[BruceZ]

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From another field, I offer an old example I used to use in finance class, I'm sure you could update it. If you pick your stocks at random, you would do better than the market 50% of the time. There were approximately 1,024 (I cheated a little) open-end public mutual funds in the 1980s that invested in stocks. By chance, you would expect 1 to beat the market 10 out of 10 years. None did. 10 should have beaten the market 9 out of 10 years. None did. 45 should have beaten the market 8 out of 10 years, 3 did, and all three managers wrote books about how smart they were.

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One of the reasons that they might not do as well as a randomly chosen portfolio is that the mutual funds have certain constraints on the types of stocks and on the number of stocks they can invest in, and in what ratios. So the completely random portfolio may not be one that they could have chosen. A fair test would compare the performance of each mutual fund to that of a portfolio chosen randomly within the same constraints as the fund. Do you know the results of any study like this?

Also, did all 1024 funds invest exclusively in stocks, or did some invest in bonds too? Equity funds would typically be expected to under perform the s&p.