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FRM Part II · FRM Exam Part II · Portfolio Credit Risk

A portfolio has two loans. Loan A has exposure 60 million and Loan B has exposure 80 million, with zero recovery. Unexpected loss (standard deviation of loss) is 6 million for A and 8 million for B, and the default correlation is 0.5 (treat each loan's loss standard deviation as given). What is the portfolio unexpected loss, in millions?

Portfolio unexpected loss is about 12.2 million. Variance equals 36 plus 64 plus twice 0.5 times 6 times 8, which is 148, whose square root is roughly 12.17. Adding standalone figures to get 14 would assume perfect correlation and overstate the risk.

  1. AApproximately 12.2Correct
  2. B14.0
  3. C10.0
  4. DApproximately 15.1

Explanation

Variance = 6^2 + 8^2 + 2(0.5)(6)(8) = 36 + 64 + 48 = 148. The square root is about 12.17 million. Simply adding the standalone figures gives 14, which wrongly assumes perfect correlation. Using zero correlation gives 10, which ignores the 0.5 correlation. Option 15.1 would take the square root of 228 (a sign slip on the cross term doubling).

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