The Gibbs Posterior and Parametric Portfolio Choice

TL;DR

This paper introduces a Bayesian framework using the Gibbs posterior for portfolio choice that updates beliefs without assuming a return model, optimizing the balance between prior information and data to improve investment decisions.

Contribution

It develops a novel Gibbs posterior approach for portfolio selection, including an algorithm to choose the optimal scaling parameter without out-of-sample validation.

Findings

Characteristic-based gains concentrated pre-2000

Optimal scaling parameter varies with risk aversion

Higher-order moments influence the posterior's weight

Abstract

Parametric portfolio policies may experience estimation risk. I develop a generalized Bayesian framework that updates priors, delivering a posterior distribution over characteristic tilts and out-of-sample returns that is the unique belief-updating rule consistent with the investor's utility function, requiring no model for the return generating process. The Gibbs posterior is the closest distribution to the prior in Kullback-Leibler divergence subject to utility maximization. The posterior's scaling parameter $\lambda$ controls the weight placed on data relative to the prior. I develop a KNEEDLE algorithm to select optimal $\lambda^*$ in-sample by trading off posterior precision against numerical fragility, eliminating the need for out-of-sample validation. I apply this to U.S. equities (1955-2024), and confirm characteristic-based gains concentrate pre-2000. I find that $\lambda^*$ varies meaningfully with risk aversion and depends on higher-order moments.