Question
A mutual fund manager has a $350 million portfolio with a beta of 1.10. The risk-free rate is 3.5%, and the market risk premium is 6.00%. The manager expects to receive an additional $150 million which she plans to invest in several different stocks. After investing the additional funds, she wants to reduce the portfolio’s risk level so that once the additional funds are invested the portfolio’s required return will be 9.20%. What must the average beta of the new stocks added to the portfolio be (not the new portfolio’s beta) to achieve the desired required rate of return?
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Answer to a math question A mutual fund manager has a $350 million portfolio with a beta of 1.10. The risk-free rate is 3.5%, and the market risk premium is 6.00%. The manager expects to receive an additional $150 million which she plans to invest in several different stocks. After investing the additional funds, she wants to reduce the portfolio’s risk level so that once the additional funds are invested the portfolio’s required return will be 9.20%. What must the average beta of the new stocks added to the portfolio be (not the new portfolio’s beta) to achieve the desired required rate of return?
Cristian
4.7111 Answers
To find the required beta of the new stocks added to the portfolio, we can use the following formula:
Required\ return = Risk-free\ rate + Beta \times Market\ risk\ premium
Let's solve for the beta by rearranging the formula:
Beta = \frac{Required\ return - Risk-free\ rate}{Market\ risk\ premium}
Given:
Current portfolio beta = 1.10
Risk-free rate = 3.5%
Market risk premium = 6.00%
Required return = 9.20%
Substituting the given values into the formula, we have:
Beta = \frac{9.20\% - 3.5\%}{6.00\%}
Simplifying the expression:
Beta = \frac{5.70\%}{6.00\%}
Converting the percentages to decimal form:
Beta = \frac{0.057}{0.06}
Simplifying further:
Beta \approx 0.95
Answer: The average beta of the new stocks added to the portfolio must be approximately 0.95 to achieve the desired required rate of return of 9.20%.
Let's solve for the beta by rearranging the formula:
Given:
Current portfolio beta = 1.10
Risk-free rate = 3.5%
Market risk premium = 6.00%
Required return = 9.20%
Substituting the given values into the formula, we have:
Simplifying the expression:
Converting the percentages to decimal form:
Simplifying further:
Answer: The average beta of the new stocks added to the portfolio must be approximately 0.95 to achieve the desired required rate of return of 9.20%.
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