Latent Variable Estimation in Bayesian Black-Litterman Models

ArXiv ID: 2505.02185 “View on arXiv”

Authors: Thomas Y. L. 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 $Ω$ 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.

Keywords: Bayesian Black-Litterman, latent variable estimation, portfolio optimization, Bayesian network, closed-form inference, Equity

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper involves advanced Bayesian statistics with latent variable models and closed-form posterior estimations, showing high mathematical density. It provides empirical results on 20-30 year datasets with specific metrics (Sharpe ratios, turnover), indicating solid backtesting and implementation focus.

  flowchart TD
    A["Research Goal:<br>Remove subjective views in<br>Bayesian Black-Litterman model"] --> B["Methodology:<br>Latent Variable Estimation<br>Learn (q, Ω) as latent variables in<br>Bayesian network with closed-form inference"]
    B --> C["Data & Inputs:<br>30-year Dow-Jones & 20-year<br>Sector-ETF market data"]
    C --> D["Computational Process:<br>Bayesian network inference<br>Closed-form posterior estimation"]
    D --> E["Key Findings:<br>50% higher Sharpe ratio<br>55% lower turnover<br>vs Markowitz/Index baselines"]
    E --> F["Outcome:<br>Fully data-driven,<br>view-free, coherent<br>portfolio optimization"]