## Reference Materials

## Omega

## How Is it Useful?

Omega represents one useful way of understanding tail risk, the impact that extreme observations have on an overall set of numbers. If the returns of a manager are close to the minimum acceptable return (MAR) breakpoint, they don’t strongly affect omega. However, if many returns lie above or below the MAR, or if the returns are extreme, those returns will impact the value of omega significantly.

## What Is a Good Number?

Similar to all of the other return-versus-risk ratios, the higher the omega the better. One hopes to see many returns above the MAR. Conversely, one hopes to see few observations below the MAR.

Omega is an absolute-return way of quantifying return and risk, so there is no breakpoint above which an omega can be considered good. Omega for an individual manager must be compared to omega for an index or omegas for a peer group to be placed in a proper context.

## What Are the Limitations?

Omega compares the good observations against the bad observations, rolled into a single number. One might want to separate these two elements and observe them independently. Two other statistics, upside omega and downside omega, accomplish this.

## What Does the Graph Show Me?

The graph below orders the monthly returns from worst-to-first. On the left-most portion of the graph is the worst month, and from left to right are the second-worst months, third-worst months, etc. until we get to the best, highest returns on the far right of the S-curve. The graph also shows the range in which most of the observations occur

The graph is split by the MAR, in this case zero percent. The count and scale of observations above the MAR line are shaded in green. This area should be large. The count and scale of observations below the MAR are shaded in red. This area should be small. Omega is the green area divided by the red area.

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## What Are Typical Values?

One would assume that omega would have very different values during the bull markets of the 1980s and 1990s versus the bear market-dominated 2000s. However, looking at the raw numbers it isn’t immediately obvious a big difference between decades. One must look more closely and think back to what omega is showing us to recognize the sizable difference between decades. Keep in mind omega represents the good, green area divided by the bad, red area in the graphs below. During the 1980s and 1990s, the ratio of green-to-red typically stood at 2-to-1. During the difficult 2000s, the ratios for many asset classes were closer to 1.25-to-1, meaning there was almost as much bad, red area as good, green area.

Omega was first proposed by Con Keating and William Shadwick in their 2002 paper “A Universal Performance Measure”. Omega is the ratio of two integrals: the area above the minimum acceptable return (MAR) in the numerator and the area below the MAR as the denominator. Omega captures all four moments of the distribution (return, standard deviation, skewness, and kurtosis) in a single measure.