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

Total Investment Amount = $500000

Creating a Portfolio as Risky as the market means we want to create a portfolio with beta of 1 as market beta is 1

Risk free asset has a beta of 0

((Investment of A x beta of A )+(Investment of BxBeta of B) + (Investment of C xBeta of C)) /500000 = 1

To CAlculate Investment in C , Multiply both sides by 500000

(ISAxBA) +(ISBxBB)+(ISCxBC) = 500000

ISC XBC = 500000 - (ISAxBA) -(ISBxBB)

ISC X 1.51 = 500000 - ( 146000x0.91) - (134000 x 1.36)

ISC =( 500000-132860 - 182240)/1.51

ISC = 122450.30

ISA , ISB and ISC respectively means Investment in stock A, Investment in Stock B and Investment in Stock C

Thus Investment in Stock C is Equal to $122450.30

b) Sum of All Stock Investment +investment in Risk free Asset = 500000

ISA +ISB+ISC +RFA = 500000

146000+134000+122450.3 +RFA = 500000

RFA = 500000 - 146000-134000-122450.30

RFA = $97549.70

Thus Investment in Risk Free Asset is equal to $97549.70

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