Question

A stock has a beta of 1.75 and an expected return of 12 percent. A risk-free asset currently earns 3.0 percent.a. What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. (e.g., 32.16)) Expected return %b. If a portfolio of the two assets has a beta of 0.98, what are the portfolio weights? (Round your answer 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 and round your answer to 3 decimal places. (e.g., 32.161)) Beta d. If a portfolio of the two assets has a beta of 3.50, what are the portfolio weights? (Negative amount should be indicated by a minus sign.)Weight of stock Risk-free weight

Answer 1

Answer:

a) Expected return of portfolio = (12*.5 ) +(3*.5)  = 6 + 1.5  = 7.5%

b)Beta of risk free asset = 0 (as there is no risk involved)

Let weight of stock = X

Weight of risk free asset = 1-X

Portfolio beta = (Beta of stock *Ws) +(Beta of risk free asset *Wd)

0.98 = (1.75 *X)+(0 *[1-X)]

0.98 = 1.75x + 0

X = 0.98 /1.75

X  = 0.56

Weight of stock = 0.56 or 56%

Weight of risk free asset = 1 - 0 .56 = 0.44 or 44%

c) Expected rate = Rf+Beta *(Market rate - Rf)

12% = 3% + 1.75*(Market rate - RF)

(Market rate - Rf) = 9%/1.75

(Market rate - Rf) = 5.1429%

Now expected rate is given as 9%

Expected rate = Rf + Beta*(Market rate - Rf)

9% = 3% + Beta*(Market rate - Rf)

Beta = 6%/5.1429%

Beta = 1.1667

d) 3.50 = [1.75*X ] + [0*(1-X)]

3.5 = 1.75X + 0

X = 3.5/1.75

X = 2

Weight of stock = 2 or 200%

Weight of risk free asset = 1 - 2 = -1 or -100%