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?

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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