# Best Math To Know To Work At A Hedge Fund The Omega Ratio – A Better Investment Performance Benchmark

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## The Omega Ratio – A Better Investment Performance Benchmark

Investors often use performance benchmarks such as 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 addresses these shortcomings and provides 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 widely displayed in fund fact 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, returns are classically bell-shaped. For many investment vehicles, this is not necessarily the case. Hedge funds and other investments often exhibit skewness and kurtosis in their returns. Skewness and kurtosis are mathematical terms that indicate distributions that are wider (or narrower) or taller (or shorter) than is typical of a normal distribution.

Second, most investors think of risk as the probability of a loss, i.e. the size of the left side of the distribution. This is not what the standard deviation represents, which only indicates the dispersion of investment returns around the mean. By discarding information from the empirical distribution of returns, the standard deviation does not adequately represent the risk of 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 partly addressed 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 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 Ratio was developed to address the errors of the Sharpe Ratio. The Omega ratio is defined as the area of ​​a distribution of returns above a threshold divided by the area of ​​a distribution of returns below a threshold. In other words, it is the probability-weighted 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 return distribution and, more 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 such as spreadsheets or other math packages.

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