Range Value at Risk

Expected Shortfall averages every loss beyond a single Value at Risk cutoff — everything past, say, the 95th percentile. That's exactly what makes it sensitive to the single worst historical observation in the sample: if the tail beyond the cutoff contains only a handful of data points, one unusually extreme (or unusually noisy) loss can swing the average a lot. Range Value at Risk (RVaR) responds by averaging losses over a band, between two confidence levels — say, from the 95th to the 99th percentile — deliberately excluding the very extreme tail beyond the upper cutoff from the calculation.

Formally, $\mathrm{RVaR}_{\alpha,\beta}(L)$ is the average loss between the $(1-\alpha)$ and $(1-\beta)$ quantiles for $\alpha < \beta$, which reduces to ordinary Expected Shortfall in the limit as $\beta \to 0$ (the upper cutoff pushed out to include everything). By excluding the most extreme observations, RVaR is more robust to a single outlier data point or to the kind of estimation noise that plagues a thinly-populated extreme tail, but it deliberately gives up sensitivity to exactly the catastrophic scenarios a risk manager might most want captured — a fund could technically look fine on RVaR while still carrying real exposure to a true tail event that RVaR's upper cutoff has excluded from the calculation.