hard · FRM Part 2 Market Risk
A risk manager backtests a portfolio's 1-day 99% VaR over 1,000 trading days and observes 4 exceptions. She applies Kupiec's unconditional coverage (POF) test and fails to reject the model. A colleague argues the model is nonetheless deficient because 3 of the 4 exceptions occurred on consecutive days during a single stressed week.
To formally support the colleague's concern, which test should be used, and what is the key statistical property that makes it distinct from the Kupiec test in this specific situation?
- The Christoffersen independence test, which conditions on whether an exception is followed by another exception and can reject a model that passes Kupiec's because it targets the clustering of failures rather than their total count
- The Christoffersen conditional coverage test, which is simply the sum of two Kupiec POF statistics and therefore cannot reject when the POF component already fails to reject the unconditional coverage hypothesis
- The Basel traffic-light test, which classifies the model into green, yellow, or red zones based purely on the cumulative exception count and would place 4 exceptions in the green zone
- The Lopez magnitude-loss function test, which penalizes the model according to the squared size of each exceedance and thus captures the severity of the clustered losses that Kupiec ignores
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