Hazel Morrison, 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%.Hazel 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?
A) 1.68
B) 1.76
C) 1.85
D) 1.94
E) 2.04

Question

Quizplus · Accepted Answer

To achieve a target return of 13.00% with a risk-free rate of 4.25% and a market risk premium of 6.00%, we use the Capital Asset Pricing Model (CAPM) formula: Required Return = Risk-Free Rate + Beta * Market Risk Premium. The target return is 13.00%, so we set up the equation: 13.00% = 4.25% + Beta * 6.00%. To find the overall beta after investing the additional $60 million, we first find the weighted average beta of the new and old portfolio. The total investment will be $40 million + $60 million = $100 million. The old portfolio has a beta of 1.00 and represents $40 million of the total investment. We need to find the beta of the new investment that makes the weighted average beta achieve the target return. Rearranging the target return equation to solve for Beta gives us Beta = (13.00% - 4.25%) / 6.00% = 1.46. However, this is the overall beta needed for the entire $100 million portfolio to achieve a 13% return. To find the beta of the new $60 million investment, we use the weighted average formula: (1.00 * $40 million + Beta_new * $60 million) / $100 million = 1.46. Solving for Beta_new gives us Beta_new = (1.46 * $100 million - 1.00 * $40 million) / $60 million = 1.76.

Hazel Morrison, a Mutual Fund Manager, Has a $40 Million