This graph is based on all US equity active open-end mutual funds that existed in any month from Jan 1980 through June 2008, a total of 482,443 fund/month observations mostly of long only funds.  Fund returns are net of automatically deducted fees and average the returns on all share classes that existed that month. The data set excludes index, allocation, mixed-asset, and 529 funds.  Actual alpha reported is the average monthly return over all funds existing that month minus the S&P 500 or Russell 3000 return for that month, summed over the 12 months (Jan, Feb,..., Dec) to obtain the annual alpha. The 2008 alpha is the Jan-Jun alpha times 2. (Source: July 2008 Thompson data base.)

These data raise a number of questions and highlights points on which the debaters disagree:

1. The data shows an upwardly sloping alpha against both indices.  However, the slope is fairly modest against the Russell 3000 and the data points are fairly dispersed.  Can it be said, with statistical significance, that there is an upward trend in alpha?  
2. In the case of the Russell 3000, the trend alpha is negative over the entire time interval. Can some of the increase in the Russell 3000 alpha slope line be attributed to a decline in expenses over the observation period?
3. One of the issues raised over the course of this debate is whether it is correct to measure all domestic equity funds against a large cap market index such as the S&P 500 or whether a broader index that is more representative of the investable universe of all domestic equity funds should be used, such as the Russell 3000.  One might also measure performance against the more commonplace style boxes so frequently used today, but neither Howard nor Loeper advocates that, although Loeper’s first response to Howard analyzed this. Howard argues that, since we are dealing with an overall average across the universe of US equity funds, such comparisons are correct.  Loeper argues that it is erroneous to draw conclusions by comparing all domestic equity funds to just a large cap benchmark. Loeper’s analysis confirmed the negative alpha against the broader Russell 3000, as shown in Howard’s chart above. However, Howard and Loeper disagree that the slope in the trend line against the Russell 3000 is evidence of increasing skill so, this issue remains unresolved.
4. The data do not adjust for two factors highlighted by previous academic research.  First is the dispersion of returns.  When the stock returns are more dispersed, there is more opportunity for fund managers to earn excess returns.  When stock returns are less dispersed, it is harder for funds to demonstrate alpha.  (Statisticians call this adjusting for heteroscedasticity.)  The second issue concerns adjusting for the relative performance of small- and large-cap stocks.  Active funds will look good anytime small-cap stocks outperform their large-cap counterparts and look bad anytime the reverse occurs.   Managers can’t underweight small-cap stocks enough to produce meaningful amounts of money to add to their large cap position even if they want to do so.   But if small caps are hot, it is easy to sell some large-cap names and get the cash to invest in small-caps.   As such, the aggregate alpha of active managers tends to correlate strongly with return differences across size categories. Should the data be adjusted to reflect these factors? Loeper’s first resonse to Howard included size and style, but should it merely be based on size alone?

The question of whether alpha is increasing has been studied widely in the literature.  The broader question is whether it is statistically possible to “prove” either the side of the argument.  If there is a lot of noise in the data, then selective choices of assumptions and applications of statistics can provide very different answers.

We invite Howard, Loeper, and other readers to continue this debate.

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