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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 a commodity, the investor should buy funds based on variables that predict return. We thus assume that the investor buys one of the following three portfolios: the ten percent of funds with the lowest past expense ratios, the highest past returns, or the highest past alphas. This results in three additional reference portfolios that represent how well smart investors do.

To gauge how well perverse investors do, we form three portfolios based on selecting the ten percent of index funds with the highest past expenses, lowest returns, and lowest alphas. Finally, we examine the return earned by the ten percent of the net cash flow that goes into the index funds with the worst past performance.

We begin with one-year holding periods. Before examining investor performance, we examine the return from buying funds based on past returns. If an investor buys the top ten percent of funds ranked on past return rather than the bottom ten percent, he earns an extra 92 basis points per year. This is not only statistically significant at the one percent level, it is clearly economically significant. How well do investors do? They do considerably better than spreading their money across all index funds in equal amounts, but four basis points worse than simply investing their money in index funds proportional to their market value. Furthermore, they do 15 basis points per year worse than simply buying the top ten percent of index funds ranked on return in the previous period.

Investors are making decisions that produce returns that are statistically significantly worse than buying based on past returns, or, even more naively, buying funds proportional to their size. Some investors are clearly making bad decisions in choosing index funds. If we examine the return earned by the ten percent of the money that flows into the funds with the lowest past return, we see that these dollars earn on average 53 basis points less per year than investing in the top ten percent of funds. Similar results hold for the three-year case shown in Table 7.

If we examine the results for buying based on past expenses or past alpha, also shown in Table 7, we find very similar results. Investors earn 20 basis points per year less than buying the ten percent of funds ranked lowest on past expenses and 14 basis points per year less than buying the ten percent of funds ranked highest on past alpha. When we examine three-year holding periods, the results are almost identical to the one-year case.

We should mention that in performing the return calculations we compute return as if loads do not exist. Although only a small percentage of index funds have loads, including the impact of loads on returns would make investors seem even more irrational.

The return investors receive on their actual portfolios would be eight basis points lower for a one-year holding period and three basis points lower for a three-year holding period.22 Since none of the top ten percent of fund portfolios has a load, those loads represent an additional loss to investors who do not buy funds based on past performance.

Many investors seem to be making decisions that violate rationality within the classic paradigm of financial economics when they purchase index funds. At the very least, many are ignoring every one of a set of indicators that predict future return. They could be relying in part on other factors, such as taxes or services.

If the portfolios investors hold have lower capital gains than the funds selected by using past data, this might provide justification for investor actions. However, the capital gains earned by the funds investors hold is higher than the capital gains for a portfolio constructed on the basis of past return, alpha, or expenses, and the differences are statistically significant at the one percent level.

The last defense we can think of for holding funds that offer a lower return is that they might provide better services. We do not have a direct measure of services, but two proxies seem appropriate. One of the major services that mutual fund investors want is the ability to switch among different types of mutual funds. Investors might prefer to hold funds that belong to fund families that offer funds of more than one type. We use the number of Morningstar categories offered by a fund family as our measure of the number It is interesting to note that funds that have front end loads almost always have higher expense ratios even when we do not include the loads in computing expense ratios.

of types of funds offered. We find that investors hold index funds with slightly fewer Morningstar categories than portfolios selected on the basis of past return, expenses, or alphas. The differences are significant at the five percent level. Diversification across fund types and the ability to switch money around cannot account for the differences in investors’ choice.

Another variable that might proxy for services is the total amount of dollars under management by the fund’s family. Large families are in a position to provide more services than smaller families. However, this cannot be a defense for investor actions, because the families of the funds held by investors are smaller than the families of funds in the top decile based on any of our three predictive variables.

What, then, can account for so many investors behaving in a manner that is inconsistent with the assumption of rationality in frictionless markets, the classical paradigm of financial economics? We believe that they rely on salesmanship rather than analysis. Although we do not have direct proof of this, we have indirect proof. The portfolios investors hold have higher 12b-1 fees, higher loads, and higher expenses than the best portfolios. Funds use almost all 12b-1 fees and loads and part of the expense ratio to reward salespersons and to market funds. Apparently, this marketing effort has the desired effect.

V. Conclusion In this paper we show that all of the characteristics of an S&P 500 index fund that an investor might care about can be easily forecast. An investor might be concerned with differential return or alpha. Future values of these variables are easily forecast by their past values or expense ratios. Likewise, there is some evidence that a fund’s risk, whether measured by R 2 or deviations of beta from one, can be forecast from prior values.

Finally, differential tax efficiency comes about primarily from differences in capital gains distributions, and these differences can also be forecast by past values.

Given that the characteristics of index funds that an investor should be concerned with can be forecast, one would expect that these characteristics would primarily determine investor cash flows to different index funds. This is not the case. Adding the standard marketing and spillover variables improves the ability to account for cash flows, but there is still a lot that is unexplained. One possible reason for this is that our analysis does not include all of the relevant marketing variables. For example, funds sign agreements with financial advisors and brokers to pay for fund flow. Although some of this is captured by 12b-1 fees, loads, and expenses less management fees, a lot of it is not.

The terms of these agreements are not observable. Thus, financial advisors or brokers who advise clients to purchase funds to improve their own profits could cause much of the flow into index funds. Although one could argue that the investor is simply paying for advice on which funds to buy, the individual supplying the advice is often motivated by a compensation system that is not compatible with the best interests of investors.

Furthermore, this is an inefficient way of compensating for allocation advice.

Finally, we examine the actual return earned by investors on their purchases of index funds and compare this with the return earned by simply purchasing the ten percent of funds with the highest differential return, alpha, or expenses in the prior period.

Investing based on any of the predictors of future performance results in substantial extra return. Furthermore, these rules lead to selections that 1) have zero loads (where actual cash flows sometimes go to funds with loads), 2) are associated with families with a greater number of options (which facilitates diversification within a fund family), 3) are more tax-efficient, and 4) have higher correlation with the index. On any dimension, selecting funds on the basis of past performance leads to owning a superior set of funds.

Instead, investors buy funds with higher marketing costs than the best-performing funds.

S&P 500 index funds are a commodity. The difference in risk across funds is very small, and differences in returns are easily forecast. Thus, the classic paradigm of financial economics would imply that a rational investor should choose based on expected return including tax efficiency. If investors acted in this way, one would expect cash flows to go to the fund or funds that expect to offer the highest return. Yet a large amount of new cash flow goes to the poorest-performing funds. Furthermore, in a frictionless rational market one would expect the low-return funds, some of which have expense ratios over one percent, to disappear. This is not the case. In fact, index funds added to the market since the beginning of our sample period are higher cost, with expense ratios averaging 0.77 (and a maximum over 2 percent) compared to an average of 0.44 percent for the funds in our sample. A higher percentage of the funds that have recently been introduced have loads and 12b-1 fees. Loads on the new funds average 1.48 percent compared to 0.93 percent for our sample, and 12b-1 fees average 0.29 percent per year compared to 0.13 percent. Finally, over our sample period the ten percent of funds with the highest expenses grow at an average annual growth rate of 20.5 percent compared to 11.8 percent for the low-cost funds.

How can we explain the results? Any market consists of a set of informed rational investors and a set of uninformed investors. Markets are made efficient by the arbitrage activities of informed investors. But the only thing an informed investor can do in the market for index funds is buy the good-performing funds—no arbitrage is possible. In such a market all that is needed for inferior funds to exist and grow is a set of uninformed investors and a set of distributors who have an economic incentive to sell inferior products. In a market where arbitrage is not possible, we may be disappointed, but we should not be surprised when inferior products exist and even prosper.

Much of the financial and economic literature assumes that the law of one price holds. As we show in this article, in markets where arbitrage is not available, the law of one price need not hold. It will hold only if all investors are rational.23 Elsewhere, Elton, Gruber, and Rentzler (1989) find that public commodity funds grow and prosper despite a return below the t-bill rate. This is another market where the lack of arbitrage allows inferior investments to exist and prosper.

References Barber, B. and T. Odean, 2000. Trading is hazardous to your wealth: The common stock investment performance of individual investors. Journal of Finance 55, 773-805.

Bergstresser, D. and J. Poterba, 2002. Do after-tax returns affect mutual fund inflows?

Journal of Financial Economics 63, 381-414.

Blume, M. and I. Friend, 1975. The asset structure of individual portfolios and some implications for utility functions. Journal of Finance 30, 585-603.

Brown, S., W. Goetzmann, R. Ibbotson, and S. Ross, 1992. Survivorship bias in performance studies. Review of Financial Studies 4, 553-580.

Carhart, M., 1997. On persistence in mutual fund performance. Journal of Finance 52, 57-82.

Chevalier, J. and G. Ellison, 1997. Risk taking by mutual funds as a response to incentives. Journal of Political Economy 105, 1167-1200.

Cohen, R., P. Gompers, and T. Vuolteenaho, 2001. Who underreacts to cash-flow news?

Evidence from trading between individuals and instititutions. Forthcoming, Journal of Financial Economics.

DelGuercio, D. and P. Tkac, 2001. Star power: The effect of Morningstar ratings on mutual fund flows. Working Paper, Federal Reserve Bank of Atlanta.

Elton, E., M. Gruber, and C. Blake, 1996a. Survivorship bias and mutual fund performance. Review of Financial Studies 9, 1097-1120.

Elton, E., M. Gruber, and C. Blake, 1996b, The persistence of risk-adjusted mutual fund performance. Journal of Business 69, 133-157.

Elton, E., M. Gruber, and J. Rentzler, 1989. New public offerings, information, and investor rationality: The case of publicly offered commodity funds. Journal of Business 62, 1-15.

Ferris, S., R. Haugen, and A. Makhija, 1998. Predicting contemporary volume with historic volume at differential price levels: Evidence supporting the disposition effect.

Journal of Finance 43, 677-697.

Froot, K. and E. Dabora, 1999. How are stock prices affected by the location of trade?

Journal of Financial Economics 53, 189-216.

Green, R. and K. Rydquist, 1997. The valuation of nonsystematic risks and the pricing of Swedish lottery bonds. Review of Financial Studies 10, 447-480.

Grinblatt, M., and M. Keloharju, 2001. What makes investors trade? Journal of Finance 56, 589-616.

Gruber, M., 1996. Another puzzle: The growth in actively managed mutual funds.

Journal of Finance 51, 783-810.

Hirshleifer, D., J. Myers, L. Myers, and S. Teoh, 2001. Do individual investors drive post-earnings announcement drift? Working Paper, The Ohio State University.

Huberman, G., 2001. Familiarity breeds investment. Review of Financial Studies 14, 659Jain, P. and J. Wu, 2000. Truth in mutual fund advertising: Evidence on future performance and fund flows. Journal of Finance 55, 937-958.

Khorana, A. and H. Servaes, 1999. The determinants of mutual fund starts. Review of Financial Studies 12, 1043-1074.

Longstaff, F., P. Santa-Clara, and E. Schwartz, 2001. Throwing away a billion dollars:

The cost of suboptimal exercise strategies in the swaptions market. Journal of Financial Economics 62, 39-66.

Odean, T., 1998. Are investors reluctant to realize their losses? Journal of Finance 53, 1775-1798.

Rietz, T., 1998. Enforcing arbitrage restrictions in experimental asset markets. Working Paper, University of Iowa.

Rosenthal, L. and C. Young, 1990. The seemingly anomalous price behavior of Royal Dutch/Shell and Unilever N.V./PLC. Journal of Financial Economics 26, 123-141.

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