Sortino ratio
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The Sortino ratio is a measure of a risk-adjusted return of an investment asset. It is an extension of the Sharpe ratio. While the Sharpe ratio takes into account any volatility in return of an asset, Sortino ratio differentiates volatility due to up and down movements. The up movements are considered desirable and not accounted in the volatility.
That is, the Sortino ratio does not penalize a fund for its upside volatility. The ratio is calculated as
![S = \frac{E[R-R_f]}{\sigma_d}](../../../math/d/0/b/d0b42e0861fb3656a34be3ceb4fe3ed8.png)
,
where R is the asset return, Rf is the return on a benchmark asset, such as the risk free rate of return, E[R − Rf] is the expected excess return, and σd is the downside volatility. The downside volatility is computed using the standard deviation formula, keeping only the contribution of negative excess returns. Other variations use the semivariance as the denominator.
The ratio was developed by Brian M. Rom.
