Latent Variable Estimation in Bayesian Black-Litterman Models

Thomas Y. L. Lin; Jerry Yao-Chieh Hu; Paul W. Chiou; Peter Lin

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arXiv · 2505.02185

Latent Variable Estimation in Bayesian Black-Litterman Models

Thomas Y. L. Lin·Jerry Yao-Chieh Hu·Paul W. Chiou·Peter Lin

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Abstract

We revisit the Bayesian Black-Litterman (BL) portfolio model and remove its reliance on subjective investor views. Classical BL requires an investor "view": a forecast vector $q$ and its uncertainty matrix $\Omega$ that describe how much a chosen portfolio should outperform the market. Our key idea is to treat $(q,\Omega)$ as latent variables and learn them from market data within a single Bayesian network. Consequently, the resulting posterior estimation admits closed-form expression, enabling fast inference and stable portfolio weights. Building on these, we propose two mechanisms to capture how features interact with returns: shared-latent parametrization and feature-influenced views; both recover classical BL and Markowitz portfolios as special cases. Empirically, on 30-year Dow-Jones and 20-year sector-ETF data, we improve Sharpe ratios by 50% and cut turnover by 55% relative to Markowitz and the index baselines. This work turns BL into a fully data-driven, view-free, and coherent Bayesian framework for portfolio optimization.

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q-fin.PM cs.LG econ.EM stat.ME stat.ML

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Thomas Y. L. Lin, Jerry Yao-Chieh Hu, Paul W. Chiou, Peter Lin. 2025-05-04. Latent Variable Estimation in Bayesian Black-Litterman Models. https://arxiv.org/abs/2505.02185

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