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

This paper is concerned with statistical inference and model evaluation in possibly misspecified and unidentified linear asset-pricing models estimated by maximum likelihood and one-step generalized method of moments. Strikingly, when spurious factors (that is, factors that are uncorrelated with the returns on the test assets) are present, the models exhibit 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, while factors that are useful are driven out of the model. Although 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, and Hou, Xue, and Zhang, 2015) do not suffer of the identification problems documented in this study.