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FRM Part II · FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment

Two loans each have EAD of $1 million, constant LGD of 100%, and PD of 10%, so each has a loss standard deviation of $300,000. The default correlation between the two is 0.25. What is the standard deviation of the two-loan portfolio loss?

Portfolio variance is the sum of both variances plus twice the covariance. That is 0.09 plus 0.09 plus 0.045, or 0.225 in millions squared, so the standard deviation is about $474,000. Assuming independence understates it at $424,000, and perfect correlation overstates it at $600,000.

  1. A$424,000
  2. B$474,000
  3. C$520,000Correct
  4. D$600,000

Explanation

Variance = 0.09 + 0.09 + 2 x 0.25 x 0.3 x 0.3 (in $ millions squared) = 0.18 + 0.045 = 0.225. Std dev = sqrt(0.225) = 0.4743, which is $474,000. Check: 0.225 under root gives 0.474, so option B is right. Zero correlation gives $424,000; perfect correlation gives $600,000.

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