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.

a. 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))

Expected return= %

b. If a portfolio of the two assets has a beta of .80, what are the portfolio weights? (Do not round intermediate calculations and round your answers 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 8 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 2.00, what are the portfolio weights? (Do not round intermediate calculations and negative amount should be indicated by a minus sign.)

Weight of stock =

Risk-free weight =

Explanation / Answer

Note: Risk free security always has zero beta.

a) Expected return = R1 * W1 + R2 * W2

= 10%*.50 + 2.2% * .50

= 6.6%

b) Portfolio beta = B1 * W1 + B2 * 0

.80 = 1 * W1 + 0 * (1 - W1)

W1 = .80

STock Weight = 80%

RIsk free security weight = 20%

c) First calculationg weights of investment:

8% = 10% * W + 2.2% * (1 - W)

.08 = .10W + .022 - .022W

W = .7435

Beta = 1 * .7435 + 0

= .7435

d) Porftfoilo beta = B1 * W1 + B2 * (1 - W1)

2 = 1 * W1 + 0 * (1 - W1)

W1 = 2

STock weight = 2

RIsk free weight = 1-2 = 1

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