Financial Risk Manager Part 1
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Three random variables X, Y, and Z have the equal variance of σ² = 2. X is independent of both Y and Z, and that Y and Z are correlated with a correlation coefficient of 0.8. What is the covariance between X and K given that K=Y+Z?
Other
Community
NNikitesh
A
0
B
2
C
3
D
4
Explanation:
Recall from the properties of the covariance that:
Cov(A, B + C) = Cov(A, B) + Cov(A, C)
So, we need:
Cov(X, K) = Cov(X, Y + Z) = Cov(X, Y) + Cov(X, Z) = 0 + 0 = 0
This is true because X is independent of both Y and Z, which means Cov(X, Y) = 0 and Cov(X, Z) = 0. The correlation between Y and Z (0.8) and their variances (σ² = 2) are irrelevant for calculating Cov(X, K) since X is independent of both Y and Z.
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