| Omega ratio 101 |
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| 24/03/2008 | |
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François Oustry, CEO of RaisePartner, answers this week's questions on the Omega ratio. 1. What is the Omega Ratio? The Omega ratio is the probability-adjusted ratio of gains to losses relative to a given threshold return. The higher Omega the better: A high Omega means that there is more density return on the right of the threshold return than on the left side. The Omega ratio uses all the information contained within the historical (or simulated) returns series of the financial instrument. It is especially adapted to asymmetric distributions where risk is not captured by the sole volatility. As pointed out by Kazemi, Schneeweis, Gupta (2003), the Omega ratio can be formulated as a call-put ratio: it is the ratio of the call price to the put price for the chosen threshold. 2. How does it compare to and differ from the Sharpe and Sortino ratios? On the one hand, the Sharpe and Sortino ratios are computed based on the sole knowledge of the two first moments of the distribution. The Sharpe ratio measures the excess return to volatility ratio while the Sortino ratio estimates the excess return to "bad" volatility ratio (also called semi-volatility or downside volatility, which is a truncated version of the second-order moment). On the other hand, the Omega ratio takes into account all the moments of the distribution (mean return, volatility, skewness, kurtosis and higher moments). As a consequence, it is valid for non-normal returns and suitable for the asymmetric nature of hedge fund returns for instance. 3. How can the Omega ratio be used to optimize a fund of hedge fund portfolio? When did it start to gain in popularity? The Omega ratio was introduced by Keating and Shadwick in 2002 ("A universal Performance Measure" - The Finance Development Centrer, London). Since then, it has become increasingly popular, partly because it is very intuitive and easy to compute. The Omega ratio derives its power from its universality: it takes into account all the moments of the distribution, hence it is valid to deal with non-normal returns. As opposed to the Sharpe ratio, it is suitable for the asymmetric nature of hedge fund returns. In 2007, the failures of standard approaches based on static second order moments led to major losses in the hedge fund industry and contributed to the growing interest for advanced measures such as the Omega ratio. Indeed, using Omega as a risk measure to construct a fund of hedge fund reduces the extreme negative risk of the portfolio: it selects the assets with the lowest density below the threshold return without altering the upside part of the distribution. 4. How has the application of the Sharpe ratio been misapplied by hedge fund portfolios and how does the Omega ratio correct that? What are its advantages and constraints? Mean-variance optimization (introduced by H. Markowitz) is equivalent to finding an optimal Sharpe ratio for a given target return. This optimization approach is suitable for (close to) normally distributed returns. But the Sharpe ratio explains only part of the risk for asymmetric returns and can even be misleading, as it assumes that all the risk is explained by the 2 first moments of the distribution. As a consequence, monitoring and optimising the Sharpe ratio in a static framework is not sufficient to determine the shape of the whole distribution of returns (fat tails, or asymmetry for instance), especially when dealing with hedge funds. The Omega ratio takes into account all the moments of the distribution of returns. It might be tempting to formulate an optimisation problem consisting in maximising the Omega ratio given some business constraints, but this approach has a major drawback: the Omega ratio is not convex and leads to unstable and dangerous solutions. The best choice in practise is not always to implement the exact formulation of the optimisation problem to be solved. To overcome this issue, it is possible to solve a robustified convex formulation of the Omega ratio optimisation problem.http://www.raisepartner.com/?rep=contact |
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