A stock has a beta of 1.23 and an expected return of 12.1 percent. A risk-free a

Question

A stock has a beta of 1.23 and an expected return of 12.1 percent. A risk-free asset currently earns 3.95 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 .83, 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 11.3 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 2.43, 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:

Explanation / Answer

1)

a)expected return of portfolio

= sum of weight of stock * return of stock

= 0.5 * 12.1% + 0.5 * 3.95%

= 8.03%

b)

beta of portfolio = sum of weight of stock * beta of stock

=>

let w be weight of stock

w * 1.23 + (1-w) * 0 = 0.83

=>

w = 0.6748

weight of stock = 0.6748

weight of risk free asset = 1 -0.6748 = 0.3252

c)

let w be weight of stock

w * 12.1% + (1-w) * 3.95% = 11.3%

=>weight of stock w = 147/163

beta = 147/163 * 1.23

= 1.11

d)

w be weight of stock

w * 1.23 + (1-w) * 0 = 2.43

=>

weight of stock w = 1.9756

weight of risk free asset = 1 -w

= 1 - 1.9756

= -0.9756

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