A stock has a beta of 1.15 and an expected return of 10.4 percent. A risk-free a
ID: 2780655 • Letter: A
Question
A stock has a beta of 1.15 and an expected return of 10.4 percent. A risk-free asset currently earns 3.8 percent.
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 percentage rounded to 2 decimal places (e.g., 32.16).)
If a portfolio of the two assets has a beta of .7, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).)
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., 32.162).)
If a portfolio of the two assets has a beta of 2.3, what are the portfolio weights? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places (e.g., 32.1616).)
A stock has a beta of 1.15 and an expected return of 10.4 percent. A risk-free asset currently earns 3.8 percent.
Explanation / Answer
a.
Expected return of the portfolio is the weighted average of individual returns.
weight of stock = 0.5
weight of stock = 1-0.5 = 0.5
Expected return = 0.5*10.4% + 0.5*3.8% = 0.0710 = 7.10%
b.
Beta of the portfolio is the weighted average of individual betas.
Let the weight of stock = x
weight of risk free asset = 1-x
Beta of risk free asset = 0
0.7 = x*1.15 + (1-x)*0
x = 0.60870
weight of the stock = 60.87%
weight of rf asset = 1-60.87% = 39.13%
c.
According to CAPM,
Expected return = risk free rate + beta*market risk premium
From the stock's return,
10.4% = 3.8% + 1.15*market risk premium
market risk premium = 5.74%
Now, for the portfolio of two assets
9% = 3.8% + beta*5.74%
beta = 0.91
d.
Beta of the portfolio is the weighted average of individual betas.
Let the weight of stock = x
weight of risk free asset = 1-x
Beta of risk free asset = 0
2.3 = x*1.15 + (1-x)*0
x = 2
weight of the stock = 200%
weight of rf asset = 1-200% = -100%
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