Global InformationRachev ratio information
The Rachev Ratio (or R-Ratio) is a risk-return performance measure of an investment asset, portfolio, or strategy. It was devised by Dr. Svetlozar Rachev[1] and has been extensively studied in quantitative finance. Unlike the reward-to-variability ratios, such as Sharpe ratio and Sortino ratio, the Rachev ratio is a reward-to-risk ratio, which is designed to measure the right tail reward potential relative to the left tail risk in a non-Gaussian setting.[2][3][4] Intuitively, it represents the potential for extreme positive returns compared to the risk of extreme losses (negative returns), at a rarity frequency q (quantile level) defined by the user.[5]
The ratio is defined as the Expected Tail Return (ETR) in the best q% cases divided by the Expected tail loss (ETL) in the worst q% cases. The ETL is the average loss incurred when losses exceed the Value at Risk at a predefined quantile level. The ETR, defined by symmetry to the ETL, is the average profit gained when profits exceed the Profit at risk at a predefined quantile level.
For more tailored applications, the generalized Rachev Ratio has been defined with different powers and/or different confidence levels of the ETR and ETL.[1]
- ^ a b Biglova, Almira; Ortobelli, Sergio; Rachev, Svetlozar T.; Stoyanov, Stoyan (2004). "Different Approaches to Risk Estimation in Portfolio Theory". The Journal of Portfolio Management. 31. The Journal of Portfolio Management, Fall 2004, Vol. 31, No. 1: pp. 103-112: 103–112. doi:10.3905/jpm.2004.443328. S2CID 153594336.
- ^ Fehr, Ben. "Beyond the Normal Distribution" (PDF). Frankfurter Allgemeine Zeitung. Archived from the original (PDF) on 1 September 2006. Retrieved 16 March 2006.
- ^ Cheridito, P.; Kromer, E. (2013). "Reward-Risk Ratios". Journal of Investment Strategies. 3 (1): 3–18. doi:10.21314/JOIS.2013.022.
- ^ Farinelli, S.; Ferreira, M.; Rossello, D.; Thoeny, M.; Tibiletti, L. (2008). "Beyond Sharpe ratio: Optimal asset allocation using different performance ratios". Journal of Banking and Finance. 32 (10): 2057–2063. doi:10.1016/j.jbankfin.2007.12.026.
- ^ Svetlozar Rachev. "Lecture 10: Performance measures" (PDF). stat.kit.edu. Retrieved 15 May 2024.