FRM Part I · FRM Exam Part I · The Building Blocks of Risk Management
Two loans each have expected loss of $50,000 and unexpected loss (standard deviation of loss) of $300,000. Their losses have a correlation of 0.5. What is the unexpected loss of the two-loan portfolio?
The portfolio unexpected loss is about $519,615. Portfolio variance is three times 9 x 10^10 given a correlation of 0.5, and its square root gives this figure. It is below the simple sum of $600,000 because diversification is imperfect but present.
- A$519,615Correct
- B$424,264
- C$600,000
- D$300,000
Explanation
Variance = 300,000^2 + 300,000^2 + 2(0.5)(300,000)(300,000) = 9e10 + 9e10 + 9e10 = 27e10. The square root is about $519,615. $600,000 assumes perfect correlation, and $424,264 assumes zero correlation. Expected loss does not enter the standard deviation.
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