45 Pages Posted: 8 Apr 2017 Last revised: 16 Apr 2017
Date Written: April 15, 2017
The existence of reversals and momentum in equity returns has challenged proponents of efficient markets for over 30 years. Although explanations for momentum profits based on cross-sectional mean return dispersion have been proposed, evidence of time-series autocorrelation from Fama-MacBeth cross-sectional regressions persists without any good risk/return explanation. In this paper I show that common implementations of the Fama-MacBeth procedure will yield upward biased estimates of time-series autocorrelation coefficients. Even in absence of autocorrelation, the bias is strictly positive, leading to apparent momentum when there is, in fact, none. This biased implementation of the Fama-MacBeth procedure has found its way into a great many other studies and may, similarly, lead to apparent effects when there are none. I outline conditions under which this bias occurs and prove the existence of bias under these conditions. I also provide a Monte Carlo simulation showing the magnitude of the bias, I demonstrate the impact of this bias with reference to published results in the literature, and I introduce a new test for misspecification of an asset pricing model. Additionally, I suggest and explore simple fixes for this bias. Some variation of a firm fixed-effects model is appropriate to correct for this bias in applications using the Fama-MacBeth method.
Keywords: Momentum, Reversals, Autocorrelation, Fama-MacBeth
JEL Classification: G12, G14
Suggested Citation: Suggested Citation
Kamstra, Mark J., Momentum, Reversals, and Other Puzzles in Fama-Macbeth Cross-Sectional Regressions (April 15, 2017). Available at SSRN: https://ssrn.com/abstract=2947340