The Link between Fama-French Time-Series Tests and Fama-Macbeth Cross-Sectional Tests

Abstract

Many papers in the empirical finance literature implement tests of asset pricing models either via Fama-French time-series regressions or via Fama-Macbeth cross-sectional regressions. This short paper explains their conceptual relationships. There is a time-series equivalent method to implementing Fama-Macbeth regressions (in a stable world). This correspondence also helps to clarify the interpretation of the estimates from the two methods: The Fama-Macbeth test is better suited for APT tests, while the plain Fama-French test is better suited for equilibrium tests. (Of course, all equilibrium model must be arbitrage-free, but not vice-versa.) It is possible to test not only whether factors can price portfolios in an equilibrium framework, but also the less restrictive requirement that the factors should not allow for arbitrage. For example, this short paper shows that the Fama-French 3-factor model fails the weaker arbitrage pricing restriction for the the 2x3 Fama-French portfolios, and not just the stronger equilibrium pricing restriction.

Keywords: Asset Pricing, Fama-French, Fama-Macbeth, APT, CAPM

JEL Classification: G12