An Investigation into Performance Rankings of the Omega Ratio vs the Sharpe Ratio Applied to South African General Equity Unit Trusts

Abstract

The Omega function is a relatively newly developed performance measure, falling in the class of downside risk measures. This measure does not make any assumptions regarding the return distributions evaluated, but incorporates the actual return distribution in the calculation.The sensitivity of this measure to simulated changes within the class of stable distributions was investigated, within a range of parameters that was representative of the South African investment environment. The Omega and Sharpe ratios calculated for these distributions were ranked and compared. Even though the rankings were largely similar, discrepancies did occur. On investigation it was found that these discrepancies were caused by the inability of the Sharpe measure to differentiate between increased volatility caused by higher probability weighted gains (or positive skewness) and losses, as the Sharpe ratio penalises funds for volatility.The simulated tests were extended to various distributions, which have different risk profiles and distribution shapes, and ranked. A higher incidence of ranking differences occurred due to the inability of the Sharpe ratio to differentiate between gains and losses, or to correctly account for the risk of positively skewed distributions. Negative Sharpe ratios, caused by the average realized returns being exceeded by the threshold (target) rate, resulted in incorrect rankings.Normally, practical performance evaluation is not initiated with a detailed analysis of the return distributions in order to determine which performance measure is more appropriate. The Omega measure, however, incorporates the distribution into the calculation, which is not the case with the Sharpe measure. If the distributions are normal, the Omega measure gives exactly the same result as the Sharpe measure. However, where return distributions diverge from normality, the Omega measure will incorporate the divergence, whilst the Sharpe measure fails in this regard. The result is a ranking of performance that is more relevant to investor decision-making.