A related quote from Nassim Taleb that I posted on Twitter this morning: “Recall that the survivorship bias depends on the size of the initial population. The information that a person derived some profits in the past, just by itself, is neither meaningful nor relevant. We need to know the size of the population from which he came. In other words, without knowing how many managers out there have tried and failed, we will not be able to assess the validity of the track record.”
In “The Drunkard’s Walk”, Caltech physicist Leonard Mlodinow’s book about how people misunderstand the amount of randomness in their lives, there’s a short but fascinating passage discussing Bill Miller’s 15-year streak, beginning in 1991, of beating the S&P 500.
Mlodinow’s book is what first came to mind when we heard the news last week that Miller was stepping down from the Legg Mason Value Trust fund, which he’d managed for thirty years. In the five years since the streak ended, Miller’s fund lost 9 per cent annually and ranked dead last out of the 840 funds in its category, according to Lipper.
Predictably, most of the commentary we’ve seen has focussed on his spectacular crash after his equally spectacular run. The obvious reason most people considered the streak so extraordinary — and Miller to be such an impressive stock-picker — was that the odds of any single mutual fund generating such a run were so infinitesimally small.
Perhaps luck could account for a few good bets or a couple of good years, the thinking went, but surely it couldn’t account for such extraordinary and sustained outperformance. A newsletter published by Credit Suisse-First Boston in 2003, a few years before the streak ended, calculated the odds of a manager outperforming the market on chance alone for 12 straight years to be one in 2.2 billion.
The statisticians like those from CSFB were considering the odds that a specific fund would outperform for 12 straight years if the fund begins investing at a specific time. But as Mlodinow explained, maybe the better question to ask is actually this: given the number of mutual funds that have existed in the modern era, what are the odds that any of them would have beaten the market over any 15-year period of time on chance alone?