A stock has a beta of 1.60 and an expected return of 10 percent. A risk-free ass

Question

A stock has a beta of 1.60 and an expected return of 10 percent. A risk-free asset currently earns 2.4 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 .88, 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 9 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 3.20, 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.)

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.)

Explanation / Answer

(a)

Expected return = 0.50 x 10% + 0.5 x 2.4%

= 5% + 1.2% = 6.20%

(b)

Let weight of the risky asset = W

then,

W x 1.6 + (1 - W) x 0* = 0.88 [* Beta of risk-free asset = 0]

1.6W = 0.88

W = 0.88 / 1.60 = 0.55

So,

Weight in risky asset = 55.0000% & weight of risk-free asset = 100% - 55% = 45.0000%

(c)

Let weight of the risky asset = W

W x 10% + (1 - W) x 2.4% = 9%

W x (10 - 2.4)% = (9 - 2.4)%

7.6W = 6.6

W = 0.8684

Portfolio beta = 0.8684 x 1.60 + (1 - 0.8684) x 0 [Since risk free asset has zero beta]

= 1.389

(d)

Let weight of the risky asset = W.

W x 1.6 + (1 - W) x 0 = 3.2

1.6W = 3.2

W = 2 (200%)

This question is incorrect. Weight can never be more than 100%. Even otherwise, when Beta of 1 stock is 1.6 and beta of the 2nd stock is 0, the weighted average (portfolio) beta can never be higher than 1.60. Please cross-check your data.

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