15. A $16,000 portfolio is invested in a risk-free security and two stocks. The

Question

15. A $16,000 portfolio is invested in a risk-free security and two stocks. The beta of stock A is 0.73 while the beta of stock B is 1.99. One-half of the portfolio is invested in the risk-free security. How much is invested in stock A if the beta of the portfolio is 0.67?

Part B Aine would like to create a portfolio that is equally invested in a risk-free asset and two stocks. The one stock has a beta of 1.14. What does the beta of the second stock have to be if Aine wants the portfolio risk to equal that of the overall market?

Part C The common stock of Modron Creations has an expected return of 13.89 percent and a beta of 1.41. The expected return on the market is 10.77 percent. What is the risk-free rate (in percents)?

Explanation / Answer

Portfolio beta is the weighted average of individual betas.

A.

Beta of a risk free rate is 0.

0.67 = 1/2*0 + x*0.73 + (1/2-x)*1.99

x = 0.2579 = 25.79% of the portfolio

Amount invested in stock A = 25.79%*16000 = $4126.98

B.

Market beta = 1

1 = 1/3*0 + 1/3*1.14 + 1/3*x

x = 1.86, Beta of the second stock = 1.86

C.

According to CAPM,

Expected return = risk free rate + beta*(Market return - risk free rate)

0.1389 = x + 1.41*(0.1077 - x)

x = 0.0316 = 3.16%

risk free rate = 3.16%

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