Back in the real world, it’s time to look at this question of expertise in more detail. Bill Miller, the manager of the Legg Mason fund has beaten the S&P 500 for 15 years in a row – from 1991 to 2006. This is a spectacular achievement that makes him a superstar fund manager and a darling of the popular business press. All credit to him. But would it be possible to achieve this by luck alone? Time for a few very simple calculations.
Let’s assume there are 8,192 funds in the USA (actually, that’s not far off the truth). Now suppose that the chance of each fund beating the S&P 500 in a given year is exactly 50%, the same as tossing a coin, and that each fund’s performance is independent of all the others. This means about 4,096 funds can be expected to beat the S&P 500 in a single year. About 2,048 of these will beat it again for a second year, then 1,024 for three years in a row, 512 for four years in a row and so on, dividing by two each time... until you get to one fund that’s made it for a whole 13 years. If Bill Miller is the only "survivor”, then his achievement of getting to 15 years already sounds less impressive.
Now, it’s important to remember that one fund out of 8,192 beating the S&P for 13 years is just an average outcome of our original assumptions and that in reality the actual number can fluctuate above and below the average. Finally, if we look more closely at the record of Bill Miller’s fund, we see that in 1994 its returns more or less tied with the S&P 500. So it’s perfectly reasonable to claim that he beat the S&P only 11 years in a row, rather than 15 – a performance well within the limits of pure chance. Sorry, Bill!
The same is true for the many other funds that have outperformed the market for several years in a row. Most of them subsequently revert back to an average or even poor performance. At the same time we never hear about the funds that did worse than the average for 15 consecutive years. Who’d want to advertise results like these?
Professor Burton G. Malkiel of Princeton University, author of the classic book, A Random Walk Down Wall Street, is one of several observers who claim that beating the market is due to chance, rather than skill. In one study, he compared the results of the top 20 equity mutual funds of the 1970s with their own performance in the 1980s. In the 1970s their average returns exceeded the average of all equity funds by a margin of 10.4% to 19% per year. In the next decade, they slumped into mediocrity. They performed worse that the average fund by 11.1% to 11.7% per year. In a second study, he made the same calculations for the 1980s and 1990s. The star 20 funds of the 1980s, whose collective results had outperformed the average of all equity funds by 14.1% to 18% a year, underperformed the average by a margin of 13.7% to 14.9% over the following ten years.
John C. Bogle, the founder and former chairman of the Vanguard Group and crusader against fund managers, carried out a similar, but shorter-term study over the two periods 1996 to 1999 and 1999 to 2002. First he looked at the top ten out of a total of 851 USA equity funds (those with assets of more than $100 million). They were paragons of success and big bonuses between 1996 and 1999. But in the following three years, the former number one dropped to a position of 841. The best performance of all ten of the formerly outstanding funds was a position of 790, out of a total of 851 funds, between 1999 and 2002. It seems fair to conclude that, as the small print so often tells us, past success is no guarantee of future performance. What’s more, it really does look as if the majority of star fund managers just got lucky
Professor Eugene F. Fama of the University of Chicago put it this way: “I’d compare stock pickers to astrologers, but I don’t want to bad-mouth astrologers.”
© Spyros Makridakis, Robin Hogarth and Anil Gaba, 2009