Investors typically use performance criteria such as the Sharpe ratio or the Sortino ratio to rank mutual funds, ETFs and index trackers. However, these common performance criteria have several drawbacks and can often be very misleading. Omega Ratio addresses these shortcomings and offers a far more sophisticated method for ranking investments.
The Sharpe ratio originated in the 1960s and is also known as the reward / risk ratio. This is the effective return of a fund divided by its standard deviation, and its main advantage is that it is widely given in the fund’s data sheets. The standard deviation is used by the Sharpe ratio as a risk proxy. However, this is misleading for several very important reasons.
First, the standard deviation assumes that the return on investment is usually distributed. In other words, the returns have the classic shape of a bell. This is not necessarily the case for many investment instruments. Hedge funds and other investments often show distortions and eccentricities in their returns. Oblique and courtesy are mathematical terms that indicate wider (or narrower) or higher (or shorter) distributions than those typical of the normal distribution.
Second, most investors think of risk as a probability of loss – in other words, the size of the left side of the distribution. This is not represented by the standard deviation, which simply shows how widely dispersed the return on investment is around the average. By discarding information from the empirical distribution of returns, the standard deviation does not adequately pose the risk of extreme losses.
Third, the standard deviation penalizes both the variation above the mean and the variation below the mean. However, most investors only worry about variations below the average, but positively encourage variations above the average. This point is partly an address in the Sortino ratio, which is similar to the Sharpe ratio, but only punishes the negative deviation.
Finally, the historical average is used to represent the expected return. This is again misleading, because the average value gives equal weight to the return in the distant past and the return in the recent past. The latter are a better indicator of future results than the previous ones.
The Omega ratio is designed to deal with the failures of the Sharpe ratio. The Omega ratio is defined as the area of the return distribution above the threshold divided by the area of the return distribution below the threshold. In other words, this is the up-weighted probability divided by the probability-weighted disadvantage (with a higher value, which is better than a lower value). This definition elegantly captures all the critical information in the return distribution and, more importantly, adequately describes the risk of making extreme losses.
However, investing in a high omega ratio may be more volatile than investing in a high Sharpe ratio.
Both the Sharpe ratio and the Omega ratio can be easily calculated using tools such as spreadsheets or other mathematical packages.