A stock has a beta of 1.05 and an expected return of 11 percent. A risk-free ass

Question

A stock has a beta of 1.05 and an expected return of 11 percent. A risk-free asset currently earns 2.4 percent.

What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. (e.g., 32.16))

If a portfolio of the two assets has a beta of 0.63, what are the portfolio weights? (Round your answer to 4 decimal places. (e.g., 32.1616))

If a portfolio of the two assets has an expected return of 7 percent, what is its beta? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))

If a portfolio of the two assets has a beta of 2.10, what are the portfolio weights? (Negative amount should be indicated by a minus sign.)

A stock has a beta of 1.05 and an expected return of 11 percent. A risk-free asset currently earns 2.4 percent.

Explanation / Answer

a. Expected return = 0.5 * 11% + 0.5 * 2.4%

= 6.7%

b. Portfolio beta = beta of stock * weightage of stock + beta of risk free asset * weightage of risk free asset

=> 0.63 = 1.05 * weightage of stock + 0

=> Weightage of stock = 0.6

Therefore, Weightage of risk free asset = 1 - 0.6

= 0.4

c. Expected return of portfolio = return of stock * weightage of stock + return of risk free asset * weightage of risk free asset

=> 7% = 11% * weightage of stock + 2.4% * (1 - weightage of stock)

=> weightage of stock = 0.535

Therefore, Beta of portfolio = 1.05 * 0.535

= 0.562

d. Portfolio beta = beta of stock * weightage of stock + beta of risk free asset * weightage of risk free asset

=> 2.10 = 1.05 * weightage of stock + 0

=> Weightage of stock = 2.0

Therefore, Weightage of risk free asset = 1 - 2.0

= -1.0

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