STARR Performance
A key step in the investment management process is measurement and evaluation of portfolio performance. A celebrated performance measure is the Sharpe ratio. It is defined as the expected return divided by the standard deviation of the return and is intended to measure the risk-adjusted return. The Sharpe ratio belongs to the class of reward-to-variability ratios since the standard deviation in the denominator can be viewed as a measure of uncertainty rather than a measure of risk.
Another type of performance measure is the class of reward-to-risk ratios. The performance ratio in which ETL is used as a risk measure is called STARR – Stable Tail-Adjusted Return Ratio. Introduced by Rachev et al. (2006), STARR was originally constructed based on the assumption that asset returns follow the stable-Paretion distribution. In fact, the concept behind STARR can be translated to any distributional assumption. Formally, STARR is defined as the ratio between expected return and the ETL. Since ETL is a downside measure, STARR can be viewed as an improved analogue of the Sortino ratio.
A reward-to-risk ratio based on ETL but emphasizing the behavior of the right tail of the return distribution in the numerator is the Rachev ratio. It is defined as the expected tail return (ETR) at a given confidence level divided by the ETL at another, potentially different, confidence level. The Rachev ratio can be viewed as an improvement of the Omega ratio.