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%.The manager expects to receive an additional $29.50 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? Do not round your intermediate calculations.
A) 2.08
B) 2.18
C) 2.60
D) 1.66
E) 1.87

Question

Quizplus · Accepted Answer

To find the average beta of the new stocks, we use the Capital Asset Pricing Model (CAPM) formula: Required Return = Risk-Free Rate + Beta * Market Risk Premium. The current portfolio's required return is 10.25% (4.25% + 1.00 * 6.00%). The manager wants a 13.00% return after investing the additional funds. The combined portfolio value will be $69.50 million ($40 million + $29.50 million). Let β_new be the beta of the new stocks. The equation becomes: 13.00% = 4.25% + [(40/69.5) * 1.00 + (29.5/69.5) * β_new] * 6.00%. Solving for β_new gives approximately 2.08.

A Mutual Fund Manager Has a $40 Million Portfolio with a Beta