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Bayesian Portfolio Optimization by Predictive Synthesis

Masahiro Kato, Kentaro Baba, Hibiki Kaibuchi, Ryo Inokuchi

TL;DR

This paper addresses portfolio optimization under distributional uncertainty in asset returns. It proposes Bayesian Predictive Synthesis (BPS) with a dynamic linear/state-space formulation to fuse predictions from multiple experts into a posterior predictive distribution $p(r_t(w) | x_{1:(t-1)}, H_{1:t})$ for portfolio returns. Three portfolio classes are developed and derived from this distribution: mean-variance, quantile-based, and risk-parity portfolios, together with constrained MV and tail-risk aware schemes using VaR/CVaR and VoR/CVoR. Empirical results on US and Japanese equities show BPPS variants, especially BPPS-VoR, delivering robust performance and illustrating resilience to inferior predictors, highlighting practical value for risk-aware asset allocation. Overall, the framework offers a principled, ensemble-based approach to portfolio optimization that adapts to changing market conditions without relying on a single forecast model.

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.

Bayesian Portfolio Optimization by Predictive Synthesis

TL;DR

This paper addresses portfolio optimization under distributional uncertainty in asset returns. It proposes Bayesian Predictive Synthesis (BPS) with a dynamic linear/state-space formulation to fuse predictions from multiple experts into a posterior predictive distribution for portfolio returns. Three portfolio classes are developed and derived from this distribution: mean-variance, quantile-based, and risk-parity portfolios, together with constrained MV and tail-risk aware schemes using VaR/CVaR and VoR/CVoR. Empirical results on US and Japanese equities show BPPS variants, especially BPPS-VoR, delivering robust performance and illustrating resilience to inferior predictors, highlighting practical value for risk-aware asset allocation. Overall, the framework offers a principled, ensemble-based approach to portfolio optimization that adapts to changing market conditions without relying on a single forecast model.

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.

Paper Structure

This paper contains 25 sections, 26 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Setting
  3. Asset Returns
  4. Portfolio
  5. Portfolio Selection Criteria
  6. BPS
  7. Experts
  8. Modeling Portfolio Returns
  9. Synthesis Function
  10. Dynamic Linear Models
  11. Posterior Predictive Distribution
  12. Bayesian Portfolio
  13. Mean-Variance Portfolio
  14. Constrained Optimization.
  15. Expected Quadratic Utility Maximization.
  16. ...and 10 more sections

Figures (2)

  • Figure 1: Experimental results with US stocks. The $y$-axis in the figures represents the cumulative returns, while the $x$-axis represents the months and years. The left figure compares the proposed method with the equally weighted portfolio (denoted as Uniform), and the right figure compares the proposed method with the results obtained using sample means and AR models to predict returns.
  • Figure 2: Experimental results with Japanese stocks. The $y$-axis in the figures represents the cumulative returns, while the $x$-axis represents the months and years. The left figure compares the proposed method with the equally weighted portfolio (denoted as Uniform), and the right figure compares the proposed method with the results obtained using sample means and AR models to predict returns.