Paper: arXiv 2602.21173

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical contribution by integrating Bayesian updating via a Gibbs posterior into the Parametric Portfolio Policies (PPP) framework to address policy parameter risk. The empirical evaluation is highly rigorous, utilizing a high-dimensional dataset of 242 signals across five decades and multiple market regimes to demonstrate superior risk-adjusted returns, lower turnover, and reduced tail risk.

Research Flowchart

  flowchart TD
    A[Research Question: How to account for policy estimation risk in Parametric Portfolio Policies?] --> B[Input Data: 242 Stock Signals & 6 Factors 1973–2023]
    B --> C[Methodology: Develop Bayesian PPP BPPP placing priors on policy coefficients]
    C --> D[Analytical Result: Utility gap proportional to parameter uncertainty & signal magnitude]
    D --> E[Empirical Optimization: High-dimensional Bayesian estimation under Risk Aversion]
    E --> F[Outcomes: Higher Sharpe ratios, lower turnover, higher welfare & reduced tail risk]

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0 of 33 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.