Investors typically use performance benchmarks like the Sharpe Ratio or the Sortino Ratio to rank mutual funds, ETFs, and index trackers. However, these common performance benchmarks have several drawbacks and can often be very misleading. The Omega Ratio, however, addresses these shortcomings and delivers a far more sophisticated method of ranking investments.
The Sharpe Ratio originated in the 1960s and is also known as the reward-to-risk ratio. It's the effective return of a fund divided by its standard deviation, and its primary advantage is that it is widely given in fund data sheets. The standard deviation is employed by the Sharpe Ratio as a proxy for risk. However, this is misleading for several very important reasons.
Firstly, standard deviation assumes that investment returns are normally distributed. In other words, the returns have the classic bell-shape. For many investment vehicles, this is not necessarily the case. Hedge funds and other investments often display skew and kurtosis in their returns. Skew and kurtosis are mathematical terms that indicate wider (or narrower) or taller (or shorter) distributions than that typical of a normal distribution.
Secondly, most investors think of risk as the probability of making a loss - in other words the size of the left-hand side of the distribution. This is not what is represented by the standard deviation, which merely indicates how widely dispersed investment returns around the mean are. By discarding information from the empirical returns distribution, standard deviation does not adequately represent the risk of making extreme losses.
Thirdly, the standard deviation penalizes variation above the mean and variation below the mean equally. However, most investors only worry about variation below the mean, but positively encourage variation above the mean. This point is partly address in the Sortino Ratio, which is similar to the Sharpe Ratio but only penalizes downside deviation.
Finally, the historical average is used to represent the expected return. This again is misleading because the average gives equal weighting to returns in the far past and returns in the recent past. The later are a better indication of future performance than the former.
The Omega Ratio was developed to address the failures of the Sharpe Ratio. The Omega Ratio is defined as the area of the returns distribution above a threshold divided by the returns of a distribution below a threshold. In other words, it's the probability-weighed upside divided by the probability-weighted downside (with a higher value being better than a lower value). This definition elegantly captures all the critical information in the returns distribution, and more importantly adequately describes the risk of making extreme losses.
However, an investment with a high Omega Ratio can be more volatile than an investment with a high Sharpe Ratio.
Both the Sharpe Ratio and Omega Ratio can be easily calculated using tools like spreadsheets or other math packages.
Samir H Khan writes for http://investexcel.net, a repository of tools and commentary for investors and quantitative analysts. For example, the website offers a spreadsheet which calculates the Omega Ratio.
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