Question

Joel Foster is the portfolio manager of the SF Fund, a $3 million hedge fund that contains the following stocks. The required rate of return on the market is 11.00% and the risk-free rate is 5.00%. What rate of return should investors expect (and require) on this fund?
Stock Amount Beta
A $1,075,000 1.20
B 675,000 0.50
C 750,000 1.40
D 500,000 0.75
TOTAL 3,000,000

(A) 10.56%
(B) 10.83%
(C) 11.11%
(D) 11.38%
(E) 11.67%

Answer 1

Answer:

(C) 11.11%

Explanation:

In this question, we use the Capital Asset Pricing Model formula which is shown below:

Expected rate of return = Risk-free rate + Beta × (Required rate of return - risk-free rate)

The beta is not given so first we have to compute it. The calculation is shown below:

Stock A = (Stock amount ÷ total amount) × Beta

             = ( $1,075,000 ÷ $3,000,000) × 1.20

             = 0.3583 × 1.20

             = 0.43

Stock B = (Stock amount ÷ total amount) × Beta

             = ($675,000 ÷ $3,000,000) × 0.50

             = 0.225 × 0.50

             = 0.1125

Stock C = (Stock amount ÷ total amount) × Beta

             = ( $750,000 ÷ $3,000,000) × 1.40

             = 0.25 × 1.40

             = 0.35

Stock D = (Stock amount ÷ total amount) × Beta

             = ( $500,000 ÷ $3,000,000) × 0.75

             = 0.1667 × 0.75

             = 0.1251

The total value of beta equals to

= 0.43 + 0.1125 +  0.35 + 0.1251

= 1.017

Now put these values to the above formula  

So, the value would equal to

= 5% + 1.017 × (11% - 5%)

= 5% + 6.102%

= 11.102%