FRM Part I · FRM Exam Part I · Measuring Credit Risk
A portfolio contains two loans, each with EAD of USD 6 million, LGD of 100%, and PD of 1%. Default events are independent. What is the standard deviation of the portfolio's credit loss, approximately?
Each loan has a loss standard deviation of about USD 0.597 million. Because defaults are independent, variances add, so the portfolio standard deviation is 0.597 times the square root of two, about USD 0.84 million. Adding standard deviations directly would overstate it.
- AUSD 0.60 million
- BUSD 0.84 millionCorrect
- CUSD 1.19 million
- DUSD 1.68 million
Explanation
Each loan SD = 6 x sqrt(0.01 x 0.99) = 6 x 0.0995 = 0.597 million. With independence, portfolio SD = 0.597 x sqrt(2) = 0.844 million. Simply adding the SDs gives 1.19 million, which wrongly assumes perfect correlation.
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