You want to create a portfolio equally as risky as the market, and you have $1,0

Question

You want to create a portfolio equally as risky as the market, and you have $1,000.000 to invest. Consider the following information: Asset Investment Beta Stock A Stock B Stock C Risk-free asset $200,000 $250,000 0.85 1.25 1.50 Required: (a) What is the investment in Stock C? (Do not round your intermediate calculations.) $327,750 $331,200 $358,800 $345,000 $208,333 (b) What is the investment in risk-free asset? (Do not round your intermediate calculations.) $213,200 $194,750 $341,667 $196,800 $205,000

Explanation / Answer

a) Investment in stock C = $ 345,000

b) Investment in risk free asset = 205000

Working

Beta of Market always = 1

Beta of Risk free asset always = 0

As mentioned in question Beta of Portfolio = Beta of Market

Hence, Beta of Portfolio = 1

Now Beta of Portfolio = Weight of Stock A * beta of stock A + Weight of Stock B * beta of stock B + Weight of Stock C * beta of stock C + Weight of Risk Free asset * beta of Risk Free asset

1 = 200000/1000000 * 0.85 +250000/1000000 * 1.25 + Weight of Stock C *1.50 + Weight of Risk Free asset * 0

Weight of Stock C = 1- 0.17 - 0.5175

Weight of Stock C = 0.345

Investment in Stock C = 0.345*1000000 = 345000

Investment in risk free asset = 1000000 - 200000-250000-3450000 = 205000

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