Question

A stock has a beta of 0.9 and an expected return of 9 percent. A risk-free asset currently earns 4 percent.

a. 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.) b. If a portfolio of the two assets has a beta of 0.5, what are the portfolio weights? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

c. 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 2 decimal places.)

Answer 1

a) The return of a portfolio is the weighted average return of the securities which constitute the porfolio.

Security	Weight	Expected Return(%)	Weight*Expected Return
Stock	0.5	9	4.5
Risk free asset	0.5	4	2

Portfolio Return = 6.50 % (4.50+2.00)

b) The beta of a portfolio is the weighted average beta of the securities which constitute the porfolio.

Let weight of Stock be x, weight of risk free asset is 1-x

Security	Weight	Beta	Weight*Beta
Stock	x	0.9	.9x
Risk free asset	1-x	0	0

.9x + 0 =.5

x = 55.56%

weight of Stock is 55.56% and weight of risk free asset is 44.44%

note: beta of risk free asset is zero

c) Calculation of portfolio beta

a) Find weight under given portfolio return

Let weight of Stock be x, weight of risk free asset is 1-x

Security	Weight	Expected Return	Weight*Expected Return
Stock	x	9	9x
Risk free asset	1-x	4	4(1-x)

9x + 4 - 4x = 8

5x = 4

x = .80

weight of Stock is 80% and weight of risk free asset is 20%

b) Calculation of portfolio beta

Security	Weight	Beta	Weight*beta
Stock	0.8	0.9	0.72
Risk free asset	0.2	0	0

Portfolio Beta = 0.72