You want to create a portfolio equally as risky as the market, and you have $500

Question

You want to create a portfolio equally as risky as the market, and you have $500,000 to invest. Information about the possible investments is given below:

How much will you invest in Stock C? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

How much will you invest in the risk-free asset? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

You want to create a portfolio equally as risky as the market, and you have $500,000 to invest. Information about the possible investments is given below:

Explanation / Answer

Let weight of Stock C be 'Wc' and investment in risk free asset be 'Wrf'

Weight of Stock A = (147,000/500,000) = 0.294

Weight of Stock B = (133,000/500,000) = 0.266

Weight of Stock C = Wc (assumed)

Weight of Risk free asset = Wrf (assumed)

As weights of all stocks add to 1

(0.294) + (0.266) + Wc+ Wrf = 1

Wc+ Wrf = 0.44........................................................................(1)

Beta of portfolio = (0.294*0.92) + (0.266*1.37) + (Wc*1.52) + ( Wrf*0)

Since Portfolio has to be created as risky as market, Beta of Portfolio will be 1.

1 = 0.27048+0.36442+ 1.52Wc + 0

1.52 Wc = 0.3651

Wc = (0.3651/1.52) = 0.240197368

Wc = 0.24

Amount invested in Stock C= (0.240197368)*(500,000) = $120,098.6842 = $120,098.68

From equation (1)

Wrf = (0.44-0.240197368) = 0.199802632

Amount Invested in Risk free asset = (0.199802632)*(500,000) = $99,901.316 = $99,901.32

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