FRM Part II · FRM Exam Part II · Backtesting VaR
A 99% VaR backtest gives LR_uc = 2.1 and LR_ind = 4.2. Critical values at 5% are 3.84 (1 df) and 5.99 (2 df). Which conclusion is correct?
Conditional coverage is rejected because LR_cc = 2.1 + 4.2 = 6.3 exceeds the 2-degree-of-freedom critical value of 5.99. Independence is also rejected since 4.2 exceeds 3.84, even though frequency alone passes.
- AReject conditional coverage, since LR_ind exceeds 3.84 so the total must be rejected at 1 df
- BReject conditional coverage because 6.3 exceeds 5.99; independence alone is also rejectedCorrect
- CDo not reject conditional coverage because LR_uc is below 3.84
- DDo not reject anything because 6.3 is below 3.84 times two
Explanation
LR_cc = 2.1 + 4.2 = 6.3, which exceeds 5.99 (2 df), so conditional coverage is rejected. LR_ind = 4.2 exceeds 3.84, so independence is rejected too. Unconditional coverage alone is not rejected, but that does not rescue the model.
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