Finite-Sample Precision Limits for Expected Shortfall Forecast Comparisons

Expected shortfall (ES) is a tail functional whose estimation precision is governed by the effective tail sample size $n\alpha$ rather than by the nominal calibration size n. The resulting ${\left(n\alpha \right)}^{-1/2}$ information limit is well established, yet no practical framework exists for deciding whether two ES forecasts can be meaningfully distinguished over a finite calibration window. This paper converts the asymptotic rate into four operational diagnostics: a plug-in precision benchmark, a sample-size rule, a precision-fragile pairwise comparison screen, and a VaR-first diagnostic linking excess ES dispersion to first-stage quantile miscalibration. An empirical application to global financial assets and heterogeneous forecasters under standard regulatory tail parameters shows that roughly one in five pairwise ES comparisons is precision-fragile, with excess dispersion concentrated in cells with poor VaR calibration. The results suggest that ES forecast rankings at typical tail levels can be constrained by effective tail information rather than by model sophistication.