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# Sortino ratio

The Sortino ratio 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. It is thus a measure of risk-adjusted returns that is demonstrably more accurate than the Sharpe ratio. [ [http://www.agsm.edu.au/eajm/0803/Paper_5_Chaudhry_Johnson.html www.agsm.edu.au] ]

The ratio is calculated as:

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

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 downside risk. The downside risk is the target semideviation = square root of the target semivariance (TSV). TSV is the return distribution's lower-partial moment of degree 2 (LPM2).

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

where $T$ is often taken to be the risk free interest rate and $f\left(\right)$ is the pdf of the returns. $DR$ can also be thought of, and calculated from a sequence of historical returns $x$ as, the root mean square underperformance $U$, where $U = x - T$ if $x - T < 0$, otherwise $U = 0$.

Thus, the ratio is the actual rate of return in excess of the investor's target rate of return, per unit of downside risk.

The ratio was created by Brian M. Rom [ [http://www.sortino.com/htm/Sortino%20Ratio.htm Sortino ratio] ] in 1986 as an element of Investment Technologies' [ [http://www.investmenttechnologies.com www.investmenttechnologies.com] ] Post-Modern Portfolio Theory portfolio optimization software.

ee also

*Post-modern portfolio theory
*Upside potential ratio

References

Wikimedia Foundation. 2010.

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