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

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.