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Possibilistic mean–variance portfolios versus probabilistic ones: the winner is..

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  • Marco Corazza

    (Ca’ Foscari University of Venice)

  • Carla Nardelli

    (University of Bergamo)

Abstract

In this paper, we compare the mean–variance portfolio modeling based on the possibilistic representation of the future stock returns to the one based on the classical probabilistic modelization of the same returns. There exist several different definitions of possibilistic mean, possibilistic variance and possibilistic covariance. In this paper, we consider definitions recently proposed in the literature for modeling portfolio selection problems: the possibilistic mean and variance à la Carlsson–Fullér–Majlender, the lower possibilistic mean and variance, and the upper possibilistic mean and variance. In particular, we mean to answer to the following research questions: first, to check whether, from a methodological and theoretical standpoint, it is possible to detect elements of superiority of one of the two approaches with respect to the other one; then, to check whether, from an operational point of view, one of the two approaches is more effective than the other one in terms of virtual-future performances. We disclosed that, on the basis of the results we obtained, the winner is the probabilistic approach.

Suggested Citation

  • Marco Corazza & Carla Nardelli, 2019. "Possibilistic mean–variance portfolios versus probabilistic ones: the winner is..," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 51-75, June.
  • Handle: RePEc:spr:decfin:v:42:y:2019:i:1:d:10.1007_s10203-019-00234-1
    DOI: 10.1007/s10203-019-00234-1
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    References listed on IDEAS

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    1. Liu, Yong-Jun & Zhang, Wei-Guo, 2013. "Fuzzy portfolio optimization model under real constraints," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 704-711.
    2. Ruey-Chyn Tsaur, 2015. "Fuzzy portfolio model with fuzzy-input return rates and fuzzy-output proportions," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(3), pages 438-450, February.
    3. Zhang, Wei-Guo & Zhang, Xi-Li & Xiao, Wei-Lin, 2009. "Portfolio selection under possibilistic mean-variance utility and a SMO algorithm," European Journal of Operational Research, Elsevier, vol. 197(2), pages 693-700, September.
    4. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
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    More about this item

    Keywords

    Mean–variance portfolio selection modeling; Possibilistic mean; variance and covariance à la Carlsson–Fullér–Majlender; Lower and upper possibilistic means; variances and covariances; Comparison;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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