Question

17) A mutual fund manager has a $20 million portfolio with a beta of 0.95. The risk-free rate is 3.75%, and the market risk premium is 7.0%. 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 13%. What should be the average beta of the new stocks added to the portfolio? Do not round intermediate calculations. Round your answer to two decimal places. Enter a negative answer with a minus sign.

Answer 1

Before investment:

Value of Portfolio = $20 million
Beta (old) = 0.95

After investment:

Value of Portfolio = $25 million
Required Return = 13%

Required Return = Risk-free Rate + Beta (new) * Market Risk Premium
13.00% = 3.75% + Beta (new) * 7.00%
1.32 = Beta (new)

Beta (new) = Weight of Old Portfolio * Beta of Old Portfolio + Weight of New Stock * Beta of New Stock
1.32 = ($20 million / $25 million) * 0.95 + ($5 million / $25 million) * Beta of New Stock
1.32 = 0.76 + 0.20 * Beta of New Stock
0.56 = 0.20 * Beta of New Stock
Beta of New Stock = 2.80

So, average beta of the new stocks is 2.80