Question

You want to create a portfolio equally as risky as the market, and you have $1,200,000 to invest. Consider the following information:

   

Asset	Investment	Beta
Stock A	$420,000	0.70
Stock B	$300,000	1.25
Stock C		1.40
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 C=$x

Hence investment in risk-free asset=1,200,000-(420,000+300,000+x)=$(480,000-x)

Portfolio beta=Respective beta*Respective investment weight

1=(420,000/1,200,000*0.7)+(300,000/1,200,000*1.25)+(x/1,200,000*1.4)+(480,000-x)/1,200,000*0[Beta of risk-free asset=0][Beta of market=1]

1=0.5575+(x/1,200,000*1.4)

x=(1-0.5575)*1,200,000/1.4

$379,285.71=investment in Stock C(Approx).

Hence investment in risk-free asset=(480,000-379285.71)=$100,714.29(Approx).