Diffuse Prior Bayesian Mean-Variance Optimization under Parameter Uncertainty: Implementation & Evaluation
Thompson, Lucas
Thompson, Lucas
Abstract
Mean-Variance Optimization (MVO) is a widely used and influential framework for portfolio selection. However, its performance is often limited by estimation errors in the expected return and covariance matrix. Because MVO treats these inputs as known, even small changes can produce unstable portfolio weights, excessive turnover, and poor out-of-sample returns. This paper addresses these limitations by placing MVO in a Bayesian framework that treats expected returns and covariance parameters as uncertain rather than fixed. Specifically, diffused-prior Bayesian MVO (DP-BMVO) refers to an allocation strategy that uses weak priors and posterior draws from historic returns to optimize portfolio weights without incorporating subject views, fundamental data, or structural assumptions. The model is evaluated using both US large-cap equity data and numerous simulated return scenarios with known parameters. Performance is compared across numerous control models (1/N, MVO, and Ledoit-Wolf Shrinkage), described later, using a wide range of metrics that evaluate risk-adjusted return, concentration, turnover, and accurate parameter recovery in simulated data. The results suggest that although an uninformed Bayesian method doesn’t deliver the highest absolute return, it modestly improves portfolio robustness by delivering better risk-adjusted return with lower tail risk and lower portfolio concentration. These advantages are most apparent when markets are noisy, sample windows are limited, or the market is undergoing regime changes. Meanwhile, the Bayesian approach is least valuable when the market is stable or when the true returns are too weak for optimization to exploit. Ultimately, the analysis suggests these benefits arise from incorporating uncertainty into the optimization step rather than materially improving the point estimates of the parameters themselves.
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2026-05-04
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http://creativecommons.org/licenses/by-nc-nd/4.0/
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Economics