FRM Part I · FRM Exam Part I · Measuring Credit Risk
A bank holds two loans, each with EAD of USD 1,000,000, LGD of 100%, and PD of 1%. The default correlation between the two borrowers is 0.20. What is the standard deviation of the portfolio loss, to the nearest USD?
Each loan has a loss standard deviation of about USD 9,950. Combining two with default correlation 0.20 gives variance of 2.4 times the single-loan variance, so the standard deviation is about USD 15,492. Perfect correlation would give USD 19,900, and zero correlation USD 14,071.
- AUSD 15,492Correct
- BUSD 14,071
- CUSD 9,950
- DUSD 19,900
Explanation
Each loan has sigma = 1,000,000 x sqrt(0.01 x 0.99) = 9,950. Portfolio variance = 2 x 9,950^2 + 2 x 0.2 x 9,950^2 = 2.4 x 99,000,000 = 237,600,000 (approx). Square root = about USD 15,492. USD 19,900 assumes perfect correlation; USD 14,071 assumes zero correlation.
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