Upside omega and downside omega are simply the numerator and denominator of the omega ratio separated into individual parts. While the omega ratio is useful for quantifying the trade-off between upside gains and downside losses, sometimes the details get lost because both the good and the bad are rolled into one number. By breaking omega into its constituent parts, one can focus only on the return or only on the risk element.
One would want the upside omega to be large, indicating 1) a large number of gains, 2) gains far above and beyond the MAR, or 3) a combination of the two. By the same token, downside omega is hoped to be small, indicating 1) few returns below the MAR, 2) losses not too far below the MAR, or 3) a combination of the two. One should keep both the time frame and the asset class being observed under consideration.
The values associated with upside and downside omega are abstractions. Taken as a stand-alone numbers it is difficult to understand what they mean. It is almost necessary to visualize the charts to the right or on the reverse side of this page in order to grasp the meaning of the upside and downside omega.
The upper graph shows the count and scale of observations above the MAR, which is the upside omega. The lower graph shows the count and scale of observations below the MAR, which is the downside omega. The graphs feature two investments: an aggressive manager in red and a conservative manager in blue. The aggressive red manager displays substantial gains coupled with a large number of losses. The conservative investment in blue differs substantially. It shows limited gains but also protects well on the downside. Omega rolls both of these numbers into a single ratio.
The numbers in the table below illustrate the usefulness of breaking omega into its upside and downside components. If one were to look only at the omega ratio in aggregate, the typical values for equity asset classes aren’t well differentiated. Most values fall in the 1.7 to 1.9 range. The omegas for large cap US stocks and emerging markets are close to identical. However, by looking at upside omega and downside omega separately, one can see that upside and downside areas are roughly half again as large for emerging markets as they are for large cap US stocks.
The upside omega is an integral, defined by the minimum acceptable return (MAR) on one axis and the count and scale of observations above the MAR at the upper bound. Downside omega is the same, but counting the observations below the MAR.
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