Eugene Fama

A Foundational Paper in Finance

Eugene Fama

At Index Fund Advisors, we often talk about the risk factors that explain the returns of diversified portfolios. In this article, we will explore the technique pioneered1 by Nobel Laureate Eugene Fama and James Macbeth for establishing the existence of a risk factor and quantifying the risk premium provided by the factor. It is this technique that was so famously used by Fama and French in their paper2 that established the three-factor asset pricing model used for equities.

A Fama-Macbeth regression involves a two-step process beginning with a set of proposed risk factors and some portfolios formed on the basis of those risk factors. For example, if we wanted to test out size as a risk factor, we could sort the market into ten different size deciles, which would allow us to quantify the impact of the varying degree of exposure to the size factor.

1) The returns of each portfolio would be regressed against the proposed risk factors to estimate the portfolio’s sensitivity to each factor. These sensitivities are sometimes referred to as "betas”, but we prefer to use beta exclusively to refer to overall market exposure. This is why we are not advocates of the popularized marketing term of "smart beta".

2) The risk premium for each factor is determined by regressing all the portfolio returns against the estimated sensitivities to determine the risk premium for each factor.

Although Fama and Macbeth only set out to test William Sharpe's single factor Capital Asset Pricing Model (CAPM), the technique they developed has since been used to identify hundreds of explanatory factors. Unfortunately, the bulk of these factors have no practical use for investors because they are either redundant of other factors or they do not meet the five criteria for a risk factor shown below.

In providing support to CAPM, Fama and Macbeth also helped to further establish Fama’s Efficient Market Hypothesis as a bedrock principle of modern finance. As the authors note in their conclusion, "Finally, the observed fair game properties of the coefficients and residuals of the risk-return regression are consistent with an efficient capital market—that is, a market where prices of securities fully reflect available information."

1Fama, Eugene F., James D. Macbeth. "Risk Return, and Equilibrium: Empirical Tests." The Journal of Political Economy, Vol. 81, No. 3 (May-Jun., 1973), 607-636.

2Fama, Eugene F., Kenneth R. French. "The Cross-Section of Expected Stock Returns." The Journal of Finance, Vol. 47, Issue 2 (Jun., 1992), 427-465.