{"title":"Sortino(γ): A Modified Sortino Ratio With Adjusted Threshold","authors":"Yoram Kroll, Andrea Marchioni, Moshe Ben-Horin","doi":"10.33423/jaf.v23i6.6699","DOIUrl":null,"url":null,"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.\nWe 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.","PeriodicalId":505950,"journal":{"name":"Journal of Accounting and Finance","volume":"75 6","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Accounting and Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33423/jaf.v23i6.6699","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.