Question

A stock has a beta of 1.38 and an expected return of 13.6 percent. A risk-free asset currently earns 4.7 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % b. If a portfolio of the two assets has a beta of .98, what are the portfolio weights? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.) Weight of the stock Weight of the risk-free asset c. If a portfolio of the two assets has an expected return of 12.8 percent, what is its beta? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Beta d. If a portfolio of the two assets has a beta of 2.58, what are the portfolio weights? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.) Weight of the stock Weight of the risk-free asset

Answer 1

1) Expected return of portfolio = 13.6% x 0.5 + 4.7% x 0.5 = 9.15%

?2) Beta of risk free asset is always zero since its return is not dependent on the market and it provides a single risk free return. Let weight of stock be W. Then, weight of risk free asset is (1 - W)

Beta of portfolio = Weight of stock x Beta of stock + Weight of risk free asset x Beta of risk free asset

or, 0.98 = W x 1.38 + (1 - W) x 0

or, W = 0.98 / 1.38 = 0.7101

Therefore, Weight of stock = ?0.7101, Weight of risk free asset = 1 - 0.7101 = 0.2899

3) We just need to find the weight of stock to compute beta of portfolio since beta of risk free asset would be zero. Let weight of stock be W and then weight of risk free asset is (1 - W).

Expected return on Portfolio = weight of stock x return of stock + weight of risk free asset x return of risk free asset

or, 12.8% = W x 13.6% + (1 - W) x 4.7%

or, 12.8% = 13.6% W + 4.7% - 4.7% W

or, W = 0.91011235955

Therefore, weight of stock = 0.91011235955

Portfolio beta = Beta of stock x weight of stock = 1.38 x 0.91011235955? = 1.255955 or 1.26

4) This is similar to part 2. Let weight of Stock be W and then weight of risk free asset is (1 - W).

Beta of portfolio = Weight of stock x Beta of stock + Weight of risk free asset x Beta of risk free asset

or, 2.58 = W x 1.38 + (1 - W) x 0

or, W = 2.58 / 1.38 = 1.8696

Therefore, ?Weight of stock = 1.8696, Weight of risk free asset = 1 - 1.8696 = (-)0.8696