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 2.00%. What rate of return should investors expect (and require) on this fund

11.18%

Explanation:

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

First of all we will calculate the weighted average portfolio beta

Portfolio bet is the average beta calculated on the basis of weightage of each investment. The beta of every investment is multiplied with the weightage of each investment in a portfolio. The all the value is added to get the portfolio beta

Portfolio Beta = ( Stock A beta x Stock A Weightage) + ( Stock B beta x Stock B Weightage) + ( Stock C beta x Stock C Weightage) + ( Stock D beta x Stock D Weightage)

Portfolio Beta = ( 1.2 x $1,075,000 / $3,000,000) + ( 0.50 x $675,00 / $3,000,000 ) + ( 1.4 x 750,000 / $3,000,000) + ( 0.75 x 500,000 / $3,000,000)

Portfolio Beta = 0.43 + 0.1125 + 0.35 + 0.125 = 1.02

Now We will use CAPM to calculate the expected rate of return using portfolio beta.

Capital asset pricing model measure the expected return on an asset or investment. it is used to make decision for addition of specific investment in a well diversified portfolio.

Formula for CAPM

Expected return = Risk free rate + beta ( Market Rate - Risk Free rate )

Expected return = 2% + 1.02 ( 11% - 2% )

Expected return = 5% + 7.2%

Expected return = 11.18%

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