FRM Part I · FRM Exam Part I · Multivariate Random Variables
Returns on X and Y are bivariate normal with sigma_Y = 10% and correlation 0.80. What is the conditional standard deviation of Y given a particular value of X?
The conditional standard deviation is sigma_Y times the square root of (1 − rho squared): 10% × sqrt(1 − 0.64) = 10% × 0.6 = 6%. It does not depend on the value of X.
- A2.0%
- B6.0%Correct
- C8.0%
- D3.6%
Explanation
Conditional variance = sigma_Y^2(1 - rho^2) = 100 x (1 - 0.64) = 36, so the standard deviation is 6%. Using 10 x 0.2 = 2% subtracts rho from 1 without squaring and takes no root of the right base; 8% mistakenly uses rho times sigma_Y.
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