A stock has a beta of 1.85 and an expected return of 14 percent. A risk-free ass
ID: 2645597 • Letter: A
Question
A stock has a beta of 1.85 and an expected return of 14 percent. A risk-free asset currently earns 3.4 percent.
What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))
If a portfolio of the two assets has a beta of .74, what are the portfolio weights? (Do not round intermediate calculations and round your answers to 4 decimal places. (e.g., 32.1616))
If a portfolio of the two assets has an expected return of 8 percent, what is its beta? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))
If a portfolio of the two assets has a beta of 3.70, what are the portfolio weights? (Do not round intermediate calculations and negative amount should be indicated by a minus sign.)
A stock has a beta of 1.85 and an expected return of 14 percent. A risk-free asset currently earns 3.4 percent.
Explanation / Answer
A stock has a beta of 1.85 and an expected return of 14 percent. A risk-free asset currently earns 3.4 percent.
a.What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))
Expected return = 14*1/2 + 3.4*1/2
Expected return = 8.7%
Answer
Expected return 8.7%
b.If a portfolio of the two assets has a beta of .74, what are the portfolio weights? (Do not round intermediate calculations and round your answers to 4 decimal places. (e.g., 32.1616))
Beta of Portfolio = weight of Stock * beta of stock + (1-weight of stock)*beta of risk free asset
0.74 = weight of Stock*1.85 + (1-weight of Stock)*0
weight of Stock = 0.74/1.85
Weight of Stock = 0.40
Risk-free weight = 1- 0.40
Risk-free weight = 0.60
Answer
Weight of stock = 0.40
Risk-free weight = 0.60
c.If a portfolio of the two assets has an expected return of 8 percent, what is its beta? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))
expected return of Portfolio = weight of Stock * expected return of stock + (1-weight of stock)*expected return of risk free asset
8 = weight of Stock*14 + (1-weight of Stock)*3.4
8 = 14weight of Stock + 3.4 - 3.4weight of Stock
8-3.4 = 10.6weight of Stock
weight of Stock = 4.6/10.6
Risk-free weight = 1- 4.6/10.6
Risk-free weight = 6/10.6
Beta of Portfolio = weight of Stock * beta of stock + Risk-free weight*beta of risk free asset
Beta of Portfolio = 4.6/10.6*1.85 + 6/10.6 * 0
Beta of Portfolio = 0.803
Answer
Beta 0.803
d.If a portfolio of the two assets has a beta of 3.70, what are the portfolio weights? (Do not round intermediate calculations and negative amount should be indicated by a minus sign.)
Beta of Portfolio = weight of Stock * beta of stock + (1-weight of stock)*beta of risk free asset
3.70 = weight of Stock*1.85 + (1-weight of Stock)*0
weight of Stock =3.70/1.85
Weight of Stock = 2
Risk-free weight = 1-2
Risk-free weight = -1
Answer
Weight of stock = 2
Risk-free weight = -1
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