Explanation

To find the variance of stock J, we need to first calculate its standard deviation using the correlation formula:

$\text{Corr}(J, K) = \rho_{J,K} = \frac{\text{Cov}(J, K)}{\sigma_J \cdot \sigma_K}$

Rearranging this formula to solve for the standard deviation of stock J:

$\sigma_J = \frac{\text{Cov}(J, K)}{\sigma_K \cdot \rho_{J,K}}$

Substituting the given values:

• Covariance (Cov(J, K)) = 0.0054
• Standard deviation of stock K (σ_K) = 0.11
• Correlation (ρ_{J,K}) = 0.37

$\sigma_J = \frac{0.0054}{0.11 \cdot 0.37} = \frac{0.0054}{0.0407} = 0.1327$

Now, the variance of stock J is the square of its standard deviation:

$\sigma_J^2 = (0.1327)^2 = 0.017609 \approx 0.0176$

Therefore, the variance of the returns on stock J is 0.0176.

Why other options are incorrect:

• B (0.0407): This is the denominator value (σ_K × ρ_{J,K}) from the standard deviation calculation, not the variance.
• C (0.0735): This appears to be unrelated to the calculation.
• D (0.1327): This is the standard deviation of stock J, not the variance.