Question #171040

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

Expert's answer

(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

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