Time Instability of the Fama-French Multifactor Models: An International Evidence

Abstract: This paper investigates the time-varying structure of Fama and French's (1993; 2015) multi-factor models using Fama and MacBeth's (1973) two-step estimation based on the rolling window method. In particular, we employ the generalized GRS statistics proposed by Kamstra and Shi (2024) to examine whether the validity of the risk factors (or factor redundancy) in the FF3 and FF5 models remains stable over time, and investigate whether the manner of portfolio sorting affects the time stability of the validity of the risk factors. In addition, we examine whether the similar results are obtained even when we use different datasets by country and region. First, we find that the effectiveness of factors in the FF3 and FF5 models is not stable over time in all countries. Second, the effectiveness of factors is also affected by the manner of portfolio sorting. Third, the validity of the FF3, FF5, and their nested models do not remain stable over time except for Japan. This suggests that the efficient market hypothesis is supported in the Japanese stock market. Finally, the factor redundancy varies over time and is affected by the manner of portfolio sorting mainly in the U.S. and Europe.