Question

Assume that you manage a $10 million mutual fund that has a beta of 1.05 and a 9.5% required return. The risk-free rate is 4.2%. You now receive another $5 million, which you invest in stocks with an average beta of 0.65. What is the required rate of return on the new portfolio? *

a) 8.83%

b) 9.05%

c) 9.27%

d) 9.51%

Answer 1

Ans) a) 8.83%

First of all let's calculate Market return

Required return = Risk free rate of return + Beta(Market return - Risk free rate of return)

9.5% = 4.2% + 1.05(Market return - 4.2%)

=5.3% = 1.05(Market return - 4.2%)

=5.0476% = (Market return - 4.2%)

=Thus market return = 5.0476% +4.2%

= 9.2476%

Now another $ 5 million worth aset has average beta of 0.65

Statement showing beta of portfolio

Amount	Weight A	Beta B	Portfolio beta A x B
10.00	0.67	1.05	0.70
5.00	0.33	0.65	0.22
Portfolio Beta	0.9167

Thus new required return

=  Required return = Risk free rate of return + Beta(Market return - Risk free rate of return)

= 4.2% + 0.9167(9.2476% -4.2%)

=4.2% + 0.9167(5.0476%)

=4.2% + 4.6271%

=8.83%