A stock has a beta of 1.25 and an expected return of 12.3 percent. A risk-free a
ID: 2720262 • Letter: A
Question
A stock has a beta of 1.25 and an expected return of 12.3 percent. A risk-free asset currently earns 4.05 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 0.85, 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 11.5 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
If a portfolio of the two assets has a beta of 2.45, what are the portfolio weights? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).)
Required: (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 percentage rounded to 2 decimal places (e.g., 32.16).)
Explanation / Answer
a) Expected return on portfolio = (Es *Ws) +(Ea* Wa)
= (12.3 * .5) +(4.05 * .5 )
= 6.15 + 2.03
= 8.18 %
b)Let weight of Stock be "X"
Weight of risk free asset = 1 -X
Beta of risk free asset = 0 ,as no risk is involved
Beta of potfolio = (Bs * Ws) +(Ba * Wa)
.85 = (1.25 * X ) + (0 * [1-x)]
.85 = 1.25X + 0
X = .85 / 1.25
= .68
Weight of stock = .68
weight of risk free asset = 1-.68 = .32
c) expected return of potfolio = (Es *Ws) +(Ea* Wa)
11.5 = (12.3 *X) + [4.05 (1-X)]
= 12.3X + 4.05 - 4.05X
= 8.25 X +4.05
11.5 -4.05 = 8.25X
7.45 = 8.25X
X (Weight of stock ) = 7.45 / 8.25
= .9030
weight of risk free asset = 1 -.9030 = .0970
beta of portfolio = (1.25 * .9030) +(0* .0970)
= 1.13 + 0
= 1.13
d)Let weight of Stock be "X"
Weight of risk free asset = 1 -X
Beta of risk free asset = 0 ,as no risk is involved
Beta of potfolio = (Bs * Ws) +(Ba * Wa)
2.45 = (1.25 *X) + [ 0* (1-X)]
= 1.25X + 0
X = 2.45 /1.25
Weight of stock = 1.96
weight of risk free asset = 1- 1.96 = -.96
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