Use the following information for problems 3 through 10: The riskfree 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+(RmRf)*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+(RmRf)*Beta of Stock E
=4%+(10%4%)*1.8 =14.80%
(Rf= risk free rate, Rm= Market rate of return)
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