Lots of people are having fun with portfolio manager Bill Miller's apparent fall from investing grace. As Barron's gloated over the weekend, Mr. Bill, of Legg Mason Value Trust, has beaten the S&P 500 for fifteen years running -- but that record is now in jeopardy.
How bad is it? Well, Miller is down 10% so far this year, and is far behind his usual pace, as well as being behind the S&P 500 index and most of his portfolio manager colleagues. It is to the point that some wiseguys are already saying that Miller has really just been a coin-flipper all along, and that his record was the law of large numbers at work in the worket: To that way of scoffing, if enough monkeys manage enough portfolios you'll get all sorts of strange results, including a Bill Miller.
So, is Miller no better than a coin-flipping monkey? In other words, assuming the odds of beating the S&P 500 index in any given year is 50% -- you either beat it or you don't -- how likely is it that Miller's 15-year streak happened purely by chance?
The math is easy: Assuming data independence (i.e., bad years don't influence managers the following year), then fifteen years of market-beating performance at a 0.5 likelihood per year gives us a probability for Miller's performance of 0.003%. Darn unlikely, in other words.
But that's not enough, of course. We need to know how many portfolio managers were running active money back in 1990 when Miller began his beat-down of the S&P. According to data I found elsewhere, there were almost 700 such funds back then (and there are probably twenty times as many now). Given that number of funds, and given the above-mentioned probability, we would expect around 0.02 fund managers to have turned in a Miller-like performance by now given the cohort size from fifteen years ago.
Trouble is, 0.02 of a portfolio manager isn't a very effective portfolio manager (even if it's cheaper), so we can reasonably say that Mr. Miller's performance is highly unlikely, especially if he is really a coin-flipping monkey. Of course, it's not inconceivable that it happened by chance -- and back at the nine-year mark it was perfectly likely -- but a 15-year streak would still have been unusual.