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

TL;DR

This paper introduces distance-based metrics for asset model comparison, integrating Bayesian interpretation to evaluate model performance and highlighting the importance of the momentum factor in the five-factor model.

Contribution

It proposes a unified distance-based framework for model comparison and interprets it within a Bayesian context, emphasizing the momentum factor's role.

Findings

Distance metrics provide a robust alternative to p-values.

Momentum factor significantly improves model performance.

Models with low dispersion of alphas are preferred.

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.