Asset Pricing Tests, Endogeneity issues and Fama-French factors

This paper features a statistical analysis of the independence of the core Fama/French factors; SMB and HML, using daily data, of the factor return series, for the USA, Developed Markets and Japan, using a sample taken from the data-sets that are available on French's website. The various series and their inter-relationships are analysed using rolling OLS regressions, so as to explore their independence and issues related to their endogeneity. The OLS analysis incorporates Ramsey's RESET tests of functional form misspecifcation. The empirical results suggest that these factors, when combined in OLS regression analysis, as suggested by Fama and French (2018), and generally in the empirical asset pricing literature featuring time-series tests, are frequently not independent, and thus likely to suffer from endogeneity. The rolling regression analysis suggests significant and time-varying relationships between the core factors and rejects their independence for long periods of time within the samples. A significant non-linear relationship exists between some of the series, as indicated by the employment of squared terms, which are frequently significant. The empirical results suggest that using these factors in linear regression analysis, such as suggested by Fama and French (2018), as a method of screening factor relevance, is likely to be problematic, in that the estimated standard errors are likely to be sensitive to the non-independence of factors. This is also likely to be a potential problem for asset pricing tests that use the popular time-series approach, as first suggested by Fama and Macbeth (1973).