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Latent Variable Estimation in Bayesian Black-Litterman Models

Thomas Y. L. Lin, Jerry Yao-Chieh Hu, Paul W. Chiou, Peter Lin

arXiv 4 May 2025 · Finance — Portfolio Management

arXiv:2505.02185 · PDF · DOI · OpenAlex · Extracted main text

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.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Petter Kolm and Gordon Ritter (2017) On the bayesian interpretation of black–litterman0.8947371%
2Fischer Black and Robert Litterman (1992) Global portfolio optimization0.84310660%
3Petter N Kolm and Gordon Ritter (2021) Factor investing with black–litterman–bayes: incorporating factor views and priors in portfolio construction0.7375340%
4Thomas Idzorek (2007) A step-by-step guide to the black-litterman model: Incorporating user-specified confidence levels0.7374450%
5Anisa Salomons (2007) The black-litterman model hype or improvement?0.7374350%
6Wai Lee (2000) Theory and methodology of tactical asset allocation, volume 650.7373367%
7Harry Markowitz (1952) Portfolio selection0.6443267%
8Steven L Beach and Alexei G Orlov (2007) An application of the black–litterman model with egarch-m-derived views for international portfolio management0.5113233%
9Andi Duqi, Leonardo Franci, and Giuseppe Torluccio (2014) The black–litterman model: the definition of views based on volatility forecasts0.5113233%
10Mahmut Kara, Aydin Ulucan, and Kazim Baris Atici (2019) A hybrid approach for generating investor views in black–litterman model0.5113233%

Showing the top 10 of 61 scored citations.