IDEAS home Printed from
   My bibliography  Save this article

Properties, formulations, and algorithms for portfolio optimization using Mean-Gini criteria


  • Ran Ji

    () (George Washington University)

  • Miguel A. Lejeune

    () (George Washington University)

  • Srinivas Y. Prasad

    () (George Washington University)


We study an extended set of Mean-Gini portfolio optimization models that encompasses a general version of the mean-risk formulation, the Minimal Gini model (MinG) that minimizes Gini’s Mean Differences, and the new risk-adjusted Mean-Gini Ratio (MGR) model. We analyze the properties of the various models, prove that a performance measure based on a Risk Adjusted version of the Mean Gini Ratio (RAMGR) is coherent, and establish the equivalence between maximizing this performance measure and solving for the maximal Mean-Gini ratio. We propose a linearization approach for the fractional programming formulation of the MGR model. We also conduct a thorough evaluation of the various Mean-Gini models based on four data sets that represent combinations of bullish and bearish scenarios in the in-sample and out-of-sample phases. The performance is (i) analyzed with respect to eight return, risk, and risk-adjusted criteria, (ii) benchmarked with the S&P500 index, and (iii) compared with their Mean-Variance counterparts for varying risk aversion levels and with the Minimal CVaR and Minimal Semi-Deviation models. For the data sets used in our study, our results suggest that the various Mean-Gini models almost always result in solutions that outperform the S&P500 benchmark index with respect to the out-of-sample cumulative return. Further, particular instances of Mean-Gini models result in solutions that are as good or better (for example, MinG in bullish in-sample scenarios, and MGR in bearish out-of-sample scenarios) than the solutions obtained with their counterparts in Mean-Variance, Minimal CVaR and Minimal Semi-Deviation models.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:annopr:v:248:y:2017:i:1:d:10.1007_s10479-016-2230-4
    DOI: 10.1007/s10479-016-2230-4

    Download full text from publisher

    File URL:
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. 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.
    2. Frank Fabozzi & Dashan Huang & Guofu Zhou, 2010. "Robust portfolios: contributions from operations research and finance," Annals of Operations Research, Springer, vol. 176(1), pages 191-220, April.
    3. Elton, Edwin J & Gruber, Martin J & Blake, Christopher R, 1996. "Survivorship Bias and Mutual Fund Performance," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1097-1120.
    4. Sergio Ortobelli & Svetlozar Rachev & Haim Shalit & Frank Fabozzi, 2009. "Orderings and Probability Functionals Consistent with Preferences," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 81-102.
    5. Pierre Bonami & Miguel Lejeune, 2009. "An Exact Solution Approach for Integer Constrained Portfolio Optimization Problems Under Stochastic Constraints," Post-Print hal-00421756, HAL.
    6. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 335-346.
    7. 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.
    8. S. V. Stoyanov & S. T. Rachev & F. J. Fabozzi, 2007. "Optimal Financial Portfolios," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 401-436.
    9. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    10. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    11. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    12. Fisher, Lawrence & Lorie, James H, 1970. "Some Studies of Variability of Returns on Investments in Common Stocks," The Journal of Business, University of Chicago Press, vol. 43(2), pages 99-134, April.
    13. 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.
    14. 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.
    15. Farinelli, Simone & Ferreira, Manuel & Rossello, Damiano & Thoeny, Markus & Tibiletti, Luisa, 2008. "Beyond Sharpe ratio: Optimal asset allocation using different performance ratios," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2057-2063, October.
    16. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    17. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    18. Bey, Roger P. & Howe, Keith M., 1984. "Gini's Mean Difference and Portfolio Selection: An Empirical Evaluation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(3), pages 329-338, September.
    19. Svetlozar Rachev & Sergio Ortobelli & Stoyan Stoyanov & Frank J. Fabozzi & Almira Biglova, 2008. "Desirable Properties Of An Ideal Risk Measure In Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 19-54.
    20. 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.
    21. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    22. Tiago P. Filomena & Miguel A. Lejeune, 2014. "Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 308-329, April.
    23. Gilles Sanfilippo, 2003. "Stocks, bonds and the investment horizon: a test of time diversification on the French market," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 345-351.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Ruchika Sehgal & Aparna Mehra, 2019. "Enhanced indexing using weighted conditional value at risk," Annals of Operations Research, Springer, vol. 280(1), pages 211-240, September.
    2. Zhenlong Jiang & Ran Ji & Kuo-Chu Chang, 2020. "A Machine Learning Integrated Portfolio Rebalance Framework with Risk-Aversion Adjustment," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 13(7), pages 1-20, July.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:248:y:2017:i:1:d:10.1007_s10479-016-2230-4. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Springer Nature Abstracting and Indexing). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.