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Bayesian Parametric Portfolio Policies

Miguel C. Herculano

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.

Bayesian Parametric Portfolio Policies

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.
Paper Structure (20 sections, 1 theorem, 40 equations, 14 figures, 9 tables)

This paper contains 20 sections, 1 theorem, 40 equations, 14 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Setup and Motivation
  3. Bayesian Parametric Portfolio Policies
  4. The role of the Prior
  5. Data
  6. Empirical Results
  7. Robustness
  8. Statistical Significance and Spanning Tests
  9. Welfare and Risk-Aversion Analysis
  10. Transaction Costs and Trading Frictions
  11. Subperiod Stability and Crisis Resilience
  12. Prior Sensitivity and Dynamic Prior Mean
  13. Sensitivity to prior tightness ($\delta$).
  14. The role of the dynamic prior mean.
  15. Horseshoe prior specification.
  16. ...and 5 more sections

Key Result

Proposition 1

Define the conditional expected utility of policy $\theta$ at date $\tau$ as and let $m_\tau = \mathbb{E}[\theta|\mathcal{D}_{T_\tau}]$ denote the posterior mean, $\Sigma_{\theta,\tau} = \operatorname{Var}(\theta|\mathcal{D}_{T_\tau})$ the posterior covariance, $U$ a strictly concave and twice continuously differentiable utility function, where $\Sigma_{\theta,\tau} \neq 0$. Moreover, to second o

Figures (14)

  • Figure 1: Factor Exposures by Model
  • Figure 2: Net Sharpe Ratio vs. Transaction Costs
  • Figure 3: Sharpe Ratios by Decade
  • Figure 4: Rolling 36-Month Sharpe Ratios
  • Figure 5: Cumulative Wealth During Crisis Episodes
  • ...and 9 more figures

Theorems & Definitions (1)

  • Proposition 1