Bayesian Parametric Portfolio Policies

TL;DR

This paper introduces Bayesian Parametric Portfolio Policies (BPPP), which incorporate policy risk into portfolio optimization, leading to improved performance metrics like higher Sharpe ratios and lower tail risk compared to traditional PPP.

Contribution

The paper develops BPPP by adding a prior on policy coefficients, correcting the overstatement of utility and risk in PPP, and demonstrates its advantages empirically in high-dimensional settings.

Findings

BPPP yields higher Sharpe ratios than PPP.

BPPP results in substantially lower portfolio turnover.

BPPP provides lower tail risk and higher investor welfare.

Abstract

Parametric Portfolio Policies (PPP) estimate optimal portfolio weights directly as functions of observable signals by maximizing expected utility, bypassing the need to model asset returns and covariances. However, PPP ignores policy risk. We show that this is consequential, leading to an overstatement of expected utility and an understatement of portfolio risk. We develop Bayesian Parametric Portfolio Policies (BPPP), which place a prior on policy coefficients thereby correcting the decision rule. We derive a general result showing that the utility gap between PPP and BPPP is strictly positive and proportional to posterior parameter uncertainty and signal magnitude. Under a mean--variance approximation, this correction appears as an additional estimation-risk term in portfolio variance, implying that PPP overexposes when signals are strongest and when risk aversion is high. Empirically, in a high-dimensional setting with 242 signals and six factors over 1973--2023, BPPP delivers higher Sharpe ratios, substantially lower turnover, larger investor welfare, and lower tail risk, with advantages that increase monotonically in risk aversion and are strongest during crisis episodes.