Distance Metrics for Comparing Asset Pricing Models

Summary

The paper proposes distance-based measures for comparing asset pricing models, motivated by concerns that statistical tests may have low power and that alpha statistics can be used without discipline. The proposed metric combines squared alphas and squared standard errors, then takes the square root, offering a single diagnostic that accounts for both estimated mispricing and uncertainty.

It also gives a Bayesian interpretation: model performance is framed as the distance between a model-implied distribution and a data-based distribution representing skepticism. In this account, models with lower alpha dispersion and greater explanatory power are preferred. The description reports that adding momentum to the Fama-French five-factor model alleviates a stated concern about annual mispricing of minus eight to plus eight percent. These metrics are presented as complements to p-values, not replacements; the supplied text does not provide methodological details or broader validation.

Key ideas

• The proposed metric combines squared alphas and squared standard errors into a distance measure.
• The Bayesian framing compares model-implied beliefs with a data-based skeptical distribution.
• The account favors models with low alpha dispersion and high explanatory power.
• The paper presents momentum as a useful addition to the Fama-French five-factor model.
• Distance metrics are intended to complement frequentist p-values as model diagnostics.

Tags

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


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









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.

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