Anyone working in finance or any prudent investor will always be interested in risk – reward ratio. The Omega ratio is one of the those ratios; which measures the performance of financial assets based on the level of returns they offer in return for the risk of investing in them.
The Omega ratio represents the cumulative probability of an investment’s outcome above an investor’s defined return level (a threshold level), to the cumulative probability of an investment’s outcome below an investor’s threshold level. The omega concept divides expected returns into two parts – gains and losses, or returns above the expected rate (the upside) and those below it (the downside).
At the time of its introduction in 2003, the Omega ratio was expected to replace the popular, but flawed, Sharpe ratio as the standard for measuring portfolio performance at financial firms.
The Sharpe ratio: The Sharpe ratio was developed by W.F. Sharpe; which helped investors to measure the return on an investment compared to the risk.
Limitations of Sharpe ratio: The Sharpe ratio is a good measure of risk for large, diversified, liquid investments; where returns follow normal distribution. Investments like hedge funds, returns for which do not follow normal distribution and generally has skewed returns with fat tails; the Sharpe ratio can only be used as one of the several indicators.
Simply put; the Sharpe ratio considers only mean and standard deviation in the calculations of risk – reward ratio which might not be appropriate for negatively skewed returns with fat tails. Any data with skewed return distribution and fat tails should consider skewness and kurtosis while calculating risk to reward ratio.
The Omega Ratio: The Omega ratio, defined as a probability-weighted ratio of gains versus losses given a certain threshold; where threshold is decided by the investor also known as minimum accepted return (MAR). The Omega ratio divides expected returns into two parts – gains and losses, or returns above the expected rate (the upside) and those below it (the downside). Therefore, in simple terms, consider omega as the ratio of upside returns (good) relative to downside returns (bad).
Omega Ratio – The Omega Ratio is a measure of performance that doesn’t assume a normal distribution of returns. Instead, it captures all the information in the historical returns distribution, and is defined by this equation.
r is the threshold return, and
F is cumulative density function of returns.
Thus Omega ratio captures both skew and kurtosis, and other higher moments present in the returns distribution. This means the Omega Ratio is suitable for assessing the risk of investments whose returns distributions are highly asymmetric like hedge fund or certain options strategies.
Advantage of Omega Ratio: The Omega ratio calculations give investor freedom to choose the minimum accepted return; then model the risk associated with investment.
Since omega considers all information available from an investment’s historical return data, it can be used to rank potential investments in a manner specific to the investor’s threshold level. However, the omega decisions are not static for at least two reasons:
- As return information is updated, the probability distribution will change and omega must be updated.
- As an investor’s threshold level changes, the rankings among comparative investments may change.
Therefore, omega allows investors to visualize the trade-off between risk and return at different threshold levels for various investment choices. Note that when the threshold is set to the mean of the distribution, the omega ratio is equal to 1.
The Shortcomings of Omega Ratio: While the Omega ratio should have been a welcome change, it didn’t succeed in replacing the simpler and more popular Sharpe ratio. One of the reasons for this is that finding an ‘optimal portfolio’ using the Omega ratio is a tough task, because it means optimizing all the moments (Skewness and Kurtosis or even higher moments) in the empirical distribution.
A second problem with the Omega ratio in its original form is that the empirical distribution is not a smooth function, because it is built using all the data points without any distributional assumptions. So its cumulative density function has plateaus and does not strictly increase. That makes it difficult to discover optimal portfolios, because optimization algorithms tend to get stuck at these plateaus instead of moving on with the exercise.
Summary: As discussed; the Omega ratio calculations consider all possible data points in other words considers entire return distribution while assessing the performance. The Omega ratio being non-parametric does not have limitations like; return distribution need not be normal which is why it is very helpful while looking into returns and rewards for hedge funds. The minimum accepted return from a portfolio is where an investor has to decide and can either be considered as an advantage or disadvantage.