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

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• 作者：Ran Ji ; Miguel A. Lejeune ; Srinivas Y. Prasad
• 关键词：Mean ; Gini model ; Mean ; Gini ratio ; Portfolio optimization
• 刊名：Annals of Operations Research
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：248
• 期：1-2
• 页码：305-343
• 全文大小：
• 刊物类别：Business and Economics
• 刊物主题：Operation Research/Decision Theory; Combinatorics; Theory of Computation;
• 出版者：Springer US
• ISSN：1572-9338
• 卷排序：248

文摘

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.