A stock has a beta of 1.2 and an expected return of 11.8 percent. A risk-free as

Question

A stock has a beta of 1.2 and an expected return of 11.8 percent. A risk-free asset currently earns 3.8 percent. Required: (a) 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 percentage rounded to 2 decimal places (e.g., 32.16).) If a portfolio of the two assets has a beta of 0.8, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).) If a portfolio of the two assets has an expected return of 11 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) If a portfolio of the two assets has a beta of 2.4, what are the portfolio weights? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).)

Explanation / Answer

a) expected return of portfolio =

(Weight of stock *expected return of stock) + (weight of risk free asset *return of risk free asset)

= 11.8%*.5. + 3.8%*.5 = 7.80%

b) .8 = weight of stock * 1.2 + weight of risk free asset*0

Weight of stock = .8/1.2 = .67

Weight of stock = 67%

Weight of risk free asset = 100-67= 33%

c) 11% = weight of stock*11.8% + (1-weight of stock)*3.8%

11%= 8*weight of stock + 3.8%

Weight of stock = .9 or 90%

Weight of risk free asset = 10%

Portfolio beta = 1.2*90% = 1.08

d) 2.4 = weight of stock * 1.2 + weight of risk free asset*0

Weight of stock = 2.4/1.2

Weight of stock = 200%

Weight of risk free asset = 0

#beta of a risk free asset is zero, since there is no risk and beta is a measure of risk

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