# Calculating the fund's beta and required rate of return

Alcoa's Inc.'s Pension Fund holds 4 stocks. The market's required rate of return is 6% and the risk free rate is 2%.

Stock Investment Beta

A $300,000 1.75

B $500,000 -0.75

C $1,000,000 1.05

D $500,000 0.75

a. What is this fund's beta?

b. Calculate the required rate of return.

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#### Solution Preview

a. What is this fund's beta?

Investment in stock A=Ia=300,000

Beta of stock A=ba=1.75

Investment in stock B=Ib=500,000

Beta of stock B=bb=-0.75

Investment in stock C=Ic=1,000,000

Beta of stock ...

#### Solution Summary

Solution describes the steps to calculate the beta and required rate of return for the given fund.

Calculate fund's required rate of return; stock's required rate of return.

See attached file.

Written Assignment: Problems: 8-7, 8-10, 8-12

8.7: Suppose you are the money manager of a $4million investment fund. The fund consists of four stocks with the following investment and betas:

Stock investment Beta

A $ 400,000 1.50

B 600,000 (0.50)

C 1,000,000 1.25

D 2,000,000 0.75

If the market's required rate of return is 40% and the risk-free rate is 6%, what is the fund's required rate of return?

8.10: Bradford Manufacturing Company has a beta of 1.45,, while Farley Industry has a beta of 0.85. The required return on an index fund that holds the entire stock market is 12.0%. The risk free rate of interest is 5%. By how much does Bradford's required return exceed Farley's required return?

8.12: Suppose rRF = 9%, rM = 14%, and bi = 1.3

a. what is r(i), the required rate of return on stock i?

b. Now suppose that rRF (1) increase to 10% or (2) increases to 8%. The slope of the SML remains constant. How would this affect rM and r(i)?

c. Now assume that rRF remains at 9% but the rM (1) increase to 16% or (2) falls to 13%. The slope of the SML does not remain constant. How would these changes affect r(i)?

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