FRM Part II · FRM Exam Part II · Credit Risk
A bank holds two uncorrelated-default loans in a simplified setting, each with EAD of USD 10 million, LGD of 100%, and PD of 2%. Treating each loss as Bernoulli, what is the standard deviation of the portfolio loss (unexpected loss), to the nearest USD 0.01 million?
Each loan has loss variance of 10^2 x 0.02 x 0.98 = 1.96, a standard deviation of USD 1.40 million. With independent defaults the variances add to 3.92, so portfolio standard deviation is USD 1.98 million. Adding standard deviations would give 2.80, which is wrong.
- AUSD 0.28 million
- BUSD 0.40 million
- CUSD 1.98 million
- DUSD 2.80 millionCorrect
Explanation
Each loan variance = EAD^2 x PD(1-PD) = 100 x 0.02 x 0.98 = 1.96, so SD = 1.40 million. With independence, portfolio variance = 3.92, SD = 1.98 million. Wait: 1.98 is correct, so the key is USD 1.98 million.
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