A. Given the following information about the returns of stocks A, B, and C, what

Question

A.

Given the following information about the returns of stocks A, B, and C, what is the expected return of a portfolio invested 30% in stock A, 40% in stock B, and 30% in stock C?

Enter answer in percents.

B.

A stock has an expected return of 10.8 percent, the risk-free rate is 4.6 percent, and the market risk premium is 7.2 percent. What must the beta of this stock be?

C.

You own a portfolio equally invested in a risk-free asset and two stocks. One of the stocks has a beta of 1.25 and the total portfolio is equally as risky as the market. What must the beta be for the other stock in your portfolio?

State of economy Probability Stock A Stock B Stock C Boom 0.16 0.35 0.2 0.25 Good 0.29 0.17 0.2 0.13 Poor 0.21 0.01 0.03 0.08 Bust -- -0.16 -0.19 -0.18

Explanation / Answer

1)

Stock A

Expected return = sum of product of weight of stock in portfolio*expected return of the stock

2)

expected return = risk-free rate + beta * (market risk premium)

10.8=4.6+beta*7.2

Beta = 0.8611

3)

Weight of risk free asset=0.3333

Weight of Stock A=0.3333

Weight of Stock B=0.3333

Portfolio beta = sum of product of weight of constituents*beta of constituents

1 = 0.3333*0+0.3333*1.25+0.3333*Beta of B

Beta of B = 1.75

1)

Stock A

Scenario Probability Return =rate of return * probability Boom 0.16 0.35 0.056 Good 0.29 0.17 0.0493 Poor 0.21 0.01 0.0021 Bust 0.34 -0.16 -0.0544 Expected return = sum of weighted return = 0.053 Stock B Scenario Probability Return =rate of return * probability Boom 0.16 0.2 0.032 Good 0.29 0.2 0.058 Poor 0.21 0.03 0.0063 Bust 0.34 -0.19 -0.0646 Expected return = sum of weighted return = 0.03 Stock C Scenario Probability Return =rate of return * probability Boom 0.16 0.25 0.04 Good 0.29 0.13 0.0377 Poor 0.21 0.08 0.0168 Bust 0.34 -0.18 -0.0612 Expected return = sum of weighted return = 0.0333 weight in portfolio stock A 0.3 Stock B 0.4 Stock C 0.3 Expected return= 3.86%

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