A stock has a beta of 1.10 and an expected return of 12 percent. A risk-free ass

Question

A stock has a beta of 1.10 and an expected return of 12 percent. A risk-free asset currently earns 2.6 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 0.77, 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 9 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 2.20, what are the portfolio weights? (Negative amount should be indicated by a minus sign.)

A stock has a beta of 1.10 and an expected return of 12 percent. A risk-free asset currently earns 2.6 percent.

Explanation / Answer

Answer: "RFR" refers to the Risk-Free asset...

a) E(r) of the portfolio = (0.50)*0.026 FREE + (0.50)0.12 = 0.013 + 0.06 = 0.073 or 7.3% rounded

b) 0.77 = weight of stock*1.10
weight of stock = 0.77/ 1.10 = 0.7, round 2 places: 70%
weight of risk-free asset = 1 - weight of stock = 1 - 0.70 = 0.30, rounded: 30%

c) if the two asset portfolio has an E(r) of 9%, then the weights must be:
0.09 = weight stock(0.12) + (1 - weight of stock)(0.026)
0.09 = 0.12X + 0.026(1 - X)
"X", weight of stock = 0.68085
(1 - X), weight of RFR = (1 - weight of stock) = 0.319148 (RFRs have beta = 0), so...
weight of stock * beta of stock = beta of portfolio = 0.68085 * 1.10 = 0.748935 round to 3 places = 0.749

d) 2.20 = 1.10(weight stock "X") + 0 (1- weight of stock), reduces to:
2.20 = 1.10X
X= 2 <weight of stock...= 200%, means "weight" of RFR is: 1 - 2= (1) or NEGATIVE 100%...(this essentially means you have borrowed at the risk free rate, perhaps to help finance the purchase of the stock in the portfolio - i.e. a leveraged portfolio)

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