CVaR Ratio (STARR)
The CVaR ratio divides the excess return by the conditional value at risk at 95%, the mean of the worst 5% of daily returns. It is the stable tail-adjusted return ratio (STARR) of Martin, Rachev and Siboulet.
Mathematical Formulation
Definition
CVaR is the reported cvar_95: the daily expected shortfall at 95% on the Acerbi-Tasche fractional tail, as a positive loss. The numerator is the Sharpe ratio's numerator.
The annualization
The daily CVaR is annualized by the same P as the mean, never by the square root of P. So the ratio equals the daily STARR and assumes nothing about independence between days. A source that annualizes CVaR by the square root of P reports a value about the square root of P times larger. Do not compare the two.
Reading it
The value is null when CVaR is zero or negative. A negative CVaR means that even the worst 5% of days were gains, and a ratio over that is not defined.
CVaR at 95% on a short window rests on few days: 5% of one year is about 12 days.
A higher ratio describes the run window only. It is not evidence that the portfolio will perform better in the future, and no method is validated out of sample.
Where FolioLab reports it
results.<method>.performance.cvar_ratio: the annual excess return over CVaR (95%) annualized by the same periods per year, or null.
The value appears on the result page under Performance Ratios, in the PDF and Excel reports, in the compare view and through the MCP explain_metric tool. A run stored before this ratio existed does not carry it.
References
- Martin, R. D., Rachev, S. T., & Siboulet, F. (2003). "Phi-alpha Optimal Portfolios and Extreme Risk Management." Wilmott Magazine, November, 70-83.
- Acerbi, C., & Tasche, D. (2002). "Expected Shortfall: A Natural Coherent Alternative to Value at Risk." Economic Notes, 31(2), 379-388.
Not investment advice. Past performance is not indicative of future results.