DRAWBACKS IN THE 3-FACTOR APPROACH OF FAMA AND FRENCH (2018)

Abstract

This paper features a statistical analysis of the monthly three factor Fama/French return series. Rolling OLS regressions explore the relationship between the 3 factors, using data from July 1926 to June 2018, available on French’s website. The results suggest there are significant and time-varying relationships between the factors. A sub-sample from July 1990 to July 2018 is used to analyze the three series using two-stage least squares and the Hausman test to check for issues related to endogeneity. The empirical results suggest that the factors, when combined in OLS regression analysis, as suggested by Fama and French (2018), are likely to suffer from endogeneity. Ramsey’s RESET tests suggest a nonlinear relationship exists between the three series. We use two instruments to estimate the market betas, and compare them to betas estimated not using instruments. Non-parametric tests of the two sets of betas suggest significant differences. The results suggest that using these factors in linear regression analysis, as recommended by Fama and French [(2018). Choosing factors. Journal of Financial Economics, 128(2), 234–252] is problematic in that the estimated coefficients are highly sensitive to the correct model specification.