FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
In an antithetic variates scheme, a simulation uses each standard normal draw Z and its mirror -Z to produce two payoff estimates X1 and X2. The variance of each estimate is 25, and the correlation between X1 and X2 is -0.60. What is the variance of the pair average (X1 + X2)/2?
The variance of the averaged pair is 5.0. With equal variances of 25 and correlation of -0.60, the variance of the sum is 50 minus 30, which is 20, and dividing by four for the average gives 5.0.
- A5.0Correct
- B10.0
- C15.0
- D20.0
Explanation
Var of average = (1/4)(25 + 25 + 2 x (-0.60) x 25) = (1/4)(50 - 30) = 5.0. Ignoring the correlation would give 12.5, and using +0.60 would give 20.
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