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

Weight of investment in stock A = 137000/ 500000 = .274 Or27.4%

Weight of investment in stock B = 143000/500000 = .286 or 28.6%

Let weight of investment in stock C= x

Weight of risk free asset = 1 -.274-.286-x = .44-x

Beta of market = 1 so Beta of paortfolio = 1

Beta of risk free asset = 0 as no risk is involved.

Beta of portfolio =weighted average beta

1 = (.82 * .274)+(1.27* .286)+(1.42*x) + [0 (.44-x)]

1 = .2247+ .3632+ 1.42x +0

1 = .5879+ 1.42x

1.42x = 1 -.5879

x = .4121 /1.42

      = .290211 [aprrox 29.0211%]

Investment in C = 500000 *29.0211% = $ 145105.5

Investment in risk free asset = 500000- 137000-143000-145105.5 = 74894.5

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