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

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 with respect to the portfolio’s risk-free vs. risky assets mix, and hence 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.