Worst-case analysis of Gini mean difference safety measure

Abstract

The paper introduces the worst-case portfolio optimization models within the robust optimization framework for maximizing return through either the mean or median metrics. The risk in the portfolio is quantified by Gini mean difference. We put forward the worst-case models under the mixed and interval+polyhedral uncertainty sets. The proposed models turn out to be linear and mixed integer linear programs under the mixed uncertainty set, and semidefinite program under interval+polyhedral uncertainty set. The performance comparison of the proposed models on the listed stocks of Euro Stoxx 50, Dow Jones Global Titans 50, S&P Asia 50, consistently exhibit advantage over their conventional non-robust counterpart models on various risk parameters including the standard deviation, worst return, value at risk, conditional value at risk and maximum drawdown of the portfolio.2010 Mathematics Subject Classification. Primary: 91G10, 91B30, 62G35; Secondary: 90C90, 90C05, 90C11.

A Machine Learning Integrated Portfolio Rebalance Framework with Risk-Aversion Adjustment

“…Yitzhaki (1982) firstly proposed adopting Gini's Mean Difference as a risk measure in portfolio analysis. Numerous studies have been contributed to the literature following the stem; see Yitzhaki (1983), Shalit and Yitzhaki (1984), Ringuest et al (2004), Ji et al (2017b), Ji et al (2018), Shalit and Greenberg (2013), Sehgal and Mehra (2017) for examples. We are motivated to use GMD for three main merits: (i) GMD is demonstrated to be consistent with second-order stochastic dominance and is a coherent measure of risk (see Artzner et al 1999); (ii) in contrast to variance, GMD does not require the normality assumption of asset returns nor the quadratic utility function of the investor; and (iii) GMD provides diversity of the constructed portfolios, which is in agreement with the Basel II Accord recommendations (Basel Committee on Banking Supervision 2004).…”