# Modified Omega Ratio Favors Rewarding Asset Behavior

The Omega Ratio can be modified so that it favors return distributions that are skewed to the right with a positive mean, and an exponentially decreasing left-tail. This penalizes dangerous asset behavior which can potentially exist as an edge case.

Shadwick and Keating proposed the Omega Ratio in 2002 to address the drawbacks of traditional performance benchmarks, like the Sharpe Ratio. It is the probability-weighted gains divided by the probability weighted-loss of an asset, and is described here.

Han Wang proposes a modified Omega Ratio that penalizes specific returns distributions that can mislead investors into accepting more risk than appropriate. It is given by the following equation.

Ω0 is the Omega Ratio with a threshold return of 0, and E[Win] and E[Loss] are the arithmetic means of the returns above and below a threshold of zero.  The threshold return is the minimum acceptable return in the standard definition of the Omega Ratio.

The basis for the modification is as follows

• max(Ω0 – 1, 0) favors an Omega Ratio that spends more time winning than losing. This change eliminates Omega Ratios of less than 1 (with a lower bound of zero)
• the multiplication by E[Win]/E[Loss] rewards returns distributions that have a positive mean, but with a tail that rapidly falls off (thus reducing the impact of low-probability, high impact events).
Assets and asset weights in a portfolio can be selected such that its Omega Ratio is maximized. This minimizes the risk of extreme losses (but with potentially greater variance than predicted by standard mean-variance optimization).

The modification further improves the potential of the Omega Ratio as an asset allocation tool to give portfolios with a more attractive returns distribution.

## Calculate the Modified Omega Ratio in Excel

The modified Omega Ratio is implemented  in Excel as follows.

{ = MAX(SUM(IF(E17:E66 > B5, E17:E66 – B5, “”)) / – SUM(IF(E17:E66 < B5, E17:E66 – B5,””)) – 1,0) * AVERAGE( IF ( E17:E66 > B5, E17:E66,””)) / -AVERAGE(IF(E17:E66 < B5, E17:E66, “”)) }

where the braces {} represent a matrix formula entered with CTRL+SHIFT+ENTER, the returns are in cells E17:E66, and B5 is equal to the threshold value of zero.