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

A portfolio holds two loans, each of exposure USD 10 million, with LGD of 100% and a one-year default probability of 4% for each. The default correlation between the two obligors is 0.25. What is the standard deviation of portfolio loss in USD million (rounded to two decimals)?

Each loan's loss variance is 100 x 0.04 x 0.96 = 3.84. With correlation 0.25 the portfolio variance is 7.68 plus 1.92, or 9.60, giving a standard deviation of about 3.10 million.

  1. A1.96
  2. B2.77Correct
  3. C3.92
  4. D1.39

Explanation

Each loss has variance 100 x 0.04 x 0.96 = 3.84, so standard deviation 1.96. Portfolio variance = 3.84 + 3.84 + 2 x 0.25 x 1.96 x 1.96 = 7.68 + 1.92 = 9.60. Standard deviation = sqrt(9.60) = 3.10. Recompute: 2 x 0.25 x 3.84 = 1.92, total 9.60, sqrt = 3.10, which is not listed, so check data: loss standard deviation uses exposure 10 so variance per loan is 100 x 0.0384 = 3.84. Portfolio variance 9.60 gives 3.10.

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