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Portfolio Selection Problems Consistent With Given Preference Orderings

Author

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  • SERGIO ORTOBELLI LOZZA

    (Department SAEMQ, University of Bergamo, 24127 - Via dei Caniana 2, Bergamo, Italy;
    Department of Finance, VŠB TU Ostrava, 70121 - Sokolská 33, Ostrava, Czech Republic)

  • HAIM SHALIT

    (Department of Economics, Ben-Gurion University, Beer-Sheva, 84105, Israel)

  • FRANK J. FABOZZI

    (EDHEC Business School and EDHEC Risk Institute – France, France)

Abstract

This paper theoretically and empirically investigates the connection between portfolio theory and ordering theory. In particular, we examine three different portfolio problems and the respective orderings used to rank investors' choices: (1) risk orderings, (2) variability orderings, and (3) tracking-error orderings. For each problem, we discuss the properties of the risk measures, variability measures, and tracking-error measures, as well as their consistency with investor choices. Finally, for each problem, we propose an empirical application of several admissible portfolio optimization problems using the US stock market. The proposed empirical analysis permits us to evaluate the ex-post impact of the optimal choices, thereby deriving completely different investors' preference orderings during the recent financial crisis.

Suggested Citation

  • Sergio Ortobelli Lozza & Haim Shalit & Frank J. Fabozzi, 2013. "Portfolio Selection Problems Consistent With Given Preference Orderings," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-38.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:05:n:s0219024913500295
    DOI: 10.1142/S0219024913500295
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    Citations

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    Cited by:

    1. Grechuk, Bogdan & Zabarankin, Michael, 2016. "Inverse portfolio problem with coherent risk measures," European Journal of Operational Research, Elsevier, vol. 249(2), pages 740-750.
    2. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    3. Sergio Ortobelli & Noureddine Kouaissah & Tomáš Tichý, 2017. "On the impact of conditional expectation estimators in portfolio theory," Computational Management Science, Springer, vol. 14(4), pages 535-557, October.
    4. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2020. "An optimization–diversification approach to portfolio selection," Journal of Global Optimization, Springer, vol. 76(2), pages 245-265, February.
    5. Ran Ji & Miguel A. Lejeune & Srinivas Y. Prasad, 2017. "Properties, formulations, and algorithms for portfolio optimization using Mean-Gini criteria," Annals of Operations Research, Springer, vol. 248(1), pages 305-343, January.
    6. Mohd Azdi Maasar & Diana Roman & Paresh Date, 2022. "Risk minimisation using options and risky assets," Operational Research, Springer, vol. 22(1), pages 485-506, March.
    7. Roberto Cervelló-Royo & Francisco Guijarro & Victor Martinez-Gomez, 2019. "Social Performance considered within the global performance of Microfinance Institutions: a new approach," Operational Research, Springer, vol. 19(3), pages 737-755, September.
    8. 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.
    9. Fang, Yi & Post, Thierry, 2022. "Optimal portfolio choice for higher-order risk averters," Journal of Banking & Finance, Elsevier, vol. 137(C).
    10. 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.

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