Question

QUESTION

 (a). ABC's stock has a 50% chance of producing a 35% return, a 30% chance of producing a 10% return, and a 20% chance of producing a 28% return. What is ABC's expected return and standard deviation?

(b). XYZ's stock had a required return of 11.50% last year, when the risk-free rate was 5.50% and the market risk premium was 4.75%. Now suppose there is a shift in investor risk aversion, and the market risk premium increases by 2%. The risk-free rate and XYZ's beta remain unchanged. What is XYZ's new required return? (Hint: First calculate the beta, then find the required return.)

(c).Consider the following information and then calculate the required rate of return for the Scientific Investment Fund, which holds 4 stocks. The market's required rate of return is 15.0%, the risk-free rate is 7.0%, and the Fund's assets are as follows:

Stock Investment Beta

A K200,000 1.5

B 300,000 0.50

C 500,000 1.25

D 1,000,000 0.75

Answer 1

(a) $expected yield=0.5\times35+0.3\times10+0.2\times28=26.1$

$standard deviation=\sqrt{\frac{(35-26.1)^2+(10-26.1)^2+(28-26.1)^2}{3-1}}=13.08$

(b)

$Re=Rf+\beta(Rm-Rf)$

Re=11.50

Rf=5.50

Rm-Rf=4.75

$11.50=5.50+\beta\times4.75$

$\beta=1.26$

$11.50=5.50+\beta\times6.75$

$\beta=0.89$

1.26-0.89=0.37

(с)

$Re=Rf+\beta(Rm-Rf)$

Rf=7.0

Re=15

$\beta=\frac{200 000}{2 000 000}\times1.5+\frac{300 000}{2 000 000}\times0.5 +\frac{500 000}{2 000 000}\times1.25+\frac{1 000 000}{2 000 000}\times0.75=0.91$

$15=7.0+0.91(Rm-Rf)$

Rm-Rf=8.79

Rm=8.79-7.0=1.79