Explanation

To calculate the covariance between two stocks given their variances and correlation coefficient, we use the formula:

Covariance = Correlation coefficient × (Standard deviation of Stock 1) × (Standard deviation of Stock 2)

Where:

• Standard deviation = √Variance

Step 1: Calculate standard deviations

• Standard deviation of Stock 1 = √0.0625 = 0.25
• Standard deviation 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

Step 3: Verify the calculation

• 0.25 × 0.30 = 0.075
• 0.4500 × 0.075 = 0.03375
• Rounded to four decimal places: 0.0338

Why the other options are incorrect:

• A. 0.0025: This is too small and might result from incorrectly using the variances directly without taking square roots.
• C. 0.0675: This is approximately double the correct answer and might result from forgetting to multiply by the correlation coefficient or using incorrect standard deviations.

Key Concept: The covariance formula shows how two variables move together, scaled by their individual volatilities (standard deviations) and their linear relationship (correlation coefficient).