Question

A mutual fund manager has a $20 million portfolio with a beta of 2.8. The risk-free rate is 5.5%, and the market risk premium is 7%. The manager expects to receive an additional $5 million, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund's required return to be 23%. What should be the average beta of the new stocks added to the portfolio? Negative value, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to one decimal place.

Answer 1

Investment in Old Portfolio = $20 million
Investment in New Stock = $5 million

Investment in New Portfolio = Investment in Old Portfolio + Investment in New Stock
Investment in New Portfolio = $20 million + $5 million0
Investment in New Portfolio = $25 million

Weight of Old Portfolio = Investment in Old Portfolio / Investment in New Portfolio
Weight of Old Portfolio = $20 million / $25 million
Weight of Old Portfolio = 0.80

Weight of New Stock = Investment in New Stock / Investment in New Portfolio
Weight of New Stock = $5 million / $25 million
Weight of New Stock = 0.20

Required Return of New Portfolio = Risk-free Rate + Beta of New Portfolio * Market Risk Premium
23.00% = 5.50% + Beta of New Portfolio * 7.00%
17.50% = Beta of New Portfolio * 7.00%
Beta of New Portfolio = 2.50

Beta of New Portfolio = Weight of Old Portfolio * Beta of Old Portfolio + Weight of New Stock * Beta of New Stock
2.50 = 0.80 * 2.80 + 0.20 * Beta of New Stock
2.50 = 2.24 + 0.20 * Beta of New Stock
0.26 = 0.20 * Beta of New Stock
Beta of New Stock = 1.30