Question

Calculating Portfolio Betas You own a stock portfolio invested 15 percent in Stock Q, 25 percent in Stock R, 40 percent in Stock S, and 20 percent in Stock T. The betas for these four stocks are . 78, 87, 1.13, and 1.45, respectively. What is the portfolio beta? Calculating Portfolio Betas You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.29 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio? Using CAPM A stock has a beta of 1.14, the expected return on the market is 10.9 percent, and the risk-free rate is 3.6 percent. What must the expected return on this stock be? Using CAPM A stock has an expected return of 11.4 percent, the risk-free rate is 3.7 percent, and the Page 384 market risk premium is 6.8 percent. What must the beta of this stock be?

Answer 1

a.Portfolio beta=Respective beta*Respective weight

=(0.15*0.78)+(0.25*0.87)+(0.40*1.13)+(0.2*1.45)

=1.0765

b.Weight of each=(1/3)

Portfolio beta=Respective beta*Respective weight

1=(1/3*1.29)+(1/3*Beta of other stock)+(1/3*0)[Beta of market=1;Beta of risk-free assets=0 ]

1=0.43+(1/3*Beta of other stock)

Beta of other stock=(1-0.43)*3

=1.71

c.Expected return=risk free rate+beta*(market rate-risk free rate)

=3.6+1.14*(10.9-3.6)

=11.922%

d.Expected rate=risk free rate+Beta*market risk premium

11.4=3.7+Beta*6.8

Beta=(11.4-3.7)/6.8

=1.13(Approx).