Question

Hazel Morrison, a mutual fund manager, has a $60 million portfolio with a beta of 1.00. The risk-free rate is 3.25%, and the market risk premium is 6.00%. Hazel expects to receive an additional $40 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 16%. What must the average beta of the new stocks be to achieve the target required rate of return? Enter your answer rounded to two decimal places. For example, if your answer is 123.45% or 1.2345 then enter as 1.23 in the answer box.

Answer 1

Solution:

Amount already invested(old stock)=$60,000,000

Amount to be invested(new Stock)=$40,000,000

Total Investment=$60,000,000+$40,000,000

=$100,000,000

Weight of old stock=$60,000,000/$100,000,000=0.60 or 60%

Weight of new Stock=$40,000,000/$100,000,000=0.40 or 40%

With the help of CAPM,we can find the beta of total investment(i.e weighted beta)

Required rate of return=Risk free rate+Beta(Market risk premium)

16%=3.25%+Beta(6%)

Beta=2.125

Now,we can find the average beta of the new stocks be to achieve the target required rate of return as follow;

Weighted beta=Beta of old stock*weight of old stock+Beta of new stock*weight of new stock

2.125=1*0.60+Beta of new stock*0.40

Beta of new stock=4.0375

Thus average beta of the new stocks is 4.04