The McGraw−Hill Companies, 2001

120 PART I Introduction managed portfolios by about 1% and that transaction fees associated with trading reduce returns by an additional .7%. In contrast, the return to the Wilshire index is calculated as though investors can buy or sell the index with reinvested dividends without incurring any expenses.

These considerations suggest that a better benchmark for the performance of actively managed funds is the performance of index funds, rather than the performance of the in- dexes themselves. Vanguards Wilshire 5000 fund was established only recently, and so has a short track record. However, because it is passively managed, its expense ratio is only about 0.25%; moreover because index funds need to engage in very little trading, its turnover rate is about 3% per year, also extremely low. If we reduce the rate of return on the index by about 0.30%, we ought to obtain a good estimate of the rate of return achiev- able by a low-cost indexed portfolio. This procedure reduces the average margin of superi- ority of the index strategy over the average mutual fund from 1.57% to 1.27%, still suggesting that over the past two decades, passively managed (indexed) equity funds would have outperformed the typical actively managed fund.

This result may seem surprising to you. After all, it would not seem unreasonable to ex- pect that professional money managers should be able to outperform a very simple rule such as "hold an indexed portfolio." As it turns out, however, there may be good reasons to expect such a result. We explore them in detail in Chapter 12, where we discuss the efficient market hypothesis.

Of course, one might argue that there are good managers and bad managers, and that the good managers can, in fact, consistently outperform the index. To test this notion, we ex- amine whether managers with good performance in one year are likely to repeat that per- formance in a following year. In other words, is superior performance in any particular year due to luck, and therefore random, or due to skill, and therefore consistent from year to year?

To answer this question, Goetzmann and Ibbotson3 examined the performance of a large sample of equity mutual fund portfolios over the 1976-1985 period. Dividing the funds into two groups based on total investment return for different subperiods, they posed the question: "Do funds with investment returns in the top half of the sample in one two-year period continue to perform well in the subsequent two-year period?"

Panel A of Table 4.4 presents a summary of their results. The table shows the fraction of "winners" (i.e., top-half performers) in the initial period that turn out to be winners or losers in the following two-year period. If performance were purely random from one pe- riod to the next, there would be entries of 50% in each cell of the table, as top- or bottom- half performers would be equally likely to perform in either the top or bottom half of the sample in the following period. On the other hand, if performance were due entirely to skill, with no randomness, we would expect to see entries of 100% on the diagonals and en- tries of 0% on the off-diagonals: Top-half performers would all remain in the top