A stock has a beta of .8 and an expected return of 12 percent. A risk-free asset

Question

A stock has a beta of .8 and an expected return of 12 percent. A risk-free asset currently earns 4.3 percent.

What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

If a portfolio of the two assets has a beta of .71, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

If a portfolio of the two assets has an expected return of 8.75 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

If a portfolio of the two assets has a beta of 1.04, what are the portfolio weights? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

A stock has a beta of .8 and an expected return of 12 percent. A risk-free asset currently earns 4.3 percent.

Explanation / Answer

A) (.12*.5) + (.043*.5) = 0.0815 or 8.15%

B) 0.71 = (0.8*X) + (1 - X) (0) = .8875 or 88.75% for stock with 0.8 Beta & 11.25% for Risk Free asset.

C) A portfolio with 58% of stock with 0.8 Beta & 42% of Risk free asset will give an expected return of 8.766%. (8.75 Approximately)
    Hence the beta of portfolio = (.58*.8) + (.42*0) = 0.464, So the beta of portfolio is 0.466
(Note: Beta of a Risk Free asset is 0)

D) 1.04 = (X+0.8) + (1 - X) (0) = 1.3, Which means the weight of asset with 0.8 beta is 1.3 & weight of risk free asset is -0.3 (A negative figure of Risk Free asset means the investor will borrow money on risk free rate & invest in risky asset in addition to its current capital)

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