Question

You want to create a portfolio equally as risky as the market, and you have $1,300,000 to invest. Consider the following information: Asset Investment Beta Stock A $325,000 0.70 Stock B $325,000 1.35 Stock C 1.60 Risk-free asset (a) What is the investment in Stock C? (b) What is the investment in risk-free asset?

Answer 1

Let investment in C=$x

Hence investment in risk-free asset=1,300,000-(325,000+325,000+x)=$(650,000-x)

Portfolio beta=Respective beta*Respective investment weight

1=(325,000/1,300,000*0.7)+(325,000/1,300,000*1.35)+(x/1,300,000*1.6)+(650,000-x)/1,300,000*0[Beta of market=1;Beta of risk-free assets=0]

1=0.5125+(x/1,300,000*1.6)

x=(1-0.5125)*1,300,000/1.6

=$396,093.75=investment in C

Hence investment in risk-free assets=$(650,000-x)=$253,906.25