The correlation coefficient is calculated using the formula:

$$\text{Corr}(R_A, R_B) = \frac{\text{Cov}(R_A, R_B)}{\sigma_A \sigma_B}$$

Where:

• Covariance = 0.315
• Standard deviation of Portfolio A = √(0.525) = √(0.525) ≈ 0.7246
• Standard deviation of Portfolio B = √(0.63) = √(0.63) ≈ 0.7937

Calculation:

$$\text{Corr}(R_A, R_B) = \frac{0.315}{0.7246 \times 0.7937} = \frac{0.315}{0.575} ≈ 0.5477$$

Key points:

1. Variance must be converted to standard deviation by taking the square root
2. Correlation coefficient ranges from -1 to +1
3. The covariance of 0.315 is positive, indicating positive correlation
4. The result of 0.5477 shows a moderate positive correlation between the two portfolios