Question

A mutual fund manager has a $140 million portfolio with a beta of 1.00. The risk-free rate is 3.25%, and the market risk premium is 7.50%. The manager 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?

Answer 1

Total Value of Portfolio = 140 mn + 60 mn = 200 mn

Weight of old Porfolio = 140 / 200 = 70%

Weight of additional fund = 60 / 200 = 30%

Return of Old Portfolio = Rf + Beta * Market Risk Premium

= 3.25% + 1 * 7.50%

= 10.75%

Expected return = Weighted Return

13% = 10.75% * 70% + Return of new Additional Funds * 30%

13% = 7.525% + Return of new Additional Funds * 30%

Return of new Additional Funds = 13% - 7.525% / 30%

Return of new Additional Funds = 18.25%

Also, Return of new Additional Funds = Rf + beta * market Risk Premium

18.25% = 3.25% + Beta * 7.50%

Beta = 18.25%- 3.25% / 7.50%

Beta = 2