Latent Variable Estimation in Bayesian Black-Litterman Models
This work provides a fully data-driven and coherent Bayesian framework for portfolio optimization, addressing the need for objective methods in finance.
The paper tackled the problem of removing subjective investor views from the Bayesian Black-Litterman portfolio model by treating view parameters as latent variables learned from market data, resulting in a 50% improvement in Sharpe ratios and a 55% reduction in turnover compared to baselines.
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 $Ω$ that describe how much a chosen portfolio should outperform the market. Our key idea is to treat $(q,Ω)$ 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.