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The Mean‐Gini Efficient Portfolio Frontier

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  • Haim Shalit
  • Shlomo Yitzhaki

Abstract

A main advantage of the mean‐variance (MV) portfolio frontier is its simplicity and ease of derivation. A major shortcoming, however, lies in its familiar restrictions, such as the quadraticity of preferences or the normality of distributions. As a workable alternative to MV, we present the mean‐Gini (MG) efficient portfolio frontier. Using an optimization algorithm, we compute MG and mean‐extended Gini (MEG) efficient frontiers and compare the results with the MV frontier. MEG allows for the explicit introduction of risk aversion in building the efficient frontier. For U.S. classes of assets, MG and MEG efficient portfolios constructed using Ibbotson (2000) monthly returns appear to be more diversified than MV portfolios. When short sales are allowed, distinct investor risk aversions lead to different patterns of portfolio diversification, a result that is less obvious when short sales are foreclosed. Furthermore, we derive analytically the MG efficient portfolio frontier by restricting asset distributions. The MG frontier derivation is identical in structure to that of the MV efficient frontier derivation. The penalty paid for simplifying the search for the MG efficient frontier is the loss of some information about the distribution of assets.

Suggested Citation

  • Haim Shalit & Shlomo Yitzhaki, 2005. "The Mean‐Gini Efficient Portfolio Frontier," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 28(1), pages 59-75, March.
    • Handle: RePEc:bla:jfnres:v:28:y:2005:i:1:p:59-75
    DOI: 10.1111/j.1475-6803.2005.00114.x
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    Cited by:

    1. Johannes König & Carsten Schröder, 2018. "Inequality-minimization with a given public budget," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 16(4), pages 607-629, December.
    2. Haim Shalit & Frank Hespeler, 2016. "Mean-Extended Gini Portfolios: The Ultimate Frontier," Working Papers 1603, Ben-Gurion University of the Negev, Department of Economics.
    3. Fontanari, Andrea & Cirillo, Pasquale & Oosterlee, Cornelis W., 2018. "From Concentration Profiles to Concentration Maps. New tools for the study of loss distributions," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 13-29.
    4. Fontanari Andrea & Cirillo Pasquale & Oosterlee Cornelis W., 2020. "Lorenz-generated bivariate Archimedean copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 186-209, January.
    5. Migliavacca, Milena & Goodell, John W. & Paltrinieri, Andrea, 2023. "A bibliometric review of portfolio diversification literature," International Review of Financial Analysis, Elsevier, vol. 90(C).
    6. Miguel A. Lejeune & John Turner, 2019. "Planning Online Advertising Using Gini Indices," Operations Research, INFORMS, vol. 67(5), pages 1222-1245, September.
    7. Doron Nisani, 2019. "Ranking Investments Using the Lorenz Curve," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(1), pages 1-9, March.
    8. Haim Shalit, 2024. "The Nonsense of Bitcoin 1n Portfolio Analysis," Working Papers 2401, Ben-Gurion University of the Negev, Department of Economics.
    9. José Claudio Isaias & Pedro Paulo Balestrassi & Guilherme Augusto Barucke Marcondes & Wesley Vieira da Silva & Carlos Henrique Pereira Mello & Claudimar Pereira da Veiga, 2021. "Project Portfolio Selection of Solar Energy by Photovoltaic Generation Using Gini-CAPM Multi-Criteria and Considering ROI Covariations," Energies, MDPI, vol. 14(24), pages 1-21, December.
    10. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
    11. Maria-Teresa Bosch-Badia & Joan Montllor-Serrats & Maria-Antonia Tarrazon-Rodon, 2017. "Analysing assets’ performance inside a portfolio: From crossed beta to the net risk premium ratio," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1270251-127, January.
    12. Doron Nisani & Amit Shelef, 2021. "A statistical analysis of investor preferences for portfolio selection," Empirical Economics, Springer, vol. 61(4), pages 1883-1915, October.
    13. Pierpaolo Angelini & Fabrizio Maturo, 2023. "Tensors Associated with Mean Quadratic Differences Explaining the Riskiness of Portfolios of Financial Assets," JRFM, MDPI, vol. 16(8), pages 1-25, August.
    14. 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.
    15. Haim Shalit, 2021. "The Shapley value decomposition of optimal portfolios," Annals of Finance, Springer, vol. 17(1), pages 1-25, March.
    16. Fontanari Andrea & Cirillo Pasquale & Oosterlee Cornelis W., 2020. "Lorenz-generated bivariate Archimedean copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 186-209, January.
    17. Habibeh Sherafatmand & Saeed Yazdani, 2014. "The management of price risk in Iranian dates: An application of futures instruments," Cogent Economics & Finance, Taylor & Francis Journals, vol. 2(1), pages 1-12, December.
    18. Clark, Ephraim & Kassimatis, Konstantinos, 2014. "Exploiting stochastic dominance to generate abnormal stock returns," Journal of Financial Markets, Elsevier, vol. 20(C), pages 20-38.
    19. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.
    20. Frank Hespeler & Haim Shalit, 2018. "Mean-Extended Gini Portfolios: A 3D Efficient Frontier," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 731-740, March.

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