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

Author

Listed:
  • Ran Ji

    (George Washington University)

  • Miguel A. Lejeune

    (George Washington University)

  • Srinivas Y. Prasad

    (George Washington University)

Abstract

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
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