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FRM Part II · FRM Exam Part II · Backtesting VaR

A desk's 99% one-day VaR is backtested over 250 days with 5 exceptions observed. Using the binomial distribution with p = 1%, which statement about the test is most accurate? (Approximate P(X>=5) is about 10.8%; P(X>=6) is about 4.2%.)

Fail to reject. The probability of seeing 5 or more exceptions when 2.5 are expected is about 10.8%, above the 5% threshold. The 4.2% figure applies to 6 exceptions. Because power is low with so few expected exceptions, the model may still be flawed.

  1. AReject at the 5% one-tailed level because 5 exceeds the expected 2.5
  2. BFail to reject at 5% one-tailed because P(X>=5) of about 10.8% exceeds 5%, though the Type II error risk remainsCorrect
  3. CReject, because the p-value of 4.2% applies to 5 exceptions
  4. DFail to reject because the Type I error rate equals 10.8%, which is acceptable

Explanation

The one-tailed p-value for observing 5 or more exceptions is about 10.8%, above 5%, so the model is not rejected. The 4.2% figure belongs to 6 exceptions. Not rejecting does not prove accuracy, as the test has limited power with few exceptions, so Type II error is a concern.

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