Omega and Kappa Statistics

Introduced in 2002 by Keating and Shadwick, Omega ratio is a relatively new addition in a hedge fund metrics library. By employing higher moments and taking into account actual shapes of distributions of returns, this measure is well-suited for hedge fund risk assessment, because of non-normality of their distributions.

What are the Omega and Kappa ratios?

The Omega ratio is the ratio of probability weighted gains and losses about a specified return threshold. As shown in the diagram, it involves partitioning returns into loss and gain above and below a return threshold and then dividing the corresponding gain area into the loss area. In turn, the Kappa ratio presents a generalization of higher moments (n) relative to a return threshold:


kappa

It is easy to show that the Omega ratio is expressed via the Kappa ratio of the first moment, i.e.

The commonly used Sortino ratio is also the equivalent of the second moment Kappa ratio i.e.

kappa3

The Omega and Kappa risk statistics are included in the following Risk Shell components and modules:

  • Screening filters
  • Risk engine
  • Peer Group Analysis, as selectable statistics
  • Side-by-Side – comparative analysis statistics
  • Portfolio Optimization, the Omega statistic is one of the objective functions available
  • Optimization Batch Backtesting

 

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