Too Good to Be True? Fallacies in Evaluating Risk Factor Models

with Nikolay Gospodinov and Raymond Kan, 2019, Journal of Financial Economics 132, pp. 451-471. [Paper] [Data and Code] [Working Paper Version] [Internet Appendix for Working Paper Version] [Data and Code for Working Paper Version]. This paper is concerned with statistical inference and model evaluation in possibly misspecified and unidentified linear asset pricing models estimated by maximum likelihood. Strikingly, when spurious factors (that is, factors that are uncorrelated with the returns on the test assets) are present, the model exhibits perfect fit, as measured by the squared correlation between the model’s fitted expected returns and the average realized returns. Furthermore, factors that are spurious are selected with high probability, and factors that are useful are driven out of the model. While ignoring potential misspecification and lack of identification can be very problematic for models with macroeconomic factors, empirical specifications with traded factors (e.g., Fama and French, 1993; Hou et al., 2015) do not suffer from the identification problems shown in this study.