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«Edwin J. Elton* Martin J. Gruber* Jeffrey A. Busse* October 2002 Abstract Financial theory is often based on the belief that the actions of rational ...»

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Are Investors Rational?

Choices Among Index Funds

Edwin J. Elton*

Martin J. Gruber*

Jeffrey A. Busse*

October 2002

Abstract

Financial theory is often based on the belief that the actions of rational investors

determine prices, which leads to the elimination of dominated financial

instruments. Recently a series of articles have been published which question the

rationality of investor behavior. Standard and Poor’s 500 index funds represent

one of the simplest vehicles for examining whether investors make rational decisions consistent with the normal paradigm of financial economics. S&P 500 index funds hold virtually the same securities, yet they differ by more than two percent per year in the fees they charge investors and the returns they offer investors. In this paper, we show that the relative returns offered by alternative S&P index funds are easily predictable. We show that the other important aspects of performance, risk and tax efficiency, are also easily predictable. Despite this predictability, the relationship between new cash flows and performance is much weaker than we would expect based on rational behavior. Marketing and spillover account for some, but only a small amount, of the cash flows not accounted for by performance. We show that selecting funds based on low expenses or high past returns leads to a portfolio that outperforms the portfolio of index funds selected by investors. Our results exemplify the fact that, in a market where arbitrage is not possible, dominated products can prosper.

* Elton and Gruber are Nomura Professor of Finance, Stern School of Business, New York University.

Busse is Assistant Professor of Finance, Goizueta Business School, Emory University. We thank LiTing Cheng for research assistance.

The classic paradigm of financial theory assumes that investors operating in frictionless markets make rational decisions. Under this paradigm, rational investors set prices, and their actions lead to the elimination of dominated financial investments. S&P 500 stock index funds represent one of the simplest vehicles for examining investor rationality under the assumption of frictionless markets. This is true because S&P index funds are a commodity that differ from each other principally in price. All of these funds hold the same securities in virtually identical percentages. However, they have substantial differences in fees and differences in return that should be economically significant to investors. For example, the difference in annual return between the best performing and worst performing S&P index fund is 2.09 percent per year. In this paper, we show that these differences in future returns, unlike those for actively managed funds, are predictable with a very high degree of accuracy. In addition, other aspects of performance that might concern investors, such as risk and tax efficiency, are also easily predictable.

We then show that although cash flows are related to performance, the relationship, while statistically significant, is much weaker than we would expect based on rational behavior in friction markets, the classic paradigm of financial economics. We investigate the ability of other influences to explain cash flows and find only modest success. Finally, we examine the actual return earned by investor cash flows into S&P 500 index funds, and we find that naïve rules for selecting index funds significantly outperform returns that investors actually earn. We would expect the investors who buy index funds to be among the most knowledgeable of all investors and to make the allocation among index funds to maximize their economics payoff.1 As we show, this is not the case. Possible explanations are that there are substantial information gathering costs or barriers to the About one seventh of the flows into mutual funds comes from 401K and 403B plans. Retirement plans typically constrain cash flows to go into funds offered by the plan. However, since the plan sponsor has a fiduciary responsibility to select the best performing funds for the plan, these flows should be allocated as rationally as direct investments.

flow of capital, that certain funds provide investors with major benefits beyond returns, or that we as a profession have overestimated the rationality of investors.

There are other research studies that question the classic paradigm of financial economics. There are studies that show that securities that are close substitutes can sometimes sell at different prices (Froot and Dabora (1999) and Rosenthal and Young (1990)). There are also studies that show that the behavior of an individual investor might not fit the classical paradigm. Some investors fail to exercise in the money options and exploit arbitrage opportunities (Longstaff, Santa-Clara, and Schwartz (1999) and Rietz (1998)). Individual investors trade too much, maintain undiversified portfolios, hold losing positions too long, require a risk premium for idiosyncratic risk, and overinvest in their own companies’ stock (Blume and Friend (1975), Ferris, Haugen and Makhija (1998), Odean (1998), Barber and Odean (2000), Grinblatt and Keloharju (2001), Cohen, Gompers, and Vuolteenaho (2001), Green and Rydquist (1997), Hirshleifer, Myers, Myers, and Theoh (2001) and Huberman (2001). This paper continues this line of research using an investment vehicle that is widely held and which exists in an extremely liquid market.





The paper proceeds as follows. Section I describes the date. Section II examines the predictability of performance, risk, and tax efficiency. Section III estimates the relationship between cash flows and performance as well as other fund characteristics.

Section IV compares the actual return investors earn with the return earned by following simple strategies. Section V concludes.

–  –  –

In this section we describe the sample that we use to test hypotheses about the predictability of payoffs and future cash flows.

We take the initial list of index fund names from the January 1997 edition of Morningstar’s Principia Plus. After eliminating any enhanced return index funds, our sample consists of 52 open-end S&P 500 index funds. We track the 52 funds through name changes (31 funds incur 36 name changes) and mergers (three funds) in subsequent editions of Morningstar Principia Plus.2 Since we include in the sample all of the S&P 500 index funds that exist at the beginning of the sample period, the sample does not suffer from survivorship bias of the sort identified in Brown et al. (1992) and Elton, Gruber, and Blake (1996a), which occurs when only funds that exist at the end of the sample period are included.

We use the January 1997-2002 editions of Principia Plus and Principia Pro Plus for fund data from January 1996 through December 2001. The data include monthly returns and annual data consisting of the net asset value, expense ratio, 12b-1 fee, actual management fee, load, capital gains in dollars, dividend income in dollars, and whether the fund is only available to institutional investors. We use the Center for Research in Security Prices (CRSP) Survivorship-free Mutual Funds Database for monthly total net assets. To improve accuracy, we compare monthly returns and annual expense ratios reported by CRSP and Morningstar and use fund prospectuses and data provided by the fund itself to reconcile differences. For each fund we also gather fund family data from Morningstar including number of funds, number of different fund objective categories, total size, and whether the family includes a fund with a five-star Morningstar rating.

We use the S&P 500 return index including dividends as our benchmark. To compute excess returns on the funds and on the S&P 500, we use the CRSP monthly T30RET 30-day t-bill return.

II. Characteristics of Index Funds and Their Predictability All mergers are between index funds. We leave out the disappearing funds in the year of the merger. This could introduce some survivorship bias. To examine this, we use the follow-the-money approach of Elton, What should an investor who is purchasing an index fund care about? First and foremost, the investor should care about the fund return relative to the index. An unsophisticated investor might simply want a fund whose return in the next period is high compared to the index or to other index funds. A more sophisticated investor might wish to adjust any return above or below the index for differences in risk from the index risk.

Second, the investor might be concerned directly with the risk of the fund. How closely does the fund track the index, and is the fund’s risk stationary over time? Finally, the investor might be concerned with the tax efficiency of the fund.

We show that all of the important characteristics of an index fund are highly predictable. We examine the predictability of return, risk, and tax efficiency each in turn.

We use two different time horizons to examine predictability, one year and three years, to see if our conclusions are robust across different potential holding periods for investors.

A. Predictability of Average Index Fund Return The first question investors should examine is whether they can predict the payoff they will receive from holding a fund. The investor who holds an index fund intended to replicate the S&P 500 index has a clear benchmark: the total return on the S&P 500 index.3 How will an investor measure the payoff? Naive investors will be concerned simply with how much the return they receive is above or below the S&P 500 index (i.e., the differential return). A more sophisticated investor will be concerned with defining the payoff as risk-adjusted return.4 This investor will adjust the return for the fund’s beta.

The risk-adjusted return is alpha, defined in:

–  –  –

Gruber, and Blake (1996a) that eliminates survivorship bias. The results are unaffected.

Unlike other work on performance measurement, we need not be concerned with identifying an appropriate benchmark or using a multi-index model.

If deviations of beta from one are random, the investor should be concerned with differential return rather than alpha.

where Ri is the monthly return on index fund i, Rf is the return on a 30-day Treasury bill, Rm is the monthly return on the S&P 500 index, β i is the sensitivity of fund i to the return on the S&P 500 index, and α i is the risk-adjusted return on fund i.

Investors who care about future differential return are likely to examine past differential return to select a fund. If they do not believe that management skill varies across funds, they might also forecast differential return by examining expenses or by examining both past differential return and expenses together. A more sophisticated investor will adjust return for systematic risk and will likely examine past values of alpha to predict future alpha. This investor might also use expenses, or alpha and expenses together, to predict future alpha.

In this section of the paper we examine the relationship between differential return or alpha and a set of variables that might be useful in predicting them. We do so in three stages. First, we examine alpha and differential return to see if their dispersion across funds is sufficiently large to make prediction a worthwhile exercise. Then, we measure the association between both of these measures and past data to see if a statistically significant relationship exists. Finally, we test directly whether ranking funds on the basis of a set of past variables leads to superior or inferior performance in the future. We look at the latter two sets of tests over both one-year and three-year holding periods.

1. Size and Dispersion of Return Variables Table 1 shows that the average differential return across S&P 500 index funds is

-0.485 percent per year with a range of –1.857 percent to 0.232 percent. Alpha averages

-0.410 percent per year with a range of –1.530 percent to 0.228 percent. Clearly, the index funds on average underperform the index by a significant amount, and there are economically significant differences in the performance of alternative funds. Expense ratios average 0.444 percent per year with a range of 0.060 percent to 1.350 percent. The size of expense ratios suggests that expenses may account for a large portion of the differential performance between index funds.

2. Association of Return with Past Variables We next examine the association between return measures and lagged values of several variables that might predict return.5 We start by examining the association over a three-year horizon, and then we examine it for a one-year horizon. For a three-year horizon we estimate the relationship in the cross section using three years to formulate predictors and three years to calculate return measures.

Panel A of Table 2 indicates that differential return has a very high R2 with past expenses (0.768). The relationship is significant at the one percent level. Furthermore, expenses on average lower differential return by the amount of the expenses, since differential return goes down by 0.999 percent for every one percent increase in expenses. If higher expenses motivate management to greater effort that leads to better future performance, we would expect a coefficient much less than one. Past expenses affect future performance very strongly, because past expenses are almost perfect predictors of future expenses. The stability of expenses is demonstrated by noting that the coefficient of determination between past and future expenses is 0.931 with a slope of 0.997.

When we examine the association between past differential return and future differential return, we get even stronger results. Panel A of Table 2 shows that the coefficient of determination increases to 0.845 when we substitute past differential return for past expenses. It appears that investors interested in differential return can choose an Persistence in active mutual fund performance has been studied by Elton, Gruber, and Blake (1996b), Gruber (1996), and Carhart (1997).

index fund simply by looking at the past expense ratio, but can do even better by looking at the past differential return.6 Panel A of Table 2 also shows that when we examine alpha as the dependent variable, the results closely parallel those for differential return. The only difference is that the future alpha is even more strongly associated with the past alpha than future differential return is with its past value.



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