# A Summary of "False Discoveries in Mutual Fund Performance: Measuring Luck in Estimating Alphas"

The authors of False Discoveries in Mutual Fund Performance: Measuring Luck in Estimating Alphas1 asked a basic yet fundamentally important question: Given the amount of apparent alpha that we actually observe, how much can be explained by skill (or true alpha) rather than luck? To clarify, if 7,000 active managers were simply throwing darts at the stock pages, we would still see a substantial number that beat their benchmark, yet we would know that skill had nothing to do with it. When a mutual fund manager has a statistically significant excess performance over a risk-appropriate benchmark (e.g., positive alpha with a t-statistic of 2 or more), there are two possible explanations: skill or luck, and it is quite difficult to disentangle the two. The authors define a "false discovery" as a mutual fund that exhibits significant alpha by luck alone.

The technique used to determine the breakdown of the population of active managers is called the “False Discovery Rate” (FDR) approach. Basically, by evaluating the distribution of alpha (or more precisely, the t-statistics of alpha) it allows us to determine the proportion of the managers that have zero true alpha. Once we have this number, determining the proportions with true positive alpha or true negative alpha is facilitated by looking at the tails of the overall distribution and seeing how much of those tails cannot be explained by the zero alpha group. The accuracy of this technique has been verified with Monte Carlo simulations where the population breakdown is known ex ante.

Using a sample of 2,076 actively managed US equity funds between 1975 and 2006, the authors found that total observed alpha is consistent with the following breakdown of the population: 75.4% of the funds have a true alpha of zero after costs and 24.0% have a true alpha that is negative, which leaves only 0.6% with a true positive alpha, a number that the authors consider to be "statistically indistinguishable from zero".2 The chart below summarizes these results:

These numbers tell a dismal story of for the prospects of the stock pickers in general and those who manage mutual funds in particular. On a going forward basis, three out of every four can be expected to add no value, while the remaining one can be expected to actually destroy value, and this does not even account for the additional risk that results from having concentrated positions.

The primary takeaway from this paper is that if the professional mutual fund managers who have substantial informational advantages over other traders cannot demonstrate verifiable skill, then the rest of us should assume that markets are efficient to the degree that stock picking will not result in excess profits, and it carries the cost of subjecting an investor to uncompensated risks.

1Barras, Laurent, Olivier Scaillet, and Russ Wermers, “False Discoveries in Mutual Fund Performance: Measuring Luck in Estimating Alphas”. Journal of Finance, Vol. 65 No. 1, pp. 179-216.

2Hulbert, Mark, “The Prescient Are Few”, New York Times, 7/13/2008.