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Momentum, Reversals, and other Puzzles in Fama-MacBeth Cross-Sectional Regressions

46 Pages Posted: 8 Apr 2017 Last revised: 10 Aug 2017

Mark J. Kamstra

York University - Schulich School of Business; Rady School of Management

Date Written: July 1, 2017

Abstract

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

Kamstra, Mark J., Momentum, Reversals, and other Puzzles in Fama-MacBeth Cross-Sectional Regressions (July 1, 2017). Available at SSRN: https://ssrn.com/abstract=2947340

Mark J. Kamstra (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

Rady School of Management ( email )

9500 Gilman Drive
Rady School of Management
La Jolla, CA 92093
United States

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