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FRM Part II · FRM Exam Part II · Backtesting VaR

A risk manager backtests a 99% one-day VaR model over 250 days and wants to test both the correct number of exceptions and whether exceptions occur in clusters. Which test statistic, following Christoffersen's framework, combines these two properties?

The conditional coverage test is correct. It adds the unconditional coverage (frequency) statistic and the independence (clustering) statistic, giving a chi-square with two degrees of freedom. Kupiec alone checks only the exception count, and the independence test alone checks only clustering.

  1. AThe conditional coverage test, equal to the sum of the unconditional coverage and independence likelihood ratio statisticsCorrect
  2. BThe Kupiec proportion-of-failures test alone, because it detects clustering through the exception count
  3. CThe independence test alone, because it also verifies the exception frequency
  4. DThe Basel traffic light test, which measures the time between consecutive exceptions

Explanation

Christoffersen's conditional coverage statistic LR_cc equals LR_uc plus LR_ind. It is tested against a chi-square with 2 degrees of freedom. Kupiec tests only frequency and the independence test only tests clustering.

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