FRM Part II · FRM Exam Part II · Backtesting VaR
A bank's 95% VaR backtest shows exactly 5% exceptions over a long sample, so the Kupiec test is not rejected. However, the independence test statistic is 9.2. Using the 5% critical value of the chi-square with 1 degree of freedom (3.84), what is the correct conclusion?
Independence is rejected because 9.2 exceeds 3.84. Exceptions are clustered, so the model fails conditional coverage even though its exception frequency is correct. Frequency and independence are separate properties, and a model can pass one while failing the other.
- AThe model passes conditional coverage because the frequency is correct
- BThe independence hypothesis is rejected, so exceptions are clustered and the model fails conditional coverage despite correct frequencyCorrect
- CThe independence statistic should be compared with 5.99, so it is rejected only for 2 degrees of freedom
- DThe model's exception frequency must be wrong, since independence is rejected
Explanation
9.2 exceeds 3.84, so independence is rejected. LR_uc is near zero, so LR_cc is about 9.2, which exceeds 5.99 and is also rejected. Correct frequency does not imply independence.
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