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%

(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%