Sortino ratio, Omega ratio क्या है?

The Sortino ratio is the mean return in excess of a minimum acceptable return, divided by the downside deviation, the root mean square of the shortfalls below it (Sortino and Price). The Omega ratio at a threshold $L$ is $\mathbb{E}[(r-L)^+]\,/\,\mathbb{E}[(L-r)^+]$, the expected gain above the threshold over the expected loss below it (Keating and Shadwick); it equals one at the mean.