Question

Use the following information for problems 3 through 10: The risk-free rate of return is 4%,...

Use the following information for problems 3 through 10: The risk-free rate of return is 4%, the required rate of return of the market portfolio is 10%. You invest $10,000 in stock A, $15,000 in stock B, $50,000 in stock C, and $50,000 in stock D. The average returns and standard deviations of the individual stocks are as follows:

Ret

Standard Deviation

Beta

Stock A

0.25

0.31

2.0

Stock B

0.16

0.36

1.0

Stock C

0.04

0.17

0.8

Stock D

0.02

0.08

0.3

1) Assume that you invest another $150,000 in a fifth stock. Stock E has an average rate of return of 0.18, a standard deviation of returns of 0.22, and a beta of 1.8. What is the new portfolio’s beta?

2)Assume that you invest another $150,000 in a fifth stock. Stock E has an average rate of return of 0.18, a standard deviation of returns of 0.22, and a beta of 1.8. What is the equilibrium expected rate of return of the new portfolio?

3)Assume that you invest another $150,000 in a fifth stock. Stock E has an average rate of return of 0.18, a standard deviation of returns of 0.22, and a beta of 1.8. What is the required rate of return of Stock E?

Homework Answers

Answer #1

1) Beta of portfolio is given by Summision of Weight* Beta, Where weight= Investement in stock i / Total Investment in portfolio.

The calcluation of beta in the given case is given by-

Stock Investement Weight Beta (w)*(B)
(w ) (B)
A 10000 3.64% 2 0.072727
B 15000 5.45% 1 0.054545
C 50000 18.18% 0.8 0.145455
D 50000 18.18% 0.3 0.054545
E 150000 54.55% 1.8 0.981818
Total 275000 1.309091

Hence Beta of the portfolio is 1.309091

2) Equilibrium rate of retrun of the portfolio is given by= Rf+(Rm-Rf)*Beta of portfolio

=4%+(10%-4%)*1.309091 (as calculated above)

= 11.8545%

3) Required rate of return for stock E is given by =Rf+(Rm-Rf)*Beta of Stock E

=4%+(10%-4%)*1.8 =14.80%

(Rf= risk free rate, Rm= Market rate of return)

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