MathMaster logo

MathMaster

  1. Home
  2. general
  3. 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 premiu
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?

Expert avatar
Cristian
4.7
114 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%.

Frequently asked questions (FAQs)
Math Question: An apple pie recipe requires 3/4 cup of sugar. If we divide the recipe into 2 equal servings, how much sugar is needed for each serving?
+
What is the factored form of the quadratic equation 6x^2 - 11x + 4?
+
Find the integral of ∫(3x^2 - 2) dx.
+
New questions in Mathematics
A pump with average discharge of 30L/second irrigate 100m wide and 100m length field area crop for 12 hours. What is an average depth of irrigation in mm unIt?
A person who weighs 200 pounds on earth would weigh about 32 pounds on the moon. Find the weight of a person on earth who would weigh 15 pounds on the moon.
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
A client did not advance L 10,000 for the rental of a parking area and it corresponds to 4 months, of which 2 months were consumed
132133333-33
What will be the density of a fluid whose volume is 130 cubic meters contains 16 technical units of mass? If required Consider g=10 m/s2
If the midpoint of point A on the x=3 line and point B on the y=-2 line is C(-2,0), what is the sum of the ordinate of point A and the abscissa of point B?
41/39 - 1/38
The equation of the straight line that passes through the coordinate point (2,5) and is parallel to the straight line with equation x 2y 9 = 0 is
The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. b) What is the profit value made by the hotel for one
The Humane Society has asked for our help again this week. Currently they are charging $50 for an adoption fee. Unfortunately they just pulled this number out of the air and do not know why they are charging this amount. They would like to charge an amount that covers all the adoption costs – both the variable costs for adoptions as well as the fixed cost for the kennel portion of the Humane Shelter operations. We can help them by doing a breakeven analysis. During a client meeting we gathered these facts. There are 2 part-time employees that each earn $1000 per month. The utilities for the kennel area (water, electricity) are $200 per month. The average food cost for animals in the kennel is $800 per month. In addition, each animal that is adopted receives a rabies vaccination that costs $4 and is micro-chipped that costs $6. At the current cost of $50, how many animals must be adopted to break-even? What would break-even be at a $60 adoption fee? What would break-even be if the fee were lowered to $40? The newspaper has suggested that the Humane Society advertise to increase pet adoptions. The package that they have recommended costs $1000 for a very small ad run every day for a month. If the Humane Society does this extra advertising, how will it affect breakeven? Based on what you have learned about elasticity, what price do you recommend for the adoption fee?
In a order to compare the means of two populations, independent random samples of 410 observations are selected from each population, with Sample 1 the results found in the table to the right. Complete parts a through e below. X1 = 5,319 S1= 143 a. Use a 95% confidence interval to estimate the difference between the population means (H - H2) Interpret the contidence interval. The contidence interval IS (Round to one decimal place as needed.) Sample 2 X2 = 5,285 S2 = 198 Aa. Use a 95% confidence interval to estimate the difference between the population means (A1 - M2) Interpret the contidence interval. The contidence interval Is (Round to one decimal place as needed.) b. Test the null hypothesis Ho versus alternative hypothesis Ha (H What is the test statistic? H2) + Give the significance level of the test, and interpret the result. Use a = 0.05. Z=
John he’s going to the carnival with his friends. He spends $25 on an admission ticket. He buys 10 games at X dollars each and two boxes of popcorn at Y dollars each. Write an expression to show the total cost of admission game, tickets and popcorn.
A hardware bill totals $857.63 with discounts of 5% and 3%. What is the net cost of the Material ?
Consider mixing 150 ml, 0.1M, HCI with 100 ml, 0.2M, KOH solution. Determine the pH of final solution.
25) Paulo saves R$250.00 per month and keeps the money in a safe in his own home. At the end of 12 months, deposit the total saved into the savings account. Consider that, each year, deposits are always carried out on the same day and month; the annual yield on the savings account is 7%; and, the yield total is obtained by the interest compounding process. So, the amount that Paulo will have in his savings account after 3 years, from the moment you started saving part of your money monthly, it will be A) R$6,644.70. B) R$ 9,210.00. C) R$ 9,644.70. D) R$ 10,319.83. E) R$ 13,319.83
To paint a 250 m wall, a number of workers were employed. If the wall were 30 m longer, 9 more workers would be needed. How many were employed at the beginning?
Mark is gluing a ribbon around the sides of a picture frame. The frame is 11 inches long and 7 includes wide. How much ribbon does Mark need?
Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2
The domain of the function f(x)=x+7x2−144 is (−∞,), ( ,), and ( , ∞).

You might be interested in