FRM Part I · FRM Exam Part I · Sample Moments
Random variables X and Z have standard deviations of 2 and 4 and a covariance of -4. Define A = -2X + 1 and B = 3Z + 4. What is the correlation between A and B?
The correlation between A and B is 0.50. The original correlation is -4 divided by 2 times 4, or -0.5. Constants do not matter, and the negative multiplier on X reverses the sign, so the correlation becomes positive 0.50.
- A0.50Correct
- B-0.50
- C24.00
- D-0.25
Explanation
Corr(X,Z) = -4/(2×4) = -0.5. Correlation is unchanged by adding constants and by positive scaling, but multiplying by a negative constant flips the sign. A has a negative multiplier and B a positive one, so Corr(A,B) = -(-0.5) = +0.50. The -0.50 option ignores the sign flip; 24 is the covariance of A and B (-2×3×-4), not the correlation.
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