Question

Using CAPM, A stock has a beta of 1. 13 and an expected return of 12. 1 percent. A risk-free asset currently earns 3. 6 percent.

a. What is the expected return on a portfolio that is equally invested in the two assets? (5 marks)

b. If a portfolio of the two assets has a beta of. 50, what are the portfolio weights? (5 marks)

c. If a portfolio of the two assets has an expected return of 10 percent, what is its beta? (5 marks)

Answer 1

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.