Question

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?

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)