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August 14, 2006
Is Bill Miller a Monkey?
Lots of people are having fun with portfolio manager Bill Miller's apparent fall from investing grace. As I have written here, and as Barron's gloated on 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 a 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.
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Shouldn't the analysis go deeper than the odds of coin flips? If a manager beats an index, it should matter whether the beat is by 0.1% or by 1 sigma.
I don't know Miller's record over these 15 years. If he beats the index by 1 sigma or more, then it should be significant also.
I'm confused. Isn't 10,000 * 0.003% = 0.3?
So how did you conclude that with 10,000 managers, "we might expect to see 10 Millers" ??
To me, the proof has always been that monkeys are *competitive* with professional fund managers.
I suspect that empirically, there's enough sector and style persistence effects that a low-turnover manager winds up effectively taking fewer coin-flips.
Ah ... "Our turnover rate has been running between 15 and 20 percent a year, implying a holding period longer than 5 years."
All in all, I'd say it's "highly unlikely" according to the very simple model, but that only disproves the combination of (monkeyhood AND very simple model). The combination of (monkeyhood AND somewhat more complex model) is still possible.
Clearly the evidence is irrefutable. Since all fund managers are monkeys, or at best educated orangutans, they should all hang up their hats.
Furthermore, since EMH teaches us that trying to beat the market is useless, everyone should index. All hail blind and dumb trend following. In deference to nihilistic, myopic, navel-gazing academic theory, all those with financial eyes and ears should be blinded and deafened post haste.
Do I sense some jealousy? I'll take 15 of 16 (or will it be 16 of 16) anyday.
Please excuse my juvenile comment, but that smoking monkey pictures is hilarious.
Bill Miller is Dead! Long Live Bill Miller!
I would suggest his fund is fairly priced for a huge rebound. He takes bigger bets and has rather large positions with few holdings. This was bound to happen sooner or later, but like Richie Freeman, there is no question he knows what he is doing. His fund has always been volatile, and is probably misnamed. Active managers can and do beat indexes. Most investors don't even get index returns anyway because they never hold on to anything long enough. I'll give Miller my money over long time horizons, no doubt.
I don't know if he's a monkey but from that picture it looks like he needs a haircut. He might also consider cutting back on his nicotene habit because he's beginning to look like a monkey. likely aided by the adverse effects of smoking.
About five years ago, when I worked at Legg Mason, I postulated that Miller had timed right one major cycle. He owned AOL at the bottom, etc. - when AOL dramatically outperformed the market. Law of large numbers - someone would. I argued that ONLY the next cycle would determine if he were lucky or smart.
Repeatability is the key. Miller went heavy into Cisco and others at the bottom. He went into Amazon early, but stuck to his guns and is up in the position. I'd argue that means he's smart.
This year - he's stuck to several large plays that are down heavily for the year (Amazon, Yahoo, eBay, Sprint-Nextel, United Health, Kodak, etc.) and continued to remain well underweight in energy (the major sector outperformer).
I'd argue that this year is the exception that proves the rule. He's made some bad picks (or stuck to them at a bad time) which proves he's human. But his track record should be attributed to smart stock picking, not luck. He's a good manager with a bad year.
More on the arithmetic of Bill Miller's feat-- http://www.poorandstupid.com/2004_01_18_chronArchive.asp#107445198663644432