Elicitability is a mathematical property, satisfied by some risk measures, that allows for the ranking of risk models’ performance. If a risk measure is elicitable, then there exists a scoring function for that risk measure that can be used for comparative tests on models. Elicitability has been proven a useful property for model selection, estimation, forecast comparison and forecast ranking. Crucially, value-at-risk (VAR) is elicitable, while expected shortfall (ES) is not. Researchers have long debated over the connection between elicitability and back-testability, fueled by the adoption of expected shortfall for the calculation of capital requirements. While doubts were cast on the back-testability of non-elicitable risk measures, recent studies confirmed that lack of elicitability prevents strict back-testing, although an approximate back-testing is generally possible for non-elicitable risk measures when certain conditions are met, as in the case of variance and ES.
ELICITABILITY
