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Resumen:
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This paper features a statistical analysis of the monthly three factor Fama/French return series. We apply rolling OLS regressions to explore the relationship between the 3 factors, using monthly and weekly data from July 1926 to June 2018, that are freely available on French's website. The results suggest there are significant and time-varying relationships between the factors. This is confirmed by non-parametric tests. We then switch to a sub-sample from July 1990 to July 2018, also taken from French's website. The three series and their interrelationships are analysed using two stage least squares and the Hausman test to check for issues related to endogeneity, the Sargan overidentification test and the Cragg-Donald weak instrument test. The relationship between factors is also examined using OLS, incorporating Ramsey's RESET tests of functional form misspecification,plus Naradaya-Watson kernel regression techniques. 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. OLS regression analysis and the application of Ramsey's RESET tests suggest a non-linear relationship exists between the three series, in which cubed terms are significant. This non-linearity is also confirmed by the kernel regression analysis. We use two instruments to estimate the market betas, and then use the factor estimates in a second set of panel data tests using a small sample of monthly returns for US firms that are drawn from the online data source “tingo”. These issues are analysed using methods suggested by Petersen (2009) to permit clustering in the panels by date and firm. The empirical results suggest that using an instrument to capture endogeneity reducesthe standard error of market beta in subsequent crosssectional tests, but thatclustering effects, as suggested by Petersen (2009), will also impact on the estimated standard errors. The empirical results suggest that using these factorsin linear regression analysis, such as suggested by Fama and French (2018), as a method of screening factor relevance, is problematic in that the estimated standard errors are highly sensitive to the correct model specification.
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