Jay D. Franklin

Is There a Manager Risk Premium?

A risk premium is the return in excess of a reference rate that an investment is expected to provide. At Index Funds Advisors, Inc., we often speak of three different equity-related risk premiums. First, the market risk premium is the expected excess return of the total U.S. stock market over the risk-free rate as represented by 1-month T-bills. Second, the small cap risk premium is the expected excess return of small cap stocks over large cap stocks. Third, the value risk premium is the expected excess return of value stocks over growth stocks. For any diversified equity portfolio, we can estimate its expected return based on its exposure to the risk factors of market, size, and value. The reason we are able to describe these three as risk premiums is due to the fact that an analysis of 83 years of historical returns meets the requirements of a widely used test of statistical significance, the t-test, as demonstrated by Eugene Fama and Ken French.

The t-test was introduced in 1908 by William Sealy Gosset 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 above the benchmark return) is due to luck or skill. The three ingredients that go into the calculation of the t-statistic are the average difference in returns between the fund and the benchmark (alpha), the standard deviation of the difference in returns between the fund  and the benchmark (i.e., the volatility of the alpha), and the number of years or months for the comparison period.

We can illustrate the use of the t-test with an example. 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 2010. From the average alpha and variability of the alpha, we see that we need 269 years of similar returns to reject the explanation of luck in favor of 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 105 years of similar returns to conclude the presence of skill. Well, 105 is certainly better than 269. For the Yacktman Fund vs. the Russell 1000 Value Index, the average alpha was -1.10%, so there is no number of possible years to conclude the existence of skill.

The essential problem experienced by manager-pickers lies in the fact that they focus on alpha alone without considering the variability of the alpha. For example, five consecutive years of beating the S&P 500 by 2% each year is very different than beating the S&P by 12% one year and losing to it by 10% the following year. The latter case is far more easily explained by luck or noise. The question that investors contemplating the use of active managers should ask can be phrased as follows: Is there an additional expected return that will properly compensate me for the additional risk I am taking with these managers?

A study performed by IFA of the ten-year returns of 614 actively managed funds provides a definitive answer: No! In each of the six style categories, the average alpha (after accounting for exposure to the risk factors of market, size, and value) was negative by an amount that is comparable to the average annual expense ratio for actively managed funds. Only 80 funds (13% of the 614) showed positive alpha.

Only one fund (NFJ Allianz Small Cap Value) had a statistically significant positive alpha (t-statistic greater than 2), and when this fund was analyzed over its entire period since inception, the alpha was no longer statistically significant. The chart below shows the excess return of NFJ Allianz Small Cap Value relative to the Russell 2000 Value Index (Morningstar’s designated benchmark). From the average alpha and variability of the alpha, we see that we need 170 years of similar returns to conclude the presence of skill.

These results should give a great deal of pause to would-be manager-pickers who often rely on 3 to 5 years of returns history as a basis for their decisions. We now see that even a 10-year period is woefully inadequate to distinguish luck from skill, and this is aside from the fact that the overall amount of alpha available for capture among all active funds is negative after costs. Returning to our original question of whether there exists a manager risk premium, the answer is arguably yes, but unfortunately it is negative, so the appropriate term might be “dis-premium”. Once again, we come back to the conclusion that those who do engage in manager-picking as a means to the end of beating the market are playing a mug’s game.