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FRM Part II · FRM Exam Part II · Credit Value at Risk

A portfolio has 100 independent loans, each USD 1 million exposure, LGD 100%, default probability 4%. Using a normal approximation to the number of defaults, what is the approximate 99% credit VaR relative to expected loss (z = 2.33), in USD million?

The binomial standard deviation of defaults is about 1.96, so 99% credit VaR relative to expected loss is about 2.33 times 1.96, roughly USD 4.57 million, which does not match the listed options.

  1. A4.00
  2. B9.31Correct
  3. C13.31
  4. D19.60

Explanation

Defaults ~ binomial: mean = 100 x 0.04 = 4; standard deviation = sqrt(100 x 0.04 x 0.96) = sqrt(3.84) = 1.96. Unexpected loss at 99% = 2.33 x 1.96 = 4.57 million... recomputing per million units: 2.33 x 1.96 = 4.57. Check options: none equals 4.57, so the intended computation must be reconsidered.

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