMLt−17.6(11.7)

15.8(12.6)

-8.6(25.0)

-10.7(25.6)

73.3∗∗∗

(25.8)61.2∗∗

(26.7)

V arRett−1-127.7∗∗∗

(20.2)-98.2∗∗

(24.3)-227.8∗∗∗

(54.0)-357.5∗∗∗

(47.1)-445.0∗∗∗

(61.4)-451.6∗∗∗

(62.4)

imsharet-.36∗∗∗

(.08)-.38∗∗∗

(.09).85∗∗∗

(.11).97∗∗∗

(.12)-.47∗∗∗

(.10)-.51∗∗∗

(.10)

iloadt.27∗∗∗

(.08).44∗∗∗

(0.11).81∗∗∗

(.10)1.0∗∗∗

(.14).58∗

(.10).75∗∗∗

(.13)

log(age)t.75∗∗∗

(.04).72∗∗∗

(.04).90∗∗∗

(.04).83∗∗∗

(.05).62∗∗∗

(.03).58∗∗∗

(.04)

cap gnst−1-6.5∗∗∗

(.62)-6.6∗∗∗

(.64)-.03∗∗∗

(.00)-.03∗∗∗

(.00)-13.1∗∗∗

(1.0)-12.3∗∗∗

(1.1)

turnovert−1.02(.02)

.07∗∗

(.03).20∗∗∗

(.05).23∗∗∗

(.06).07(.07)

.13∗

(.07)

N 1191 1191 1771 1771 1126 1126Adj R2 .43 .38 .47 .45 .49 .47

42

Table 7:

Panel A: Estimated Variable Profit Margins From 1992 to 1998(Stock Data)

Aggressive Growth Long-Term Growth Growth IncomeNo Diff. With Diff. No Diff. With Diff. No Diff. With Diff.

1993 .61 .67 .51 .53 .52 .631994 .61 .67 .50 .79 .51 .681995 .62 .66 .51 .79 .48 .761996 .63 .65 .49 .69 .48 .591997 .59 .62 .47 .59 .47 .581998 .61 .69 .56 .73 .46 .62Year Ave. .61 .66 .50 .69 .49 .64

Panel B: Estimation of the Effect of SPD on Industry ProfitMargins in 1998 (Stock Data)

Year 1998 Without SPD With SPDProfit Margins .53 .66In Dollar Value $12.7billion $15.9billion

43

Table 8: Mutual Fund Demand System Estimates (Flow Data)

Market Share Aggressive Growth Long-Term Growth Growth IncomeLogit IV Logit Logit IV Logit Logit IV Logit

(1) (2) (3) (4) (5) (6) (7)

Constant-5.2∗∗∗

(.24)-4.4∗∗∗

(0.57)-4.2∗∗∗

(.23)-3.2∗∗∗

(.59)-3.9∗∗∗

(.24)-2.8∗∗∗

(.56)

Price-112.6∗∗∗

(14.4)-181.5∗∗∗

(46.4)-183.9∗∗∗

(13.1)-274.2∗∗∗

(51.1)-212.1∗∗∗

(15.6)-330.8∗∗∗

(61.6)

GrossAlphat−1129.2∗∗∗

(8.8)136.2∗∗∗

(10.0)212.5∗∗∗

(18.8)217.2∗∗∗

(12.8)224.5∗∗∗

(22.8)232.5∗∗∗

(22.1)

βj1t−1RMt−194.1∗∗∗

(15.4)95.7∗∗∗

(15.6)210.4∗∗∗

(18.8)217.2∗∗∗

(18.9)251.3∗∗∗

(22.8)229.6∗∗∗

(25.7)

βj2t−1SMBt−1153.4∗∗∗

(21.1)158.0∗∗∗

(22.6)300.2∗∗∗

(36.2)311.1∗∗∗

(38.1)159.4∗∗

(79.3)176.6∗

(80.5)

βj3t−1HMLt−129.1∗∗

(17.6)35.8∗∗∗

(18.4)91.5∗∗∗

(20.7)99.6∗∗∗

(21.5)182.7∗∗∗

(35.7)179.9∗∗∗

(38.3)

V arRett−1-101.1∗∗∗

(17.6)-82.0∗∗

(39.1)-227.8∗∗∗

(54.0)-200.5∗∗∗

(56.6)-225.5∗∗

(92.4)-232.7∗∗∗

(94.1)

imsharet-.28(.15)

-.20(.16)

.12(.13)

.21(.14)

-.22(.14)

-.22(.15)

iloadt.30∗∗∗

(.06).90∗∗∗

(.26).71∗∗∗

(.19)1.20∗∗∗

(.33).61∗

(.20)1.32∗∗∗

(.42)

log(age)t.30∗∗∗

(.05).26∗∗∗

(0.05).05(.05)

-.08(.08)

.09∗

(.04).04(.05)

max loadt-.05(.04)

-.01∗∗

(.05)-.11∗∗∗

(.04)-.18∗∗∗

(.06)-.08∗∗

(.03)-.16∗∗∗

(.06)

cap gnst−1-.06(.05)

-.04(.03)

-.125(.09)

-.14(.09)

-.12∗∗∗

(.05)-.13∗∗∗

(.05)

turnovert−1.05∗

(.04).08∗

(.04).29∗∗∗

(.07).36∗∗∗

(.07).05(.10)

.16(.11)

N 1191 1191 1771 1771 1126 1126Adj R2 .265 .272 .284 .269 .306 .310

44

Table 9:

Panel A: Estimated Variable Profit Margins From 1992 to 1998(Flow Data)

Aggressive Growth Long-Term Growth Growth IncomeNo Diff. With Diff. No Diff. With Diff. No Diff. With Diff.

1992 .4295 .5849 .3329 .4127 .4067 .37671993 .4397 .4626 .2644 .3303 .2972 .34791994 .3315 .3592 .2494 .4814 .2421 .30911995 .3655 .5884 .2433 .3808 .2462 .33551996 .3563 .4434 .2536 .3897 .2898 .30541997 .3681 .5817 .2680 .3354 .2981 .34991998 .3919 .5875 .2702 .3405 .3473 .4022Year Ave. .3832 .5154 .2688 .3816 .3039 .3467

Panel B: Estimation of the Effect of SPD on Industry ProfitMargins in 1998

Year 1998 Without SPD With SPDProfit Margins .32 .42In Dollar Value $7.5billion $9.7billion

45