The term “alpha” represents the difference between the return on an investment and the return which could have been achieved in an index with identical risk exposure, quantifying a fund manager’s skill. A recent study by Laurent Barras, Olivier Scaillet, and Russ Wermers investigates the presence of true alpha in the results of 2,076 open-end domestic equity mutual funds for the thirty-two years from January 1975 to December 2006.
The study, “False Discoveries in Mutual Fund Performance: Measuring Luck in Estimated Alphas,” employs the use of t-statistic hypothesis testing and statistical data to compare funds’ relative performance, employing a “False Discovery Test” to avoid errors which commonly plague statistical analysis and mitigate the effects of false positive and negative results. Unlike many previous studies of mutual fund performance, this method allows for distinctions to be made between fund results based on luck and those based on skill.
The conclusions of the study decisively reveal the folly of chasing alpha. Using data which prevents survivorship biases and excludes funds with less than five years of performance history, and taking into account the large effects of active management fees, the study concludes that 99.4% of all fund managers failed to demonstrate true stock-picking ability.
In a July 2008 New York Times article titled, “The Prescient Are Few”, journalist Mark Hulbert digs into the results of the landmark study and its implications as described by Prof. Russ Wermers who headed up the study. “The number of funds that have beaten the market over their entire histories is so small that the False Discovery Rate test can’t eliminate the possibility that the few that did were merely false positives,” says Prof. Wermers--or as Hulbert puts it “just lucky.”
In a study of the Morningstar Direct database, the same conclusions were reached. Virtually no evidence of stock picking skill was found. A multivariable regression analysis of historical returns was conducted to determine whether or not a fund manager has skill, or to put it in academic speak, reliably delivered alpha. The three variables used were the Fama-French three risk factors of market, size and value. This analysis reveals the extent to which the returns can be replicated with a combination of index funds, as well as the value added or subtracted by the manager (i.e., alpha).
One way to test the claim that a manager can beat a market is to see if we have enough years of performance data to be statistically significant. The statistical test called the Student’s t-test was introduced in 1908 by William Sealy Gosset, referred to as the “Student,” while working for the Guinness brewery in Dublin, Ireland to evaluate the quality of the brewery’s ingredients. The t-test can be used to determine if a series of historical returns is reliably superior to a risk-equivalent benchmark. This can determine whether alpha (any return over the benchmark return) is due to luck or skill. A t-stat of 2 or higher indicates that we are at least 95% confident that the manager actually earned a return higher than his benchmark due to skill, with up to a 5% chance that it was due to luck.
In Figure 3-6B-i, the t-test is applied to U.S. equity funds in six different style classifications over a 20-year period. Out of 207 mutual funds that were constructed with at least 90% U.S. equities, only 60 had positive excess returns and only two appeared to have skill (a t-stat of 2). But when the time period was extended back to their inception dates, the t-stat dropped below 2 for one of them, indicating that skill evaporated.
Another way to view this data is to draw a line that separates statistical significance on a Alpha versus Standard Deviation of Alpha Scatter Plot. Funds that fall above the line indicated that there is a 95% chance that their excess returns may be explained by skill.
Bill Miller of Legg Mason Capital Management holds the distinction of being the only manager to have ever beaten the S&P 500 index for fifteen consecutive years (1991 to 2005). Unfortunately, his returns after 2005 fell short of the S&P 500, so those of his investors who put their money in after he became well-known discovered the meaning of disappointment. The chart below shows how the Legg Mason Capital Management Value Trust fared against the Russell 1000 Index (Morningstar’s designated benchmark) on a calendar year basis from inception through 2012. From the average alpha and variability of the alpha, we see that we need 456 years of similar returns to anoint Mr. Miller with having stock picking skill.
Two funds that have recently received attention from the financial media are the Yacktman Fund and the Yacktman Focused Fund, both managed by Donald and Stephen and Yacktman. The chart below shows the excess return of Yacktman Focused relative to the Russell 1000 Value Index (Morningstar’s designated benchmark). From the average alpha and variability of the alpha, we see that we need 122 years of similar returns to conclude the presence of skill. Well, 122 is certainly better than 456.
For the Yacktman Fund vs. the Russell 1000 Value Index, the variability of alpha is so high relative to its average that over 1,000 years of similar returns is needed to conclude the presence of skill.
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