Expected Shortfall
Average the bad tail beyond VaR, and the risk measure becomes coherent.
Expected shortfall repairs VaR’s most quoted flaw: VaR is insensitive to everything beyond its own threshold, so two portfolios with identical 99 percent VaR can carry wildly different tails. Expected shortfall, also called conditional VaR or CVaR, averages the losses that exceed the VaR level, so thicker tails produce a higher number. Artzner and colleagues codified the desiderata as coherence axioms; VaR can violate subadditivity, the principle that diversification should not raise risk, while expected shortfall satisfies all four axioms. That argument persuaded the Basel Committee to replace VaR with expected shortfall at 97.5 percent confidence in the Fundamental Review of the Trading Book.