Latent Variable Estimation in Bayesian Black-Litterman Models
Thomas Yuan-Lung Lin, Jerry Yao-Chieh Hu, Paul W. Chiou, Peter Lin
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.
BibTeX
@inproceedings{
lin2025latent,
title={Latent Variable Estimation in Bayesian Black-Litterman Models},
author={Thomas Yuan-Lung Lin and Jerry Yao-Chieh Hu and Paul W. Chiou and Peter Lin},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=v8ipdsBPEx}
}