Answer:
The beta of the portfolio is 0.87.
Step-by-step explanation:
a. To calculate the expected return on a portfolio that is equally invested in the two assets, we can use the weighted average approach. Since the portfolio is equally invested, each asset receives a weight of 0.5.
Expected Return of the Portfolio = (Weight of Asset A × Expected Return of Asset A) + (Weight of Asset B × Expected Return of Asset B)
Expected Return of the Portfolio = (0.5 × 12.1%) + (0.5 × 3.6%)
Expected Return of the Portfolio = 6.05% + 1.8%
Expected Return of the Portfolio = 7.85%
Therefore, the expected return on the equally invested portfolio is 7.85%.
b. Given that the portfolio of the two assets has a beta of 0.50, we can calculate the portfolio weights using the following formula:
Beta of the Portfolio = (Weight of Asset A × Beta of Asset A) + (Weight of Asset B × Beta of Asset B)
0.50 = (Weight of Asset A × 1.13) + (Weight of Asset B × ?) -- We need to solve for the weight of Asset B.
Since the sum of the weights is 1 (or 100%), we can solve for the weight of Asset B:
1 - Weight of Asset A = Weight of Asset B
1 - Weight of Asset A = Weight of Asset B
1 - Weight of Asset A = 1 - Weight of Asset A
Therefore, the portfolio weights are equally divided between the two assets, with a weight of 0.50 (or 50%) for each asset.
c. If a portfolio of the two assets has an expected return of 10%, we can calculate its beta using the following formula:
Expected Return of the Portfolio = (Weight of Asset A × Expected Return of Asset A) + (Weight of Asset B × Expected Return of Asset B)
10% = (Weight of Asset A × 12.1%) + (Weight of Asset B × 3.6%) -- We need to solve for the beta of the portfolio.
Using the weights obtained in part b (weight of Asset A = 0.50, weight of Asset B = 0.50), we can calculate the beta of the portfolio:
Beta of the Portfolio = (Weight of Asset A × Beta of Asset A) + (Weight of Asset B × Beta of Asset B)
Beta of the Portfolio = (0.50 × 1.13) + (0.50 × ?) -- We need to solve for the beta of Asset B.
Substituting the weights:
1 = (0.5 × 1.13) + (0.5 × ?)
Simplifying the equation:
1 = 0.565 + 0.5 × ?
0.5 × ? = 1 - 0.565
0.5 × ? = 0.435
? = 0.87
Therefore, the beta of the portfolio is 0.87.