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 $240,000 0.60

Stock B $360,000 1.25

Stock C 1.60

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

• We need to understand that the beta of market portfolio is 1 and that of the risk free asset is 0
• We have a total of 1200000 to invest of which we have already made the following investments:

  • Security	Investment	Beta
    Stock A	240,000	0.60
    Stock B	360,000	1.25
    Stock C	Need to find out	1.60
    Risk Free Asset	Need to find out	0

  • Let's assume the amount invested in Stock C is x so the remaining amount will be invested in Risk free asset which will be 1,200,000-240,000-360,000-x

  • Portfolio Beta should equal 1 and is basically a weighted average beta of the asset betas

  • Now we need to solve the following equation:

  • 

  • 

  • 

  • So the investment in stock C was 378,750

  • Therefore the investment in risk free asset = 1,200,000-240,000-360,000-378,750 = 221,250