Investors often use performance benchmarks like the Sharpe ratio or 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 addresses these shortcomings and offers a much more sophisticated method of classifying investments.

The Sharpe ratio originated in the 1960s and is also known as the reward-risk ratio. It is the effective return of a fund divided by its standard deviation, and its main advantage is that it is widely provided in fund fact sheets. The standard deviation is used by the Sharpe index 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 show bias and kurtosis in their returns. Bias and kurtosis are mathematical terms that indicate distributions that are wider (or narrower) or taller (or shorter) than typical of a normal distribution.

Second, most investors think of risk as the probability of taking 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 penalizes variation above the mean and variation below the mean equally. However, most investors only care about below-average variance but positively encourage above-average variance. This point is addressed in part in the Sortino Ratio, which is similar to the Sharpe Ratio but only penalizes for 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 Sharpe’s 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 (where a higher value is better than a lower value). This definition elegantly captures all the critical information in the distribution of returns and, most importantly, adequately describes the risk of 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 the Omega ratio can be easily calculated using tools like spreadsheets or other math packages.