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

beta of the market = 1

beta of risk-free asset = 0

Stock A weights = 133,000/500,000 = 0.266

Stock B weights = 147,000/500,000 = 0.294

let  Investment in Stock C be X

Stock C weights = X/500,000

Risk-Free Asset weights = (500,000-133,000-147,000-X)/500,000 = (220,000-a)/500,000

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As the portfolio is as risky as the market,

then beta of the portfolio = beta of the market = 1

0.266*0.78 + 0.294*1.23 + X/500,000*1.38 + (220,000-a)/500,000*0 = 1

X = 156,123.19

Thus, Investment in Stock C = 156,123.19

Investment in Risk-Free Asset = 220,000 - 156,123.19 = 63,876.81

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