Why Choose Us?
0% AI Guarantee
Human-written only.
24/7 Support
Anytime, anywhere.
Plagiarism Free
100% Original.
Expert Tutors
Masters & PhDs.
100% Confidential
Your privacy matters.
On-Time Delivery
Never miss a deadline.
A stock has a beta of 1
A stock has a beta of 1.37 and an expected return of 13.5%. a risk free asset currently earns 4.65%.
a. What is the expected return on a portfolio that is equally invested in the two assets? (provide answer as a percent rounded two decimal places, e.g., 25.13%)
b. If a portfolio of the two assets has a beta of .97, what are the portfolio weights? ( round answer to 4 decimal places, e.g., .2546)
c. If a portfolio of the two assets has an expected return of 12.7%, what is its beta? (round answer to 2 decimal places, e.g., 25.13)
d. If a portfolio of the two assets has a beta of 2.57, what are the portfolio weights? ( round answer to 4 decimal places, e.g., .4525)
Expert Solution
a). Computation of the expected return on portfolio:-
Expected return on portfolio = (Weight of stock * Return of stock) + (Weight of risk free asset * Return of risk free asset)
= (50% * 13.5%) + (50% * 4.65%)
= 6.75% + 2.33%
= 9.08%
b). Computation of the portfolio weights:-
W = Weight of stock
Beta of portfolio = (Weight of stock * Beta of stock) + (Weight of risk free asset * Beta of risk free asset)
0.97 = (W * 1.37) + ((1 - W) * 0)
0.97 = W * 1.37
W = 0.97 / 1.37
= 0.7080
Weight of risk free asset = 1 - W
= 1 - 0.7080
= 0.2920
c). Computation of the beta:-
Expected return on portfolio = (Weight of stock * Return of stock) + (Weight of risk free asset * Return of risk free asset)
12.7% = (W * 13.5%) + ((1-W) * 4.65%)
12.7% = (W * 13.5%) + 4.65% - (W * 4.65%)
12.7% - 4.65% = (W * 8.85%)
W = 8.05% / 8.85%
= 0.9096
W = Weight of stock = 0.9096
Weight of risk free asset = 1 - W
= 1 - 0.9096
= 0.0904
Beta of portfolio = (Beta of stock * Weight of stock) + (Beta of risk free asset * Weight of risk free asset)
= (1.37 * 0.9096) + (0 * 0.0904)
= 1.25
d). Computation of the portfolio weights:-
Beta of portfolio = (Beta of stock * Weight of stock) + (Beta of risk free asset * Weight of risk free asset)
2.57 = (1.37 * W) + (0 * (1 - W))
2.57 = 1.37 * W
W = 2.57 / 1.37
= 1.8759
Weight of risk free asset = 1 - W
= 1 - 1.8759
= -0.8759
Archived Solution
You have full access to this solution. To save a copy with all formatting and attachments, use the button below.
For ready-to-submit work, please order a fresh solution below.
