Paper: arXiv 2603.02455

Authors: Christopher G. Lamoureux

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 $λ$ controls the weight placed on data relative to the prior. I develop a KNEEDLE algorithm to select optimal $λ^$ 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 $λ^$ varies meaningfully with risk aversion and depends on higher-order moments.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10 (capped from 8.0: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides an innovative, mathematically sound generalized Bayesian framework using Gibbs posteriors for parametric portfolio choice without requiring a likelihood function or return-generating process. It combines robust theory with extensive empirical analysis across seven decades of U.S. stock data (1955-2024), offering an elegant in-sample solution to regularization via a custom KNEEDLE algorithm.

Research Flowchart

  flowchart TD
    A["Research Goal: Mitigate Estimation Risk in Parametric Portfolio Choice"] --> B["Data Inputs: U.S. Equities (1955–2024) & Asset Characteristics"]
    B --> C["Gibbs Posterior Framework: Update priors using utility function via KL-Divergence"]
    C --> D["KNEEDLE Algorithm: Select optimal scaling parameter (λ*) in-sample"]
    D --> E["Outcomes: Optimal λ* varies with risk aversion & higher-order moments"]
    D --> F["Outcomes: Confirms characteristic-based gains concentrate pre-2000"]