Hazel Morrison, a mutual fund manager, has a $40 million portfolio with a beta of 1.00. The risk-free rate is 4.25%, and the market risk premium is 6.00%. Hazel expects to receive an additional $60 million, which she plans to invest in additional stocks. After investing the additional funds, she wants the fund's required and expected return to be 13.00%. What must the average beta of the new stocks be to achieve the target required rate of return?

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DeniceSandidge DeniceSandidge · Answer 1 · 2019-12-22T09:00:32+01:00

Answer:

average beta of the new stocks to achieve the target required rate of return is 2.29

Explanation:

given data

Portfolio amount invested = $40,000,000

Beta = 1

Risk free rate = 4.25%

Market risk premium = 6%

Hazel expects = $60 million

expected return new investments = 13.00%

to find out

average beta of new stocks be to achieve the target required rate of return

solution

we will use here CAPM formula that is

Expected return = Risk free rate + Beta × Market risk premium .........1

put here value we get

13% = 4.25% + Beta × 6%

0.06 × Beta = 13% - 4.25%

Beta = 1.458

now we get Weighted beta that is express as

Weighted beta = weight of old stock in new portfolio × 1 + Weight of new stock in new portfolio × beta of new stock ..................2

put here value we get

1.458 = [tex]\frac{40}{(40+22)} * 1 +\frac{22}{(22+22)} * debt[/tex]

solve it we get

beta = 2.29

so that average beta of the new stocks to achieve the target required rate of return is 2.29