Bayesian Portfolio Optimization by Predictive Synthesis

ArXiv ID: 2510.07180 “View on arXiv”

Authors: Masahiro Kato, Kentaro Baba, Hibiki Kaibuchi, Ryo Inokuchi

Abstract

Portfolio optimization is a critical task in investment. Most existing portfolio optimization methods require information on the distribution of returns of the assets that make up the portfolio. However, such distribution information is usually unknown to investors. Various methods have been proposed to estimate distribution information, but their accuracy greatly depends on the uncertainty of the financial markets. Due to this uncertainty, a model that could well predict the distribution information at one point in time may perform less accurately compared to another model at a different time. To solve this problem, we investigate a method for portfolio optimization based on Bayesian predictive synthesis (BPS), one of the Bayesian ensemble methods for meta-learning. We assume that investors have access to multiple asset return prediction models. By using BPS with dynamic linear models to combine these predictions, we can obtain a Bayesian predictive posterior about the mean rewards of assets that accommodate the uncertainty of the financial markets. In this study, we examine how to construct mean-variance portfolios and quantile-based portfolios based on the predicted distribution information.

Keywords: Bayesian Predictive Synthesis, Meta-learning, Portfolio Optimization, Mean-Variance Portfolio, Quantile-based Portfolios, Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats
• Why: The paper is mathematically dense, using advanced Bayesian statistics, state-space models, and dynamic linear models with heavy LaTeX and derivations. However, it lacks backtest results, code, or statistical metrics, presenting a conceptual framework rather than an implementation-heavy empirical study.

  flowchart TD
    A["Research Goal:<br>Portfolio Optimization with<br>Uncertain Return Distributions"] --> B["Methodology:<br>Bayesian Predictive Synthesis<br>with Dynamic Linear Models"]
    
    B --> C{"Data Inputs"}
    C --> C1["Historical Asset<br>Return Data"]
    C --> C2["Multiple Asset Return<br>Prediction Models"]
    
    C1 & C2 --> D["Computational Process:<br>Combine predictions via BPS<br>to estimate predictive<br>posterior distribution<br>of asset mean rewards"]
    
    D --> E["Portfolio Construction"]
    E --> F["Mean-Variance Portfolio"]
    E --> G["Quantile-Based Portfolio"]
    
    F & G --> H["Key Findings/Outcomes"]
    H --> H1["Dynamic distribution<br>estimation accommodates<br>market uncertainty"]
    H --> H2["BPS effectively synthesizes<br>multiple prediction models"]
    H --> H3["Robust portfolio optimization<br>without requiring known<br>return distribution"]