In a recent paper, Heaton, Polson, and Witte set out to explain why active equity managers tend to underperform a benchmark index. It is commonly accepted that the driving force behind active manager underperformance is high fees, however new research suggests that there may be another culprit. The research concludes that “the much higher cost of active management may be the inherently high chance of underperformance that comes with attempts to select stocks, since stock selection disproportionately increases the chance of underperformance relative to the chance of overperformance.”

This conclusion is based on the empirical observation that the best performing stocks in an index perform much better than the remaining stocks in that index. Worded mathematically, the median return for all possible actively managed portfolios will tend to be lower than the mean return. In plain English, the average performance of an index tends to be attributable to a small number of stocks. While choosing a subset of the total available stocks in an index (as an active fund manager does) leads to the possibility of outperforming the index, it also leads to the possibility of underperforming the index, where the chance of underperforming is greater than the chance of outperforming.

This can be (and is in the paper) explained with a simple mathematical example:

If we have an index consisting of five securities, four of which will return 10% and one of which will return 50% over a given time period, and we suppose that active managers will create portfolios using an equally weighted subset of one or two securities, there will be a set of fifteen possible actively managed portfolios. Ten of the fifteen portfolios will earn a 10% return due to omitting the 50% stock, and five of the fifteen portfolios will earn either a 30% return or a 50% return due to holding the 50% stock, depending on whether it is a one or two security portfolio. In this example, the mean average return of the stocks in the index, and all active fund managers, will be 18% (before fees), while the median will be 10%; two-thirds of the actively managed portfolios will underperform the index due to their omitting the 50% returning security, which is always included in the index.

We have been aware that higher explicit fees are a major factor in active manager underperformance, but the risk of missing top performing stocks due to holding only a subset of the total market may be an even bigger hurdle for active managers to overcome.