Problem 1127 Analyzing a Portfolio LO 2 You want to create a

Problem 11-27 Analyzing a Portfolio [LO 2) You want to create a portfolio equally as risky as the market, and you have $500,000 to invest. Information about the possible investments is given below Asset Investment $148,000 Stock A Stock B Stock C Risk-free asset Beta 93 1.38 1.53 132000 33 How much will you invest in Stock C? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Investment in Stock C How much will you invest in the risk-free asset? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Investment in risk-free asset

Solution

Let investment in C=$x

Hence investment in risk free asset=500,000-(148000+132000+x)

=$(220,000-x)

Portfolio beta=Respective betas*Respective weights

1=(148000/500000*0.93)+(132000/500000*1.38)+(x/500,000*1.53)+(220,000-x)/500000*0[Beta of market =1 while Beta of risk free assets=0]

1=0.6396+(x/500000*1.53)

Hence x=(1-0.6396)*500,000/1.53

=$117,777.78(Approx)=investment in Stock C.

Hence investment in risk free assets=(220,000-117,777.78)=$102,222.22(Approx).