Expected shortfall
Measure how severe the selected loss tail is
Expected shortfall averages the worst specified fraction of a loss distribution, using a quantile-integral definition that handles discrete distributions correctly. It therefore summarises tail severity beyond the information in a single VaR threshold. The shorthand conditional expectation beyond VaR needs care when the distribution has probability mass at the threshold. Estimation and backtesting still require adequate tail information.
Choose this when the severity of extreme losses matters, provided the data or simulation model can represent the relevant tail. Evaluate it jointly with VaR and stress scenarios rather than treating one number as complete risk coverage.
Strengths
- Includes loss severity within the selected tail
- Has coherence properties under its standard mathematical definition
Limitations
- Extreme-tail observations can be sparse and unstable
- Forecast validation needs more than counting threshold breaches
Know the boundary
Expected shortfall can be backtested. Its lack of stand-alone elicitability in general does not imply impossibility of statistical validation.