Latent Variable Estimation in Bayesian Black-Litterman Models
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.
Cite
Text
Lin et al. "Latent Variable Estimation in Bayesian Black-Litterman Models." Proceedings of the 42nd International Conference on Machine Learning, 2025.Markdown
[Lin et al. "Latent Variable Estimation in Bayesian Black-Litterman Models." Proceedings of the 42nd International Conference on Machine Learning, 2025.](https://mlanthology.org/icml/2025/lin2025icml-latent/)BibTeX
@inproceedings{lin2025icml-latent,
title = {{Latent Variable Estimation in Bayesian Black-Litterman Models}},
author = {Lin, Thomas Yuan-Lung and Hu, Jerry Yao-Chieh and Chiou, Paul W. and Lin, Peter},
booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
year = {2025},
pages = {37846-37873},
volume = {267},
url = {https://mlanthology.org/icml/2025/lin2025icml-latent/}
}