Financial Risk Manager Part 1

Calculation Explanation

To calculate the correlation between stocks X and Y, we use the formula:

$\rho_{X,Y} = \frac{\text{Cov}(X,Y)}{\sigma_X \cdot \sigma_Y}$

From the covariance matrix:

• Variance of X (σ²_X) = 650
• Variance of Y (σ²_Y) = 450
• Covariance between X and Y = 120

Step 1: Calculate standard deviations $\sigma_X = \sqrt{650} = 25.50$ $\sigma_Y = \sqrt{450} = 21.21$

Step 2: Calculate correlation $\rho_{X,Y} = \frac{120}{25.50 \times 21.21} = \frac{120}{540.855} = 0.22$

Therefore, the correlation coefficient between stocks X and Y is 0.22, which corresponds to option B.