FRM Part I · FRM Exam Part I · Measuring Credit Risk
A portfolio contains two loans. Loan 1 has a standalone unexpected loss of 1.0 million and Loan 2 has a standalone unexpected loss of 2.0 million. The correlation between their losses is 0.25. What is the portfolio unexpected loss?
The portfolio unexpected loss is about 2.45 million. Combine the standalone losses using the two-asset variance formula: 1 plus 4 plus 2 times 0.25 times 1 times 2 equals 6, and the square root of 6 is 2.45. This is less than the simple sum of 3.00 million, showing diversification.
- A2.45 millionCorrect
- B3.00 million
- C2.24 million
- D2.65 million
Explanation
UL = sqrt(1^2 + 2^2 + 2 x 0.25 x 1 x 2) = sqrt(1 + 4 + 1) = sqrt(6) = 2.45 million. Simple addition (3.00) assumes perfect correlation. 2.24 assumes zero correlation. 2.65 corresponds to a correlation of 0.5.
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