Latent Variable Estimation in Bayesian Black-Litterman Models

Thomas Yuan-Lung Lin, Jerry Yao-Chieh Hu, Paul W. Chiou, Peter Lin
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:37846-37873, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v267-lin25g, title = {Latent Variable Estimation in {B}ayesian 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}, pages = {37846--37873}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/lin25g/lin25g.pdf}, url = {https://proceedings.mlr.press/v267/lin25g.html}, 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.} }
Endnote
%0 Conference Paper %T Latent Variable Estimation in Bayesian Black-Litterman Models %A Thomas Yuan-Lung Lin %A Jerry Yao-Chieh Hu %A Paul W. Chiou %A Peter Lin %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-lin25g %I PMLR %P 37846--37873 %U https://proceedings.mlr.press/v267/lin25g.html %V 267 %X 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.
APA
Lin, T.Y., Hu, J.Y., Chiou, P.W. & Lin, P.. (2025). Latent Variable Estimation in Bayesian Black-Litterman Models. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:37846-37873 Available from https://proceedings.mlr.press/v267/lin25g.html.

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