FRM Part II · FRM Exam Part II · Credit Value at Risk
A portfolio manager combines two loans with equal exposure, each with a standalone unexpected loss (standard deviation of loss) of 4 million. The default correlation between them is 0.25. What is the portfolio unexpected loss?
The portfolio unexpected loss is about 6.32 million. Portfolio variance equals 16 plus 16 plus 2 times 0.25 times 16, which is 40, and its square root is 6.32. Adding the two standalone figures to get 8 million would wrongly assume perfect correlation.
- AApproximately 6.32 millionCorrect
- B8.00 million
- C5.66 million
- D7.07 million
Explanation
Variance = 4^2 + 4^2 + 2(0.25)(4)(4) = 16 + 16 + 8 = 40. Standard deviation = sqrt(40) = 6.32 million. Simple addition (8) assumes perfect correlation; 5.66 is the zero-correlation result.
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