Lucky or Good or Both?

Sam Arbesman shines some light on the relative impressiveness of the market-beating streak of Bill Miller, who recently stepped down:

Unlike the real world, we found nothing that approached Bill Miller’s streak. In fact, streaks of fifteen years only occurred 30 times out of 10,000 runs, far below a reasonable expectation based on luck. In fact, the next longest streaks in the real world were only eleven years long (these occurred twice). Now this doesn’t sound like much of a difference. But remember, these are streaks. To beat the market year after year isn’t a little bit harder, it’s geometrically harder. This can be seen by looking at how often an eleven-year streak occurred in the null model. While still somewhat unlikely, these occurred in nearly a third of our simulations.

The impressiveness of Bill Miller’s streak is magnified by looking at its timing. Our analysis shows that the streak, begun in the early Nineties, occurred during an unlikely period when compared to the Seventies or early Two Thousands. Surprisingly, despite the market’s good overall performance in the Nineties, it was one of the worst decades for active managers. For example, only about one in ten funds beat the market in 1995 and 1997, demonstrating that a long streak during this time is far from inevitable.

All sorts of interesting work has been done on the expected probability of streaks (in investing, in baseball) and whether or not "hot hands" do in fact exist in activities such as basketball (in general, they don't, as a matter of reflecting performance). But Sam shows that, once in a while, an impressive streak can be pulled off with luck and skill.

Comments

[Andrey Goder]

Wait, his streak is supposed to be more impressive because active managers all sucked? That doesn't seem to make sense. Shouldn't the reference point be an index instead?