Elicitability of Risk Measures

A risk measure is "elicitable" if there's a scoring function that rewards accurate forecasts of it and is minimized, on average, exactly when the forecast equals the true value — meaning you can rank competing risk models by how low their average score is, and the best model genuinely is the one that predicted risk correctly. The mean is elicitable (squared-error loss does the job); so, less obviously, is Value-at-Risk, using an asymmetric "pinball" loss that penalizes misses on one side more than the other, matching VaR's definition as a quantile.

Expected Shortfall — the average loss beyond the VaR threshold, and the risk measure regulators increasingly prefer because it's coherent and captures tail severity that VaR ignores — turned out, in a well-known 2011 result, to not be elicitable on its own. There is no scoring function whose average is minimized uniquely by the true Expected Shortfall, so you cannot directly rank two competing ES forecasts by a simple loss the way you can for VaR or the mean. This caused real concern when Basel moved bank capital rules toward ES: the risk measure regulators wanted was, in this narrow technical sense, harder to validate than the one it was replacing.

The practical resolution is that Expected Shortfall is jointly elicitable together with VaR — a scoring function exists that is jointly minimized by the correct pair (VaR, ES) — so backtesting in practice reports both quantities together rather than ES alone. Desks and regulators have adapted their validation frameworks around this joint approach rather than abandoning ES.