Latent Variable Estimation in Bayesian Black-Litterman Models

Thomas Yuan-Lung Lin, Jerry Yao-Chieh Hu, Paul W. Chiou, Peter Lin

TL;DR: We reformulate the Black-Litterman model to infer investor views as latent variables, directly estimating asset returns from data.

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.

Lay Summary: Many investment models ask human experts to state which assets they think will beat the market and by how much. This “investor-view” step is subjective and hard to quantify. Our work turns that step into a data problem. We treat the view and its uncertainty as hidden (latent) variables inside a single Bayesian model and let market data and asset-specific features learn them automatically. The resulting formulas stay fully analytical, so portfolio weights are quick to compute and less erratic than the classic Markowitz approach. When tested on 30 years of Dow Jones stocks and 20 years of sector-ETF data, the model raised risk-adjusted returns (Sharpe ratio) by roughly 50 percent and cut trading turnover by more than half. In short, we remove guesswork from the Black–Litterman framework and deliver a purely data-driven, coherent way to build more stable portfolios.

Link To Code: https://github.com/Raccoon103/Latent_Variable_Estimation_Black_Litterman_Model_2025

Primary Area: Applications->Time Series

Keywords: Black-Litterman Models, Portfolio Optimization, Bayesian Networks, Graphical Models, Hierarchical Models, Latent Variable Models, Uncertainty Quantification

Submission Number: 7292