Assume that you are 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
$3,000,000

11.11%

Explanation:

In this question, we apply the Capital Asset Pricing Model (CAPM) formula which is shown below  for computing the rate of return

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

For Stock A

= 5% + 1.20 × (11% - 5%)

= 5% + 1.20 × 6%

= 5% + 7.2%

= 12.2%

For Stock B

= 5% + 0.5 × (11% - 5%)

= 5% + 0.5 × 6%

= 5% + 3%

= 8%

For Stock C

= 5% + 1.40 × (11% - 5%)

= 5% + 1.40 × 6%

= 5% + 8.4%

= 13.4%

For Stock D

= 5% + 0.75 × (11% - 5%)

= 5% + 0.75 × 6%

= 5% + 4.5%

= 9.5%

Now the rate of return would be

= (Stock A amount × expected return + Stock B amount × expected return + Stock C amount × expected return + Stock D amount × expected return) ÷ (Total amount)

= ($1,075,000 × 12.20% + $675,000 × 8% + $750,000 × 13.40% + $500,000 × 9.50%) ÷ ($3,000,000)

= ($131,150 + $54,000 + $100,500 + $47,500)  ÷ ($3,000,000)

= 11.11%

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