# Sortino ratio

The Sortino ratio, was created by Brian M. Rom at the software development company, Investment Technologies in 1983. The ratio is named for Dr. Frank A. Sortino, an early popularizer of downside risk optimization. It measures the risk-adjusted return of an investment asset, portfolio or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target, or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted returns, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The ratio is calculated as:

$S = \frac{R-T}{DR}$,

where R is the asset or portfolio realized return; T is the target or required rate of return for the investment strategy under consideration, (T was originally known as the minimum acceptable return, or MAR); DR is the target semideviation = square root of the target semivariance (TSV). TSV is the return distribution's lower-partial moment of degree 2 (LPM2).

$DR = \left( \int_{-\infty}^T (T - x)^2\,f(x)\,dx \right)^{1/2},$

where $T$ is a target rate of return, typically strictly greater than the risk free rate, and $f(\cdot)$ is the pdf of the returns. This can be thought of as the root mean squared underperformance, where the underperformance is the amount by which a return is below target (and returns above target are treated as underperformance of 0).

Thus, the ratio is the actual rate of return in excess of the investor's target rate of return, per unit of downside risk; or, overperformance divided by root-mean-square underperformance.