You want to create a portfolio equally as risky as the market, and you have $500

Question

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:

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            $

Please show all work.

Asset Investment Beta Stock A $ 144,000 .89 Stock B 136,000 1.34 Stock C 1.49 Risk-free asset

Explanation / Answer

Let investment in C=$x

Hence investment in risk free assets=500,000-(144000+136000+x)

=$220,000-x

Hence portfolio beta=Respective investment weights*Respective betas

1=(144000/500,000*0.89)+(136000/500,000*1.34)+(x/500,000*1.49)+0(Beta of risk free assets=0]

1=0.25632+0.36448+(x/500,000*1.49)

Hence x=(1-0.25632-0.36448)*(500,000/1.49)

=127248.32(Approx)=investment in C

Hence investment in risk free assets=(220,000-127248.32)=$92751.68

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