Bayesian Portfolio Optimization by Predictive Synthesis

2025-10-08

AI Summary

Portfolio optimization typically relies on the assumed distribution of asset returns; however, this distribution is unknown in practice, and model forecasting performance degrades under market non-stationarity, undermining the robustness of conventional approaches. To address this, we propose a Bayesian Predictive Synthesis (BPS)-based portfolio optimization framework—the first application of BPS to asset allocation. It dynamically aggregates forecasts from multiple heterogeneous models via time-varying weights, yielding a posterior predictive distribution for asset returns with time-varying means. Integrated with dynamic linear models, the framework supports both mean–variance and quantile-based portfolio construction. Empirical results demonstrate that our method significantly improves the robustness of distributional forecasts, effectively adapts to model performance drift, and achieves superior risk-adjusted returns in uncertain, evolving market environments.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Estimating asset return distributions under financial market uncertainty
• Combining multiple prediction models using Bayesian ensemble methods
• Constructing optimal portfolios based on synthesized predictive distributions

Innovation

• Bayesian predictive synthesis for portfolio optimization
• Dynamic linear models combine multiple prediction models
• Generates Bayesian predictive posterior for asset returns