A stock has a beta of 1.45 and an expected return of 13 percent. A risk-free ass

Question

A stock has a beta of 1.45 and an expected return of 13 percent. A risk-free asset currently earns 4 percent.

What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))

If a portfolio of the two assets has a beta of .87, what are the portfolio weights? (Do not round intermediate calculations and round your answers 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 2.90, what are the portfolio weights? (Do not round intermediate calculations and negative amount should be indicated by a minus sign.)

A stock has a beta of 1.45 and an expected return of 13 percent. A risk-free asset currently earns 4 percent.

Explanation / Answer

Note: It is assumed that one asset is stock and another asset is risk free asset

a) Expected Return of portfolio = (13 + 4)/2 = 8.5%

b) let the weight of stock be x. So weight of risk free asset is (1-x)

Beta of portfolio = Beta of stock x weight of stock + Beta of risk free asset x weight of risk free asset

0.87 = 1.45x + 0

x = 0.60 (weight of stock )

weight of risk free asset = 0.40

c) let the weight of stock be x. So weight of risk free asset is (1-x)

9 = 13x + 4 - 4x

x = 0.55

Beta of Portfolio = 1.45x0.55 = 0.798

d)let the weight of stock be x. So weight of risk free asset is (1-x)

Beta of portfolio = Beta of stock x weight of stock + Beta of risk free asset x weight of risk free asset

2.90 = 1.45x + 0

x = 2

x cannot be more than one. Since it is not possible to have beta of 2.90 with assets having beta of 1.45 and 0. This solution is not possible.

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