Abstracts

There has recently been renewed debate about the relative merits of the VaR and CVaR risk measures, particularly since the Basel Committee issued a recommendation that the former be replaced by the latter for bank regulation. The standard objections to VaR are that it is not coherent and takes no account of the magnitude of large losses. Recently, CVaR has in turn been criticised on the grounds of computational instability (Cont, Deguest and Scandolo, 2010) and for not being ‘elicitable’ (Gneiting, 2007, Ziegel 2013). We take a different approach to this question, addressing it from the point of view of probability forecasting and A.P. Dawid’s ‘prequential statistics’ (Dawid 1984). We introduce the concept of ‘consistency’ of a risk measure estimate and discuss its relation to elicitability. We study consistency for quantile estimates and expectation-based estimates like CVaR, and show that there are sharp differences between the two, quantile estimates being consistent under much more general conditions than any other risk measure. We use martingale limit theory to study the expectation-based case. Finally, we define a simple but remarkably effective algorithm for quantile prediction of financial data, designed to achieve the consistency criterion.