A stock has a beta of 1.00 and an expected return of 10 percent. A risk-free ass

Question

A stock has a beta of 1.00 and an expected return of 10 percent. A risk-free asset currently earns 2.2 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, e.g., 32.16.)

If a portfolio of the two assets has a beta of .80, 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 8 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 3 decimal places, e.g., 32.161.)

If a portfolio of the two assets has a beta of 2.00, what are the portfolio weights? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Enter your answers as a whole number.)

A stock has a beta of 1.00 and an expected return of 10 percent. A risk-free asset currently earns 2.2 percent.

Explanation / Answer

Solution.

A. Calculation for expected return.

a) E(r) of the portfolio = (0.50)0.022 + (0.50)0.10 = 0.011 + 0.05 = 0.061, or 6.1% rounded

B. Calculation for portfolio weights.

b) 0.80 = weight of stock*1.20
weight of stock = 0.80/ 1.20 = 0.666667, round 2 places: 66.67%
weight of risk-free asset = 1 - weight of stock = 1 - 0.666667 = 0.333334, rounded: 33.34% .

D. Calculation for portfolio weights

Solving for the of the portfolio as we did in part a, we find:

P = 2.00 = w S (1.00) + (1 w S )(0)

w S = 2.00/1.00 = 2

w Rf = 1 2 = 1

In other words, the portfolio is invested 200% in the stock and 100% in the risk-free asset. This represents borrowing at the risk-free rate to buy more of the stock

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