Question

The $10.00 million mutual fund Henry manages has a beta of 1.05 and a 9.50% required return. The risk-free rate is 4.20%. Henry now receives another $3.75 million, which he invests in stocks with an average beta of 0.65. What is the required rate of return on the new portfolio? (Hint: You must first find the market risk premium, then find the new portfolio beta.) Select the correct answer.

a. 9.03%

b. 8.95%

c. 9.11%

d. 9.19%

e. 8.87%

Answer 1

Currently:

Required return=risk free rate+beta*(market rate-risk free rate)

9.5=4.2+1.05*(Market rate-4.2)

(9.5-4.2)=1.05*(Market rate-4.2)

Market rate=(9.5-4.2)/1.05+4.2

=9.24761905%

Hence required return for $3,750,000=4.2+(9.24761905-4.2)*0.65

=7.48095238%

Total value=(10,000,000+3,750,000)=$13,750,000

Portfolio return=Respective return*Respective weight

=(10,000,000/13,750,000*9.5)+(3,750,000/13,750,000*7.48095238)

=8.95%(Approx)