Financial Risk Manager Part 1

Calculation Explanation

The correlation coefficient between Stock X and Stock Y is calculated using the formula:

$\text{Corr}(Rₓ, Rᵧ) = \frac{\text{Cov}(Rₓ, Rᵧ)}{\sigma(Rₓ) \cdot \sigma(Rᵧ)}$

Given:

• Covariance: Cov(Rₓ, Rᵧ) = 0.093
• Variance of Rₓ = 0.69
• Variance of Rᵧ = 0.36

Step 1: Calculate Standard Deviations Since variance = σ²:

• σ(Rₓ) = √0.69 = 0.8306
• σ(Rᵧ) = √0.36 = 0.6

Step 2: Calculate Correlation $\text{Corr}(Rₓ, Rᵧ) = \frac{0.093}{0.8306 \times 0.6} = \frac{0.093}{0.49836} = 0.1865$

Verification:

• 0.8306 × 0.6 = 0.49836
• 0.093 ÷ 0.49836 = 0.1865

Therefore, the correlation coefficient is 0.1865, which corresponds to option B.