Empirical analysis on construction of mimicking factors and its effect on model adequacy in the Fama-French three-factor model

Abstract

Since the empirical failure of the CAPM, the Fama-French three-factor model that attempts to address some of its greatest issues has become widely popular. However, the choice of the two “mimicking” factors in the model are based mostly on empirical merit, and their construction is purely arbitrary. This paper investigates whether the model is robust with respect to changes in how the two mimicking factors are constructed, and its model adequacy, using US stocks data over a longer period (including more recent years) from July 1926 to June 2022. The conclusion is that the model is largely robust to an alternative formulation of the two factors, though the model is clearly inadequate particularly when tested using data over the longer period. Model fit is especially poor for portfolios formed by small stocks with low book-to-market equity ratio. Hence, caution needs to be taken when using the model for these stocks, and alternative models need to be sought.