A risk premium is the return in excess of a reference rate that an investment is expected to provide. At Index Fund 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 85 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 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 his fund fared against the Russell 1000 Index (Morningstar’s analyst-assigned benchmark) on a calendar year basis from inception. From the average alpha and variability of the alpha, we see that we need an unreasonably large number years of similar returns to reject the explanation of luck in favor 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 twenty-year returns of over 200 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. Less than 10% of the funds analyzed showed positive alpha of 1% or more.

The benchmarking methodology used in this analysis was based on Nobel Laureate Eugene Fama and Kenneth French's Three-Factor regression on monthly returns. Only two funds had a statistically significant positive alpha (t-statistic greater than 2). When we performed a second type of tests on these funds (Franklin Flex Cap Growth and Mairs & PowerGrowth) comparing their annual returns to their Morningstar analyst-assigned benchmarks, they no longer showed significant alpha.

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.

Here is a calculator to determine the t-stat. Don't trust an alpha or average return without one.

The Figure below shows the formula to calculate the number of years needed for a t-stat of 2. We first determine the excess return over a benchmark (the alpha) then determine the regularity of the excess returns by calculating the standard deviation of those returns. Based on these two numbers, we can then calculate how many years we need (sample size) to support the manager's claim of skill.

## About Index Fund Advisors

Index Fund Advisors, Inc. (IFA) is a fee-only advisory and wealth management firm that provides risk-appropriate, returns-optimized, globally-diversified and tax-managed investment strategies with a fiduciary standard of care.

Founded in 1999, IFA is a Registered Investment Adviser with the U.S. Securities and Exchange Commission that provides investment advice to individuals, trusts, corporations, non-profits, and public and private institutions. Based in Irvine, California, IFA manages individual and institutional accounts, including IRA, 401(k), 403(b), profit sharing, pensions, endowments and all other investment accounts. IFA also facilitates IRA rollovers from 401(k)s and 403(b)s.

To find out more about the value of IFA click here. To determine your risk capacity, take the Risk Capacity Survey.