Question

You want to create a portfolio equally as risky as the market, and you have $900,000 to invest. Consider the following information:

  

Asset	Investment	Beta
Stock A	$180,000	0.90
Stock B	$180,000	1.10
Stock C		1.55
Risk-free asset

  

Required:

(a)	What is the investment in Stock C? (Do not round your intermediate calculations.)

  

(b)	What is the investment in risk-free asset? (Do not round your intermediate calculations.)

Answer 1

Let investment in stock C=$x

Hence  investment in risk-free asset=900,000-(180,000+180,000+x)=$540,000-x

Portfolio beta=Respective betas*Respective investment weights

1=(180,000/900,000*0.9)+(180,000/900,000*1.1)+(x/900,000*1.55)+(540,000-x/900,000)*0[Beta of risk free asset=0]

1=0.18+0.22+(x/900,000*1.55)

Hence x=(1-0.18-0.22)*900,000/1.55

=$348,387.10(Approx)=investment in Stock C

Hence investment in risk free asset=(540,000-348,387.10)=$191,612.90(Approx)