Copula-based Black–Litterman portfolio optimization

Maziar Sahamkhadam, Andreas Stephan*, Ralf Östermark

*Corresponding author for this work

    Research output: Contribution to journalArticleScientificpeer-review

    3 Citations (Scopus)
    6 Downloads (Pure)


    We extend the Black-Litterman (BL) approach to incorporate tail dependency in portfolio optimization and estimate the posterior joint distribution of returns using vine copulas. Our novel copula-based BL (CBL) model leads to flexibility in modeling returns symmetric and asymmetric multivariate distribution from a range of copula families. Based on a sample of the Eurostoxx 50 constituents (also for S&P 100 as robustness check), we evaluate the performance of the suggested CBL approach and portfolio optimization technique using out-of-sample back-testing. Our empirical analysis and robustness check indicate better performance for the CBL portfolios in terms of lower tail risk and higher risk-adjusted returns, compared to the benchmark strategies.

    Original languageEnglish
    Pages (from-to)1055-1070
    Number of pages16
    JournalEuropean Journal of Operational Research
    Issue number3
    Publication statusPublished - 16 Mar 2022
    MoE publication typeA1 Journal article-refereed


    • Black–Litterman framework
    • Conditional value-at-risk
    • Finance
    • Portfolio optimization
    • Tail constraints
    • Truncated regular vine copula


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