The Omega Ratio is used for analyzing the performance data which includes a large numbers of trades, such that the outliers are given minimal weight. The higher the Omega ratio, the better the strategy performance. The Omega calculation involve dividing the returns distribution in two parts- gains and losses, or returns above a threshold and returns below a threshold. In simple forms, it is calculated as the sum of probability weighted gains divided by the losses. Or, the upside potential divided by the downside potential.
r is the threshold return, and
F is cumulative density function of returns.
Traditional performance benchmarks (like Sharpe, Sterling or Sortino Ratio) intrinsically use the mean and standard deviation for returns distribution. This methodology inherently assumes that returns are normally distributed while discarding effects like skew and kurtosis. The Sharpe Ratio considers only the first two moments of return distribution, while the Omega ratio considers all four moments (mean, variance, skewness and kurtosis respectively).
This implicitly assumes that the returns are normally distributed, and discards effects like skew and kurtosis.
The Omega Ratio, however, captures all the information in the returns distribution. It divides the returns distribution into two parts; one part above a threshold and one part below a threshold.
For those using R, the Performance Analytics package includes Omega: https://www.r-bloggers.com/maximizing-omega-ratio/
A spreadsheet for studying the Omega can be found here: https://investexcel.net/omega-ratio-maximize/
More Information: https://www.evestment.com/resources/investment-statistics-guide/omega-ratio