## Omega

Omega compares the count and scale of individual return points above a minimum accepted return threshold (MAR) against the count and scale of individual return points below the MAR threshold.

Like many statistical ratios, Omega is a return-vs.-risk tradeoff metric.  It is a ratio where the analyst hopes to see a large numerator and a small denominator, resulting in an overall ratio that is large number.  Omega is a relative metric where the Omega of one data series must be compared to an index or its peers in order to judge if the Omega is “good” or “bad”; there is no hard-and-fast breakpoint or cut-off point delineating a good Omega from a bad Omega.

In order to calculate Omega it is essential to establish a MAR as a starting point.  The next step in the calculation is that the entire history of periodic returns are sorted from lowest to highest.  The sorted returns are plotted on an S-shaped cumulative distribution chart with the MAR bisecting the distribution in to “bad” points that fall below the MAR cut-off and “good” points that fall above the MAR line.  The areas above and below MAR are calculated.  The area above and below the MAR threshold will be impacted by two things: the number of observations above or below the MAR (i.e. the count) and the distance of the observations from the MAR dividing line (i.e. the scale).

Thus, one hopes Omega’s numerator is large with 1) many observations falling above the MAR and 2) the scale of the observations being far above and beyond the MAR breakpoint.  Conversely one hopes Omega’s denominator is small with 3) few observations falling below the MAR and 4) when occurring, the negative observations are not too far below the MAR cut-off.  As stated before, one would want the overall Omega to be large.

Formula:

Upside Omega and Downside Omega: Upside/Downside Omega simply breaks the two halves of Omega in to its separate parts.  The Upside Omega is numerator as described above; the Downside Omega is the denominator.

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