Calculating Portfolio Betas You own a stock portfolio invested 10 percent in Sto

Question

Calculating Portfolio Betas You own a stock portfolio invested 10 percent in Stock Q, 35 percent in Stock R, 20 percent in Stock S, and 35 percent in Stock T. The betas for these four stocks are.75,1.90, 1.38, and 1.16, 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 1.65 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 1.15, the expected return on the market is 11 percent, and the risk-free rate is 5 percent. What must the expected return on this stock be? Using CAPM A stock has an expected return of 10.2 percent, the risk-free rate is 4 percent, and the market risk premium is 7 percent. What must the beta of this stock be?

Explanation / Answer

10.

Stock Beta Percentage of portfolio Beta times % of portfolio

Q 0.75 10% 0.075

R 1.90 35% 0.665

S 1.38 20% 0.276

T 1.96 35% 0.686

Portfolio beta = 0.075+0.665+0.276+0.686 = 1.7

12.

Expected return = Rf + beta(Rm - Rf)

= 0.05 + 1.15(0.11 - 0.05)

= 0.05 + 1.15(0.06)

= 0.05 + 0.069 = 0.119 or 11.9%

13. 0.102 = 0.04 + beta (0.07 - 0.04)

0.102 = 0.04 + beta ( 0.03)

0.102 - 0.04 = beta (0.03)

0.062 = beta 0.03

beta = 0.062 / 0.03 = 2.066

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