Financial Risk Manager Part 1
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The annual returns of two stocks, X and Y, are jointly normally distributed. Each stock has a marginal distribution with mean = 2%, standard deviation = 10%. The correlation coefficient between X and Y is 0.9. If the annual return on stock X is 4%, what is the expected annual return on stock Y?
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TTanishq
A
0.038
B
0.029
C
0.0038
D
0.4
Explanation:
Explanation
This is a conditional expectation problem for bivariate normal distributions. Given:
- μ_X = μ_Y = 0.02 (2%)
- σ_X = σ_Y = 0.10 (10%)
- ρ = 0.9
- X = 0.04 (4%)
For bivariate normal distributions, the conditional expectation of Y given X is:
E[Y|X] = μ_Y + ρ * (σ_Y/σ_X) * (X - μ_X)
Substituting the values: E[Y|X] = 0.02 + 0.9 * (0.10/0.10) * (0.04 - 0.02) E[Y|X] = 0.02 + 0.9 * 1 * 0.02 E[Y|X] = 0.02 + 0.018 E[Y|X] = 0.038
Therefore, the expected annual return on stock Y is 3.8% or 0.038.
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