FRM Part I · FRM Exam Part I · The Building Blocks of Risk Management
Two loans each have a stand-alone unexpected loss (standard deviation of loss) of USD 3 million and USD 4 million. The correlation between their losses is 0.5. What is the unexpected loss of the two-loan portfolio?
Portfolio unexpected loss is about USD 6.08 million. Variance equals 3 squared plus 4 squared plus twice 0.5 times 3 times 4, which is 37, and its square root is 6.08. Simple addition of USD 7 million ignores diversification.
- AUSD 5.57 millionCorrect
- BUSD 7.00 million
- CUSD 6.08 million
- DUSD 5.00 million
Explanation
Variance = 9 + 16 + 2 x 0.5 x 3 x 4 = 37, giving a standard deviation of sqrt(37) = 6.08. Check: the question asks for the portfolio value, so 6.08 is correct and the listed option must be 6.08.
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