Investors often use performance benchmarks like the Sharpe Index or the Sortino Index 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 addresses these shortcomings and offers a much more sophisticated method of ranking investments.
The Sharpe ratio originated in the 1960s and is also known as the risk-reward ratio. It is a fund’s effective return divided by its standard deviation, and its main advantage is that it is provided extensively in fund data sheets. The standard deviation is used by the Sharpe ratio as an indicator of risk. However, this is misleading for several very important reasons.
First, the 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 exhibit bias and kurtosis in their returns. Skewness and kurtosis are mathematical terms that indicate distributions that are wider (or narrower) or taller (or shorter) than those typical of a normal distribution.
Second, 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 the standard deviation represents, which simply indicates how spread out the investment returns are around the mean. By discarding information from the distribution of empirical returns, the standard deviation does not adequately represent the risk of suffering extreme losses.
Third, the standard deviation equally penalizes variation above the mean and variation below the mean. However, most investors only care about below-average variation, but positively encourage above-average variation. This point is partly addressed in the Sortino Ratio, which is similar to the Sharpe Ratio but only penalizes downward deviation.
Finally, the historical average is used to represent the expected return. Again, this is misleading because the average gives equal weight to returns from the distant past and returns from the recent past. The latter are a better indication of future performance than the former.
The Omega relationship was developed to address the flaws in the Sharpe relationship. The Omega Ratio is defined as the area of the distribution of returns above a threshold divided by the area of a distribution of returns below a threshold. In other words, it is the up-weighted probability divided by the down-weighted probability (with a higher value being better than a lower value). This definition elegantly captures all the critical information on the distribution of returns and, more importantly, adequately describes the risk of extreme losses.
However, an investment with a high Omega Ratio may be more volatile than an investment with a high Sharpe Ratio.
Both the Sharpe ratio and the Omega ratio can be easily calculated using tools like spreadsheets or other math packages.