Let's break this down step by step: ### **Given Data** | | Expected Return (\( E[R] \)) | Standard Deviation (\( \sigma \)) | |-----------------|------------------------------|------------------------------------| | Johnson & Johnson (J&J) | 7.7% | 15.5% | | Walgreen Company | 9.2% | 20.0% | Correlation (\( \rho \)) between J&J and Walgreen = **21.3%** = **0.213** Portfolio weights: Since the portfolio is equally invested: \( w_{J\&J} = 0.5 \), \( w_{Walgreen} = 0.5 \) --- ## **a. Expected Return of the Portfolio** The expected return of a two-asset portfolio is: \[ E[R_p] = w_1 E[R_1] + w_2 E[R_2] \] Plugging in values: \[ E[R_p] = 0.5 \times 7.7\% + 0.5 \times 9.2\% \] \[ E[R_p] = 0.5 \times 7.7 + 0.5 \times 9.2 \] \[ E[R_p] = 3.85 + 4.60 = 8.45\% \] **Rounded to one decimal place:** \[ \boxed{8.5\%} \] --- ## **b. Volatility (Standard Deviation) of the Portfolio** The standard deviation of a two-asset portfolio is: \[ \sigma_p = \sqrt{w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \rho_{12} \sigma_1 \sigma_2} \] Let's plug in the numbers: - \( w_1 = w_2 = 0.5 \) - \( \sigma_1 = 15.5\% = 0.155 \) - \( \sigma_2 = 20.0\% = 0.20 \) - \( \rho_{12} = 0.213 \) \[ \sigma_p = \sqrt{(0.5)^2 \times (0.155)^2 + (0.5)^2 \times (0.20)^2 + 2 \times 0.5 \times 0.5 \times 0.213 \times 0.155 \times 0.20} \] Calculate each term step by step: ### Step 1: \( (0.5)^2 = 0.25 \) ### Step 2: \( (0.155)^2 = 0.024025 \) ### Step 3: \( (0.20)^2 = 0.04 \) ### Step 4: \( 0.25 \times 0.024025 = 0.00600625 \) ### Step 5: \( 0.25 \times 0.04 = 0.01 \) ### Step 6: \( 2 \times 0.5 \times 0.5 = 0.5 \) ### Step 7: \( 0.155 \times 0.20 = 0.031 \) ### Step 8: \( 0.213 \times 0.031 = 0.006603 \) ### Step 9: \( 0.5 \times 0.006603 = 0.0033015 \) ### Step 10: Add all terms inside the square root: \[ 0.00600625 + 0.01 + 0.0033015 = 0.01930775 \] ### Step 11: Take the square root: \[ \sigma_p = \sqrt{0.01930775} \approx 0.1389 \] \[ 0.1389 = 13.89\% \] **Rounded to one decimal place:** \[ \boxed{13.9\%} \] --- ## **Final Answers** a. **The expected return of the portfolio is** \(\boxed{8.5\%}\) b. **The volatility (standard deviation) of the portfolio is** \(\boxed{13.9\%}\)