The Rachev Ratio

The Sharpe ratio treats a strategy's entire return distribution as if only its mean and standard deviation mattered, which is a poor summary for a strategy with skewed or fat-tailed returns — exactly the kind common in options selling, merger arbitrage, or any strategy that harvests a risk premium punctuated by occasional sharp losses. The Rachev ratio instead focuses purely on the tails, comparing the expected size of extreme good outcomes to the expected size of extreme bad outcomes.

Formally, for confidence levels $\alpha$ and $\beta$ (commonly both set to 5%), the Rachev ratio is:

$$RR(\alpha,\beta) = \frac{\text{ETL}_\alpha(-R)}{\text{ETL}_\beta(R)}$$

where $\text{ETL}_\alpha(-R)$ is the expected tail loss of the negated returns at level $\alpha$ — in effect the average size of the best $\alpha\%$ of outcomes — and $\text{ETL}_\beta(R)$ is the expected shortfall of the actual returns at level $\beta$, the average size of the worst $\beta\%$ of outcomes. A Rachev ratio above 1 means the average magnitude of the best 5% of days genuinely exceeds the average magnitude of the worst 5% of days — a strategy with a long right tail and a short left tail, the profile most investors actually want, will score well here even if its overall Sharpe ratio looks unremarkable, while a strategy that quietly harvests small gains funded by rare large losses (a classic "picking up nickels in front of a steamroller" profile) will score poorly on Rachev despite a potentially high Sharpe.