A stock has a beta of 1.15 and an expected return of 13 percent. A risk-free ass
ID: 2777743 • Letter: A
Question
A stock has a beta of 1.15 and an expected return of 13 percent. A risk-free asset currently earns 2.8 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % b. If a portfolio of the two assets has a beta of .92, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places, e.g., 32.1616.) Weight of stock Risk-free weight c. If a portfolio of the two assets has an expected return of 9 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 3 decimal places, e.g., 32.161.) Beta d. If a portfolio of the two assets has a beta of 2.30, what are the portfolio weights? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Enter your answers as a whole number.) Weight of stock Risk-free weight
Explanation / Answer
a. Expected return = 0.5 * 13% + 0.5 * 2.8%
= 7.90%
b. Portfolio beta = Weightage of stock * beta of stock + Weightage of risk-free asset * beta of risk-free asset
=> 0.92 = Weightage of stock * 1.15 + Weightage of risk-free asset * 0
=> Weightage of stock = 0.80
So, Weightage of risk-free asset = 1 - 0.80
= 0.20
c. Expected return = Weightage of stock * Return of stock + (1 - Weightage of stock) * Return of risk-free asset
=> 9.00% = Weightage of stock * 13.00% + (1 - Weightage of stock) * 2.80%
=> Weightage of stock = 0.61
So, Portfolio beta = 1.15 * 0.61
= 0.70
d.
Portfolio beta = Weightage of stock * beta of stock + Weightage of risk-free asset * beta of risk-free asset
=> 2.30 = Weightage of stock * 1.15 + Weightage of risk-free asset * 0
=> Weightage of stock = 2.00
So, Weightage of risk-free asset = 1 - 2.00
= -1.00 (negative sign indicates that the money has been raised at risk-free rate)
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