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On the impact of semidefinite positive correlation measures in portfolio theory

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  • Sergio Ortobelli
  • Tomáš Tichý

Abstract

In this paper potential usage of different correlation measures in portfolio problems is studied. We characterize especially semidefinite positive correlation measures consistent with the choices of risk-averse investors. Moreover, we propose a new approach to portfolio selection problem, which optimizes the correlation between the portfolio and one or two market benchmarks. We also discuss why should correlation measures be used to reduce the dimensionality of large scale portfolio problems. Finally, through an empirical analysis, we show the impact of different correlation measures on portfolio selection problems and on dimensionality reduction problems. In particular, we compare the ex post sample paths of several portfolio strategies based on different risk measures and correlation measures. Copyright Springer Science+Business Media New York 2015

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  • Sergio Ortobelli & Tomáš Tichý, 2015. "On the impact of semidefinite positive correlation measures in portfolio theory," Annals of Operations Research, Springer, vol. 235(1), pages 625-652, December.
    • Handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:625-652:10.1007/s10479-015-1962-x
    DOI: 10.1007/s10479-015-1962-x
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    10. Sergio Ortobelli Lozza & Enrico Angelelli & Daniele Toninelli, 2011. "Set-Portfolio Selection with the Use of Market Stochastic Bounds," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 47(0), pages 5-24, November.
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    2. David Neděla & Sergio Ortobelli & Tomáš Tichý, 2024. "Mean–variance vs trend–risk portfolio selection," Review of Managerial Science, Springer, vol. 18(7), pages 2047-2078, July.
    3. Anlan Wang & Aleš Kresta & Tomáš Tichý, 2024. "Evaluation of strategy portfolios," Computational Management Science, Springer, vol. 21(1), pages 1-27, June.
    4. Noureddine Kouaissah & Sergio Ortobelli Lozza & Ikram Jebabli, 2022. "Portfolio Selection Using Multivariate Semiparametric Estimators and a Copula PCA-Based Approach," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 833-859, October.
    5. repec:prg:jnlpep:v:preprint:id:636:p:1-28 is not listed on IDEAS
    6. Kouaissah, Noureddine, 2021. "Using multivariate stochastic dominance to enhance portfolio selection and warn of financial crises," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 480-493.
    7. Juszczuk, Przemysław & Kaliszewski, Ignacy & Miroforidis, Janusz & Podkopaev, Dmitry, 2022. "Mean--variance portfolio selection problem: Asset reduction via nondominated sorting," The Quarterly Review of Economics and Finance, Elsevier, vol. 86(C), pages 263-272.
    8. Bohumil Stádník & Václav Žďárek, 2017. "Volatility Strangeness of Bonds - How to Define and What Does it Bring?," Prague Economic Papers, Prague University of Economics and Business, vol. 2017(5), pages 602-629.
    9. Sergio Ortobelli & Noureddine Kouaissah & Tomáš Tichý, 2019. "On the use of conditional expectation in portfolio selection problems," Annals of Operations Research, Springer, vol. 274(1), pages 501-530, March.
    10. Mohammad Mehdi Hosseinzadeh & Sergio Ortobelli Lozza & Farhad Hosseinzadeh Lotfi & Vittorio Moriggia, 2023. "Portfolio optimization with asset preselection using data envelopment analysis," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(1), pages 287-310, March.

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