The properties of expectiles explored

Expectiles have been mooted as an alternative risk measure to value-at-risk (VAR) and expected shortfall. Here, Richard Martin derives their saddlepoint approximation and shows that their risk contributions are essentially the same as those of expected shortfall

A recent criticism of the expected shortfall risk measure is that it is not elicitable (Gneiting 2011). This means that one cannot, in a backtesting procedure, make point forecasts of it and check whether the forecasting procedure works (see Cont, Deguest and Scandolo (2010) for a fuller discussion of this concept). The discussion of this is still at an early stage, and the author is not convinced that it is an insuperable problem. However, Ziegel (2013) has recently pointed out that expectiles, introduced by Newey and Powell (1987), are an elicitable risk measure, in addition to being coherent. It therefore seems like a good idea to explore the properties of expectiles further.

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