FRM Part I · FRM Exam Part I · Random Variables
A portfolio payoff is Y = 5 - 2X, where X has mean 6 and standard deviation 3. What are the mean and standard deviation of Y?
The mean is 5 - 2(6) = -7 and the standard deviation is |−2| × 3 = 6. The additive constant shifts the mean only, and standard deviation is never negative because variance scales by the squared coefficient.
- AMean -7; standard deviation 6Correct
- BMean -7; standard deviation -6
- CMean 17; standard deviation 6
- DMean -7; standard deviation 13
Explanation
E[Y] = 5 - 2(6) = -7. Var(Y) = (-2)^2 (9) = 36, so standard deviation is 6. Negative standard deviation is impossible; the constant 5 does not change dispersion.
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