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?

297

likes
1483 views

## 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
4.7
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%
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%.

Frequently asked questions $FAQs$
Find the value of x that satisfies the cubic equation 4x^3 - 5x^2 + 2x - 1 = 0.
+
Math question: Find the absolute extrema of the function f$x$ = x^2 - 4x + 5 on the interval [-3, 5].
+
What is the solution set to the inequality system: 3x + 5y ≥ 15 and y < 2x - 3, graphed on the coordinate plane?
+