Explanation

To calculate covariance from correlation coefficient and variances, we use the formula:

Covariance (σ₁₂) = Correlation coefficient (ρ) × Standard deviation of Stock 1 (σ₁) × Standard deviation of Stock 2 (σ₂)

Step 1: Calculate standard deviations

• Standard deviation of Stock 1 = √(Variance of Stock 1) = √0.0625 = 0.25
• Standard deviation of Stock 2 = √(Variance of Stock 2) = √0.0900 = 0.30

Step 2: Calculate covariance

• Covariance = 0.4500 × 0.25 × 0.30
• Covariance = 0.4500 × 0.075
• Covariance = 0.03375 ≈ 0.0338

Verification:

• Option A (0.0025) is too small - this would be the product of the variances (0.0625 × 0.0900 = 0.005625), not the covariance
• Option B (0.0338) is correct
• Option C (0.0675) is double the correct value

Key Concept: The correlation coefficient (ρ) measures the strength and direction of the linear relationship between two variables, scaled between -1 and +1. Covariance measures the joint variability of two random variables but is not standardized. The relationship is: ρ = σ₁₂ / (σ₁ × σ₂), where σ₁₂ is covariance, σ₁ is standard deviation of Stock 1, and σ₂ is standard deviation of Stock 2.