Question

You want to create a portfolio equally as risky as the market, and you have $800,000 to invest. You've already allocated a portion of your wealth to Stock A and Stock B, and you've decided to also invest money in Stock C and the risk-free asset. Consider the following information:

  

Asset	Investment	Beta
Stock A	$200,000	0.80
Stock B	$160,000	1.30
Stock C	?	1.50
Risk-free asset	?	?

  

Required:

(a)	How much should you invest in Stock C? (Do not round your intermediate calculations.)
	(Click to select)  $276,480  $273,600  $288,000  $299,520  $186,667

  

(b)	How much should you invest in the risk-free asset? (Do not round your intermediate calculations.)
	(Click to select)  $144,400  $145,920  $253,333  $152,000  $158,080

Answer 1

Let investment in C=$x

Hence investment in risk free asset=800,000-(200,000+160,000+x)

=$(440,000-x)

Portfolio beta=Respective beta*Respective weight

1=(200,000/800,000*0.8)+(160,000/800,000*1.3)+(x/800,000*1.5)+(440,000-x)/800,000*0[Beta of market=1;Beta of risk-free assets=0]

1=0.46+(x/800,000*1.5)

x=(1-0.46)*800,000/1.5

=$288000=investment in C

Hence investment in risk free asset=$(440,000-x)

=$152000

Beta of risk free asset=0