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Uncertainty in the Black-Litterman Model: A Practical Perspective

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Fuhrer, A., Hock, T. Uncertainty in the Black-Litterman Model: A Practical Perspective. Credit and Capital Markets – Kredit und Kapital, 57(1–4), 157-183. https://doi.org/10.3790/ccm.2025.1447405
Fuhrer, Adrian and Hock, Thorsten "Uncertainty in the Black-Litterman Model: A Practical Perspective" Credit and Capital Markets – Kredit und Kapital 57.1–4, 2025, 157-183. https://doi.org/10.3790/ccm.2025.1447405
Fuhrer, Adrian/Hock, Thorsten (2025): Uncertainty in the Black-Litterman Model: A Practical Perspective, in: Credit and Capital Markets – Kredit und Kapital, vol. 57, iss. 1–4, 157-183, [online] https://doi.org/10.3790/ccm.2025.1447405
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Uncertainty in the Black-Litterman Model: A Practical Perspective

Fuhrer, Adrian | Hock, Thorsten

Credit and Capital Markets – Kredit und Kapital, Vol. 57(2024), Iss. 1–4 : pp. 157–183 | First published online: July 02, 2025

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Article Details

Publisher Name
Duncker & Humblot GmbH
DOI
https://doi.org/10.3790/ccm.2025.1447405
Language
English
Pages
27
License
open-access https://creativecommons.org/licenses/by/4.0
Keywords

Author Details

Dr. Adrian Fuhrer, Department of Banking and Finance, University of Zurich, Switzerland.

Prof. Dr. Thorsten Hock, Weiden Business School, OTH Amberg-Weiden, Germany.

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Abstract

Deriving an optimal asset allocation hinges crucially on the quality of inputs used in the optimization. If the vector of expected returns and the covariance matrix are known with certainty, mean-variance optimization produces optimal portfolios. If, however, these parameters are estimated with uncertainty, mean-variance optimization maximizes estimation error. We provide a literature review of procedures developed in academia to incorporate parameter uncertainty in the asset allocation process, focusing on common heuristics and Bayesian methods. The Black-Litterman model, an application of the Bayesian framework, has practical appeal for investors as it permits the specification of subjective views. Calibration of the model is, however, not trivial and induces rigidity. In Fuhrer and Hock (2023), a generalization of the Black-Litterman model was introduced and a fully quantitative, objective parameterization was derived. Here, we start with the same generalization, but present a qualitative, more intuitive approach for setting parameters. This gives the investor more control over the mixing of views and equilibrium returns, while lending intuition to the parameter choice in the classical setting.

Table of Contents

Section Title Page Action Price
Adrian Fuhrer / Thorsten Hock: Uncertainty in the Black-Litterman Model: A Practical Perspective 157
Abstract 157
I. Introduction 157
II. Literature Review 159
III. Theory 162
1. The Black-Litterman model 162
2. Deviation from the Black-Litterman model 164
IV. Intuition through Judgemental Approach 165
1. Symmetric Confidence Intervals 166
2. Asymmetric Confidence Intervals 167
3. Correspondence to τ 168
V. Illustration 169
1. A Four-Asset Example 169
2. Asset Allocation without Views 170
Using the Black-Litterman Model 170
Using the Flexible Model 172
3. Investor’s Subjective Views 174
4. Asset Allocation with Views 175
Using the Black-Litterman Model 175
Using the Flexible Model 176
VI. Conclusion 178
References 178
VII. A. Appendix 181
A.1. Alternative Interpretation of τ 181
A.2. Construction of Time Series 181
1. A.3. Portfolio Weights for Different Target Risk Levels 182

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