value: 10.00 points A stock has a beta of 0.7 and an expected return of 8 percen

Question

value: 10.00 points A stock has a beta of 0.7 and an expected return of 8 percent. A risk-free asset currently earns 3 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. Omit the "%"' sign in your response.) Expected return b. If a portfolio of the two assets has a beta of 0.6, what are the portfolio weights? (Round your answers to 2 decimal places. Omit the'%" sign in your response.) Weight Xs c. If a portfolio of the two assets has an expected return of 6 percent, what is its beta? (Round your answer to 2 decimal places.) Beta d. If a portfolio of the two assets has a beta of 1.40, what are the portfolio weights? (Negative amounts should be indicated by a minus sign. Omit the "%" sign in your response.) Weight Xs Xrf

Explanation / Answer

a.

Expected return is the weighted average of individual returns

Expected return = 0.5*0.08 + 0.5*0.03 = 5.5%

b.

Portfolio beta is the weighted average of individual betas.

Let xs be the weight invested in stock.

0.6 = xs*0.7 + (1-xs)*0

xs = 0.8571 = 85.71%

Xrf = 1-0.8571 = 0.1429 = 14.29%

c.

According to CAPM,
Expected return = risk free rate + beta*market risk premium

8% = 3% + 0.7*market risk premium

Market risk premium = 7.14%

Beta of the stock:

6% = 3% + beta*7.14%

beta = 0.42

d.

Portfolio beta is the weighted average of individual betas.

Let xs be the weight invested in stock.

1.4 = xs*0.7 + (1-xs)*0

xs = 2 = 200%

Xrf = 1-2 = -100%

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