The risk of a financial position is usually summarized by a risk measure.
As this risk measure has to be estimated from historical data, it is important to be able to verify and compare competing estimation procedures. In
statistical decision theory, risk measures for which such verification and comparison is possible, are called elicitable. It is known that quantile based risk
measures such as value-at-risk are elicitable. However, the coherent risk measure expected shortfall is not elicitable. Hence, it is unclear how to perform
forecast verification or comparison. We address the question whether coherent and elicitable risk measures exist (other than minus the expected value).
We show that one positive answer are expectiles, and that they play a special role amongst all elicitable law-invariant coherent risk measures.