Multiple VaR Levels

The Basel backtests are focused on determining the adequacy of a VaR measure at a single level, p. In general, however, there is no need to restrict attention to a single VaR level. The unconditional coverage and independence property of an accurate VaR measure should hold for any level of p.

This means that if portfolio risk is adequately modeled then the 1% VaR should be violated 1% of the time, the 5% VaR should be violated 5% of the time, the 10% VaR should be violated 10% of the time and so on.

Furthermore, a VaR violation at any level should be independent from a VaR violation at any other level so that, for example, a violation of a portfolio’s 5% VaR today should not portend a violation of the portfolio’s 1% VaR tomorrow. In short, VaR violations at all levels should be independent from each other and follow the uniform distribution on the interval between 0 and 1.

Currently p-values are calculated for BFC portfolio only. The graph below shows the empirical cumulative distribution function of p-values for BFC portfolio, for the period between October 1, 2013 and September 24, 2014, and cumulative distribution function of the uniform distribution on the interval between 0 and 1.

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