Consistency of Risk Measure Estimates

Recently there has been renewed debate about the relative merits of VaR and CVaR as measures of financial risk. VaR is not coherent and does not quantify the risk beyond VaR, while CVaR shows some computational instabilities and is not 'elicitable' (Gneiting 2010, Ziegel 2013). It is argued in this paper that such questions are best addressed from the point of view of probability forecasting or Dawid's 'prequential statistics.' We introduce a concept of 'consistency' of a risk measure, which is close to Dawid's 'strong prequential principle,' and show that VaR indeed has special properties not shared by any other risk measure