Rarer Than Rare

A version of this article was published in the July 2013 issue of Morningstar ETFInvestor. Download a complimentary copy here.

Life would be a lot easier (and more interesting) if everyone had a number floating above their heads quantifying something important about them--it could be kindness, trustworthiness, or whatever. Because they don't, we rely on signals that may or may not be correlated to the qualities we care to learn about. Fortunately, personality traits are highly persistent. Five years from now, the odds are good that a kind person will still be kind. Cause and effect is clean and reliable.

Because this type of reasoning is so useful in everyday life, investors can't help but apply it to investing. They mistakenly infer that a manager or asset with good past performance will have good future performance. Of course, anyone who knows anything about investing pays lip service to the notion that they know this isn't true, but their behavior indicates otherwise. Every manager has a performance record, and most investors cannot resist treating it as if it were a number floating above the manager's head indicating his true merit.

Sadly, we will never see that number. Past performance clearly isn't it, because as a whole, managers with the best records don't continue to outperform in a reliable way. A manager's true skill, or alpha, expressed as an annualized return value, is his expected outperformance if he were to manage a portfolio for a very long time. In other words, if a manager's true alpha is 2%, then he will beat the market by 2 percentage points annualized over a long enough horizon. This number exists only in the mind of God.

But what if we could figure out the distribution of that true number in the population? It would be like taking a small peek behind the veil. While knowing the distribution won't help you pinpoint any particular managers, it could help you figure out how much evidence you need to conclude that any particular manager is truly skilled.

Eugene Fama and Kenneth French took a stab at this question in a 2010 study, "Luck Versus Skill in the Cross-Section of Mutual Fund Returns." In setting up the study, they restricted themselves to equity mutual funds that existed for at least eight months during the period from 1984 to 2006 with at least $5 million (in 2006 dollars) in assets.

Fama and French then set out to answer an interesting question: What would that sample of funds have looked like if none of their managers had a whit of skill? To do this, they stripped out the above-benchmark return of each fund. Of course, doing this doesn't really tell you anything by itself. Remember, they were trying to figure out the distribution of true skill, and this can't be found by looking at any particular manager's realized performance, which is the product of a tiny amount of skill and a huge amount of luck.

To generate their own luck, they created a simulation of the sample by randomly selecting the monthly returns of each fund. The simulation was like an alternate universe in which no mutual fund manager is skilled. They repeated the simulation 10,000 times.

Within each simulation, there inevitably were outperformers and stinkers. But no one is actually skilled in them; any over- or underperformance is purely by chance. Fama and French sorted the funds in each simulation by their outperformances. They then averaged the outperformances across every simulation by percentiles. So for the 95th-percentile bucket, they averaged 10,000 excess returns from each simulation's 95th-percentile fund. (I'm grossly simplifying here. They averaged the t-stats of Fama-French or Carhart alphas.)

This allowed Fama and French to look at the probability of outliers if no one was skilled, compared with the number of outlier mutual funds in the real world. If we lived in Bill Bernstein's "Randomovia," where markets are efficient and no one can beat them, then the actual historical distribution of excess returns wouldn't look much different from the distribution generated from 10,000 alternate universes where no one is skilled. They found that mutual funds at the extreme tails of performance appeared more often than predicted by simulations that assumed no skill.

Fama and French, in other words, found that skilled and unskilled managers almost certainly exist.

So what does the distribution of true skill look like? To answer that question, they "injected" different distributions of skill into their simulations. They found that an injected standard deviation of 1.25% annual returns from skill made their simulations look like the historical distribution. A fund one standard deviation above the average is in the top 16%. A fund two standard deviations above the mean is in the top 2%. In other words, if you had a crystal ball that could sort every equity mutual fund manager by true skill level, the top 16% would be skilled enough to generate 1.25% or greater outperformance over the long run, and the top 2% would be able to generate 2.50% outperformance--before fees.

Remember that I'm talking about true skill, not historical outperformance, which is the product of mostly luck over short periods. If you picked managers who are in the top 2% relative to their peers, they are almost certainly not going to earn 2.50% annualized outperformance before fees going forward because many of the top 2% are lucky.

Once fees are taken into account, the evidence of skilled managers becomes even weaker. One interpretation is more skilled managers charge higher fees, extracting more of their outperformance.

A big caveat is Fama and French assume that excess returns arising from exposure to value and momentum stocks are attributable to risk, not skill. Under a more inclusive rubric that doesn't debit a manager's performance for exploiting such strategies, the top 40% of managers show evidence of skill before fees. After fees, the top 10% of managers add value.

I don't think this yardstick is applicable today. Value and momentum strategy index funds are cheap and widely available. The hurdle for true alpha is now higher than it was 20 years ago, when value and momentum weren't widely known.

A mitigating factor to equity managers' dismal collective performance may be closet indexing. According to data from Antti Petajisto, from 1980 to 1995, closet indexers averaged around 5% of equity assets. Closet indexing started taking off during the dot-com bubble and has stayed elevated since. From 1999 to 2009, closet indexers averaged 29% of all equity fund assets, or about 35% of actively managed equity fund assets. Closet indexing obscures the true relationship between skill and luck, especially when looking at after-fee performance. It's reasonable to believe that even skilled managers generate less outperformance on their lower-conviction ideas--perhaps even none. If this is the case, then closet indexing dilutes their ability to outperform.

When managers index half of their portfolios, they effectively double the fees they charge on their active portfolios. According to a study by AQR researchers, Warren Buffett's stock portfolio, estimated from  Berkshire Hathaway's (BRK.A)/(BRK.B) 13F filings, beat the market by about 2.4% annualized from 1991 to 2011. He ran a concentrated portfolio to produce those results. If Buffett indexed half his holdings, maintained proportional weights for his active picks, and charged a 1% fee on the whole pie, his stock portfolio's outperformance would've shrunk to 0.2% (2.4%/2 – 1%)--a statistically and economically insignificant level.

So all hope is not lost for the investor looking for skilled managers. The data, however, suggest that strong past performance is not sufficient to identify one, unless perhaps if his record is exceptionally long. A manager who can be reasonably expected to beat the market after fees is rarer than rare and requires a heck of a lot more information to identify than historical performance. 

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