Comparing Asset Pricing Models: Distance-based Metrics and Bayesian Interpretations

Abstract: In light of the power problems of statistical tests and undisciplined use of alpha-based statistics to compare models, this paper proposes a unified set of distance-based performance metrics, derived as the square root of the sum of squared alphas and squared standard errors. The Bayesian investor views model performance as the shortest distance between his dogmatic belief (model-implied distribution) and complete skepticism (data-based distribution) in the model, and favors models that produce low dispersion of alphas with high explanatory power. In this view, the momentum factor is a crucial addition to the five-factor model of Fama and French (2015), alleviating his prior concern of model mispricing by -8% to 8% per annum. The distance metrics complement the frequentist p-values with a diagnostic tool to guard against bad models.