  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. In this paper we show that law-invariant
spectral risk measures such as expected shortfall are not elicitable unless
they reduce to minus the expected value. Hence, it is unclear how to perform
forecast verification or comparison. However, the class of elicitable
law-invariant coherent risk measures does not reduce to minus the expected
value. We show that it consists of certain expectiles.
