FRM Part II · FRM Exam Part II · Credit Risk
A portfolio has two loans, each with exposure of USD 10 million, one-year default probability of 2%, and loss given default of 50%. Defaults are independent and exposures are fixed. What is the standard deviation of the portfolio's one-year credit loss (in USD million, approximate)?
The standard deviation is about USD 0.99 million. Each loan loses USD 5 million on default, giving variance 25 x 0.02 x 0.98 = 0.49. With independent defaults the variances add to 0.98, whose square root is roughly 0.99. Adding standard deviations would wrongly assume perfect correlation.
- A0.70
- B0.99Correct
- C1.40
- D0.20
Explanation
Loss per loan = 10 x 0.5 = 5 if default. Variance per loan = 25 x 0.02 x 0.98 = 0.49, so SD = 0.70. With independence, portfolio variance = 0.98, SD = 0.99. Option 0.70 is a single loan; 1.40 simply adds the SDs, which assumes perfect correlation.
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