Explanation

To solve this problem, we use the formula for correlation:

$\text{Corr}(X, Y) = \frac{\text{Cov}(X, Y)}{(\sigma_X \times \sigma_Y)}$

Given:

• Correlation = 0.50
• Covariance = 0.005
• Standard deviation of Y (σ_Y) = 0.26

Substituting the values:

$`$0.50` = \frac{0.005}{(\sigma_X \times 0.26)}$$

Solving for σ_X:

$`$0.50` \times \sigma_X \times 0.26 = 0.005$$

$`$0.13` \sigma_X = 0.005$$

$\sigma_X = \frac{0.005}{0.13} = 0.0385$

Now, variance of X = σ_X²:

$\text{Variance}(X) = (0.0385)^2 = 0.00148$

Therefore, the variance of returns for stock X is 0.00148.