A stock has a beta of 1.12 and an expected return of 10.8 percent. A risk-free a

Question

A stock has a beta of 1.12 and an expected return of 10.8 percent. A risk-free asset currently earns 2.7 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? b. If a portfolio of the two assets has a beta of.92, what are the portfolio weights? (Do c. If a portfolio of the two assets has an expected return of 9 percent, what is its beta? d. If a portfolio of the two assets has a beta of 2.24, what are the portfolio weights? (Do (Do not round intermedlate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) not round Intermediate calculations and round your answers to 4 decimal places, e.g .1616.) (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) not round intermediate calculations. A negative answer should be indicated by a minus sign.) a. Expected return b. Weight of stock Weight of risk-free c. Beta d. Weight of stock Weight of risk-free

Explanation / Answer

b) Let share in stock be x:
1.12*x+(1-x)*0=.92
x=0.92/1.12=0.8214
Weight of Stock =0.8214
Weight of risk free= 0.1786

c)Return =risk free+beta(premium)
risk free=2.7%
10.8=2.7+1.12*premium
Premium =7.2321%

Now for 9%:
9=2.7+beta*7.2321
beta=0.871

d)weight of stock=2.24/1.12=2.000
Weight of risk free =-1.000 ( it means there is borrowing at risk free rate to invest in stock)

Stock Risk free Return 10.80% 2.70% beta 1.12 0 a) Expected portfolio return 6.75% (10.8+2.7)/2=6.75

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