Answer: 0.00148

## 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**.

Author: Tanishq Prabhu