Measuring Chance

Managers of active funds aim to outperform the stock market by picking what they think are the hottest stocks. When these managers succeed in beating the market, it may seem to investors that this is a sure sign of talent. But according to a recent study by Chicago Booth professor Eugene F. Fama and Kenneth R. French of Dartmouth College, it is impossible to tell whether an active fund manager's stellar performance is due to skill or just sheer luck. In fact, Fama and French show that most active fund managers do not do better than would be expected by chance.

In the study, "Luck versus Skill in the Cross-Section of Mutual Fund Returns," Fama and French analyze a portfolio of actively managed US equity mutual funds, where each fund's contribution to the portfolio depends on the value of assets under management. The authors measure the portfolio's alpha—the difference between the portfolio's actual return and expected return—which is typically used to assess an active fund manager's performance. Fama and French estimate that from 1984 to 2006 the aggregate active fund portfolio underperformed by 0.8 percentage points per year.

Managers of active funds charge high fees and expenses to cover the costs of putting together a portfolio they hope will outperform the market. Active funds are considerably more expensive than passive funds, which simply track the performance of a benchmark index such as the overall stock market. Fees and expenses may weigh down returns, but Fama and French showed that, even if each active fund's expense ratio is added back to the calculations, the aggregate portfolio's alpha rises to only 0.1 percentage point per year. Thus, even before fees and expenses, there is no evidence that active fund managers significantly enhance returns.

Although these results suggest that active fund managers on average are unable to earn returns high enough to justify costs, it is possible that there are skillful managers out there who can produce high alphas but that there are also less talented managers with negative alphas. The challenge, however, is in distinguishing skill from luck, because funds can do well or poorly purely by chance.

Accounting for Luck

A common approach in previous studies is to test for persistence in fund returns, that is, whether funds that outperformed or underperformed in a particular year continue to do so in succeeding years. But an important weakness of persistence tests, say Fama and French, is that funds are ranked based on short-term performance. Fama and French take a different tack by analyzing the long histories of individual fund returns. Their objective is to determine if the range of performance of active funds is wider than would be expected by chance.

To obtain a distribution of the performance of active funds, Fama and French estimate the alpha of each fund from 1984 to 2006 using a three-factor model of stock returns that they proposed in a previous collaboration. They then take the ratio of that estimate to its standard error, a measure of precision or reliability—a relatively small standard error leads to a relatively large precision-adjusted estimate of alpha. Hence, a ranking of active funds based on precision-adjusted alphas allows for a more meaningful comparison of funds.

Based on these estimates, the top 10 percent of active fund managers have an implied alpha of about 3.4 percentage points per year over the life of the fund. Fund managers who are in the top two percent produced a remarkable alpha of 6.5 percentage points per year. However impressive, funds can produce extreme values of alpha just by luck, that is, even if the fund's true alpha is actually zero.

To find out whether active managers do better than managers who are strictly lucky, the authors compare the precision-adjusted alpha estimates of actual fund returns to the performance of a cloned population of lucky funds. The cloned funds have the same characteristics as the actual funds except that Fama and French set their true alphas to zero; that is, any excess return can only be due to luck. In this case, funds that generate high alphas owe their success to good luck, while those that perform poorly do so only because of bad luck.

If brilliant stock pickers exist, then the actual funds should produce more high values of precision-adjusted alphas than the cloned population of lucky funds. In other words, these active fund managers are not just lucky, but they also have the skill to earn returns that are high enough to beat the market and cover costs. On the other hand, if the distribution of the alpha estimates of the actual funds shows more extreme negative values than that of the cloned funds, then the weak performance of active fund managers cannot be entirely blamed on bad luck.

When Skill Looks Too Much Like Luck

Fama and French find that poorly performing fund managers did far worse than expected if bad luck was the only factor affecting returns. Even most of the stronger performers did not do better than managers with purely good luck. Indeed, except for the top five percent of fund managers, the precision adjusted alphas for lucky funds beat actual funds 90 percent of the time. Altogether the results suggest that the majority of actively managed funds probably have negative true alphas; that is, managers do not have enough skill to produce excess returns that cover costs.

There is a small fraction of active fund managers—the top three percent—who do about as well as expected if they have just enough skill to cover their costs. This result suggests that there is some evidence of skill among the top fund managers, but it is not likely to be of much benefit to investors.

One can imagine a mix of funds that might generate the results that Fama and French find. The top three percent, for instance, could be comprised of talented managers with positive true alphas and less skillful managers with negative true alphas who are extremely lucky. As a result, an investor who buys a portfolio of funds from the top three percent of active managers can expect an alpha of zero. It would be impossible to pick out the truly skillful managers from this group since their returns are simply not high enough to clearly distinguish them from the lucky bad managers who also land on top.

It seems that an investor would be better off investing in passive funds that are typically much less expensive than active funds. In fact, Fama and French show that the excess return on investing in a portfolio of passive funds is quite close to zero; that is, it comes close to covering costs. Fama and French expect that a portfolio of low cost index funds will perform about as well as a portfolio of the top three percent of active funds and certainly better than the rest of the active fund universe.