PORTFOLIA REQUIRED RETURN Suppose you are themoney manager of a $4 million inves

Question

PORTFOLIA REQUIRED RETURN Suppose you are themoney manager of a $4 million investment fund. The fundconsists of four stocks with the following investments andbetas:

                       Stock              Investment                Beta

                       A                    $400,000                    1.50

                       B                     600,000                  (0.50)

                       C                    1,000,000                   1.25

                       D                    2,000,000                   0.75

If the market’s required rate of return is 14% and therisk-free rate is 6%, what is the fund’s required rate ofreturn?

Explanation / Answer

Calculating Portfolio Beta (ßP):

Portfolio weight of Stock A = ($400,000 /$4,000,000)   = 0.10 (or) 10%

Portfolio weight of Stock B = ($600,000 /$4,000,000)   = 0.15 (or) 15%

Portfolio weight of Stock C = ($1,000,000 /$4,000,000)= 0.25 (or) 25%

Portfolio Weight of Stock D = ($2,000,000 / $4,000,000)= 0.50 (or) 50%

Portfolio Beta(ßP) = (0.10 * 1.50) +(0.15 * -0.50) + (0.25 * 1.25) + (0.50 * 0.75)

Portfolio Beta(ßP) = 0.15 + (-0.075)+ 0.3125 + 0.375

Market’s Required Rate of Return(RM) = 14%

Risk-free Rate (Rf) = 6%

RE = Rf + ß (RM– Rf)

RE = 0.06 + 0.7625 (0.14 – 0.06)

Required Rate of Return (RE) = 0.06 +0.061

Required Rate of Return (RE) = 0.121 (or)12.10%

Required Rate of Return(RE) = 12.10%

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