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
115 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)
Find the value of x if f(x) = √(x + 4) - 2.
+
What is the value of f(x) = 2x^2 - 5x + 3 when x = 4?
+
Question: What is the derivative of f(x) = ∫(a to x) 2t^3 dt using the Fundamental Theorem of Calculus?
+
New questions in Mathematics
If we have the sequence: 3, 6, 12, 24 Please determine the 14th term.
find the value of the tangent if it is known that the cos@= 1 2 and the sine is negative. must perform procedures.
Calculate the 6th term of PA whose 1st term is 6.5 and the ratio 5
I) Find the directional derivative of 𝑓(𝑥, 𝑦) = 𝑥 sin 𝑦 at (1,0) in the direction of the unit vector that make an angle of 𝜋/4 with positive 𝑥-axis.
what is the annual rate on ​$525 at 0.046​% per day for 3 months?
Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}
What’s the slope of a tangent line at x=1 for f(x)=x2. We can find the slopes of a sequence of secant lines that get closer and closer to the tangent line. What we are working towards is the process of finding a “limit” which is a foundational topic of calculus.
reduce the expression (7.5x 12)÷0.3
89, ÷ 10
How to do 15 x 3304
When Sara was 15 years old, an uncle left her as inheritanceà a sum of 10,000 euros which he invested in a bank that applies the interest rate of 2,5% annual. Today Sara is 18 years and wants to buy a'car, how much she can ò withdraw from the bank?
Associate each 2nd degree equation with its respective roots. A) x2+6x+8=0 B)x2-5x-6=0
The average undergraduate cost per tuition, fees, room, and board for all institutions last year was $26,025. A random sample of 40 institutions of higher learning this year indicated that the mean tuition, fees, room, and board for the sample was $27,690, and the population standard deviation is $5492. At the 0.05 level of significance, is there sufficient evidence that the cost has increased? (Remember to follow the steps in hypothesis testing)
Consider the function f(x)=1/2(x+1)^2-3. Use the preceding/following interval method to estimate the instantaneous rate of change at 𝑥 = 1.
Find I (Intrest) using simple interest formula of 17700 @ 15% for 4 years
8. Measurement Jillian measured the distance around a small fish pond to be 27 yards. What would be a good estimate of the distance across the pond: 14 yards, 9 yards, or 7 yards? Explain how you decided.
g(x)=3(x+8). What is the value of g(12)
A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 55.0 min at 100.0 km/h, 14.0 min at 65.0 km/h, and 45.0 min at 60.0 km/h and spends 20.0 min eating lunch and buying gas. (a) Determine the average speed for the trip.
Find the number of liters of water needed to reduce 9 liters of lotion. shave containing 50% alcohol to a lotion containing 30% alcohol.
Construct a set of six pieces of data with​ mean, median, and midrange of 67 and where no two pieces of data are the same.