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Comparison and robustification of Bayes and Black-Litterman models

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  • Katrin Schöttle
  • Ralf Werner
  • Rudi Zagst

Abstract

For determining an optimal portfolio allocation, parameters representing the underlying market—characterized by expected asset returns and the covariance matrix—are needed. Traditionally, these point estimates for the parameters are obtained from historical data samples, but as experts often have strong opinions about (some of) these values, approaches to combine sample information and experts’ views are sought for. The focus of this paper is on the two most popular of these frameworks—the Black-Litterman model and the Bayes approach. We will prove that—from the point of traditional portfolio optimization—the Black-Litterman is just a special case of the Bayes approach. In contrast to this, we will show that the extensions of both models to the robust portfolio framework yield two rather different robustified optimization problems. Copyright Springer-Verlag 2010

Suggested Citation

  • Katrin Schöttle & Ralf Werner & Rudi Zagst, 2010. "Comparison and robustification of Bayes and Black-Litterman models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 453-475, June.
    • Handle: RePEc:spr:mathme:v:71:y:2010:i:3:p:453-475
    DOI: 10.1007/s00186-010-0302-9
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    References listed on IDEAS

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    2. Erindi Allaj, 2020. "The Black–Litterman model and views from a reverse optimization procedure: an out-of-sample performance evaluation," Computational Management Science, Springer, vol. 17(3), pages 465-492, October.
    3. I-Chen Lu & Kai-Hong Tee & Baibing Li, 2019. "Asset allocation with multiple analysts’ views: a robust approach," Journal of Asset Management, Palgrave Macmillan, vol. 20(3), pages 215-228, May.
    4. Sergio Ortobelli Lozza & Tommaso Lando & Filomena Petronio & Tomáš Tichý, 2016. "Asymptotic Multivariate Dominance: A Financial Application," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1097-1115, December.
    5. Kouaissah, Noureddine, 2021. "Robust conditional expectation reward–risk performance measures," Economics Letters, Elsevier, vol. 202(C).
    6. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2022. "Well Posedness of Utility Maximization Problems Under Partial Information in a Market with Gaussian Drift," Papers 2205.08614, arXiv.org, revised Jul 2024.
    7. Peng W. He & Andrew Grant & Joel Fabre, 2013. "Economic value of analyst recommendations in Australia: an application of the Black–Litterman asset allocation model," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 53(2), pages 441-470, June.
    8. Jörn Sass & Dorothee Westphal & Ralf Wunderlich, 2017. "Expert Opinions And Logarithmic Utility Maximization For Multivariate Stock Returns With Gaussian Drift," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-41, June.
    9. Jorn Sass & Dorothee Westphal & Ralf Wunderlich, 2018. "Diffusion Approximations for Expert Opinions in a Financial Market with Gaussian Drift," Papers 1807.00568, arXiv.org, revised Mar 2020.
    10. Abdelali Gabih & Ralf Wunderlich, 2023. "Portfolio Optimization in a Market with Hidden Gaussian Drift and Randomly Arriving Expert Opinions: Modeling and Theoretical Results," Papers 2308.02049, arXiv.org, revised Jun 2024.
    11. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2024. "Power utility maximization with expert opinions at fixed arrival times in a market with hidden Gaussian drift," Annals of Operations Research, Springer, vol. 341(2), pages 897-936, October.
    12. Qi, Yue & Liao, Kezhi & Liu, Tongyang & Zhang, Yu, 2022. "Originating multiple-objective portfolio selection by counter-COVID measures and analytically instigating robust optimization by mean-parameterized nondominated paths," Operations Research Perspectives, Elsevier, vol. 9(C).
    13. Jorn Sass & Dorothee Westphal & Ralf Wunderlich, 2016. "Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift," Papers 1601.08155, arXiv.org, revised Mar 2016.
    14. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2023. "Power Utility Maximization with Expert Opinions at Fixed Arrival Times in a Market with Hidden Gaussian Drift," Papers 2301.06847, arXiv.org, revised Jun 2024.
    15. Antonio Santos, 2016. "Static and dynamic portfolio allocation with nonstandard utility functions," EcoMod2016 9375, EcoMod.
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    17. Abdelali Gabih & Hakam Kondakji & Jorn Sass & Ralf Wunderlich, 2014. "Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift," Papers 1402.6313, arXiv.org.

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