A stock has a beta of 1.20 and an expected return of 14 percent. A risk-free ass

Question

A stock has a beta of 1.20 and an expected return of 14 percent. A risk-free asset currently earns 3.0 percent.

a. 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))

Expected return=___ %

b. If a portfolio of the two assets has a beta of 0.72, what are the portfolio weights? (Round your answer to 4 decimal places. (e.g., 32.1616))

Weight of stock= ?

Risk-free weight= ?

c. If a portfolio of the two assets has an expected return of 10 percent, what is its beta? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))

Beta= ?

d. If a portfolio of the two assets has a beta of 2.40, what are the portfolio weights? (Negative amount should be indicated by a minus sign.)

Weight of stock= ?

Risk-free weight=?

Explanation / Answer

Beta of Stock = 1.2

Expected Return = 0.14

Risk-free asset return = 0.03

a.

Expected return of a portfolio is the weighted average of the individual asset expected returns. Here the weightage is 0.50, as it is equally invested in the two assets.

Expected return = Risk-free return X Weight + Expected return X Weight

                         = 0.03 X 0.50 + 0.14 X 0.50 = 8.5%

b.

Beta of Portfolio = 0.72

Weight of stock = Beta of Portfolio/Beta of Stock = 0.72/1.2 = 0.6000

Risk-Free Weight = 1 - Weight of Stock = 1 - 0.6000 = 0.4000

c.

0.10 = Weight of stock(0.14) + (1 - Weight of stock)(0.03)

Consider Weight of stock = x

Then,

0.10 = 0.14x + (1-x)0.03

0.10 = 0.14x + 0.03 - 0.03x

0.10 = 0.11x + 0.03

0.11x = 0.07

x = 0.07/0.11 = 0.6363 which is the Weight of stock

1 - Weight of Stock = 1 - 0.6363 = 0.3636

Beta of portfolio = Weight of stock X Beta of Stock = 0.6363 X 1.2 = 0.764

d.

Beta of Portfolio = 2.4

Weight of stock = Beta of Portfolio/Beta of Stock = 2.4/1.2 = 2.0

Risk-Free Weight = 1 - Weight of Stock = 1 - 2.0 = -1.0

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