Sortino(γ): A Modified Sortino Ratio With Adjusted Threshold

Yoram Kroll, Andrea Marchioni, Moshe Ben-Horin
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Abstract

A portfolio’s Sortino ratio is strongly affected by the risk-free vs. risky assets mix, except for the case where the threshold, T is equal to the risk-free rate. Therefore, if T differs from the risk-free rate, the portfolio’s Sortino ratio could potentially be increased by merely changing the mix of the risk-free and the risky components. The widely used Sharpe ratio, on the other hand, does not share this caveat. We introduce a modified Sortino ratio, Sortino(γ), which is invariant concerning the portfolio’s risk-free vs. risky assets mix and eliminates the above deficiency. The selected threshold T(γ), mimics the portfolio composition in the sense that it equals to the risk-free rate plus γ times the portfolio’s equity risk premium. Higher selected γ reflects higher risk/loss aversion. We propose a procedure for optimizing the composition of the risky portion of the portfolio to maximize the Sortino(γ) ratio. In addition, we show that Sortino(γ) is consistent with first and second-order stochastic dominance with riskless asset rules.
Sortino(γ):调整阈值的修正 Sortino 比率
投资组合的 Sortino 比率受无风险资产与风险资产组合的影响很大,但临界值 T 等于无风险利率的情况除外。因此,如果 T 与无风险利率不同,只需改变无风险与风险资产的组合,就有可能提高投资组合的 Sortino 比率。我们引入了修正的 Sortino 比率 Sortino(γ),它对投资组合的无风险与风险资产组合保持不变,并消除了上述缺陷。所选阈值 T(γ) 模拟投资组合的构成,即等于无风险利率加上投资组合股票风险溢价的 γ 倍。所选 γ 越高,表明风险/损失规避程度越高。我们提出了一个优化投资组合风险部分构成的程序,以最大化 Sortino(γ)比率。此外,我们还证明了 Sortino(γ)符合无风险资产规则下的一阶和二阶随机优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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