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Mean-Extended Gini Portfolios: A 3D Efficient Frontier

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Listed:
  • Frank Hespeler

    (Sciences Po)

  • Haim Shalit

    (Ben-Gurion University of the Negev)

Abstract

Using a numerical optimization technique we construct the mean-extended Gini (MEG) efficient frontier as a workable alternative to the mean-variance efficient frontier. MEG enables the introduction of specific risk aversion into portfolio selection. The resulting portfolios are stochastically dominant for all risk-averse investors. Solving for MEG portfolios allows investors to tailor portfolios for specific risk aversion. The extended Gini is calculated by the covariance of asset returns with a weighing function of the cumulative distribution function (CDF) of these returns. In a sample of asset returns, the CDF is estimated by ranking returns. In this case, analytical optimization techniques using continuous gradient approaches are unavailable, thus the need to develop numerical optimization techniques. In this paper we develop a numerical optimization algorithm that finds the portfolio optimal frontier for arbitrarily large sets of shares. The result is a 3-dimension MEG efficient frontier in the space formed by mean, the extended Gini, and the risk aversion coefficient.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:51:y:2018:i:3:d:10.1007_s10614-016-9636-6
    DOI: 10.1007/s10614-016-9636-6
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    References listed on IDEAS

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    1. 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.
    2. Haim Shalit & Shlomo Yitzhaki, 2009. "Capital market equilibrium with heterogeneous investors," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 757-766.
    3. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-185, March.
    4. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    5. Shalit, Haim & Yitzhaki, Shlomo, 1984. "Mean-Gini, Portfolio Theory, and the Pricing of Risky Assets," Journal of Finance, American Finance Association, vol. 39(5), pages 1449-1468, December.
    6. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-628, October.
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