You own a portfolio equally invested in a risk-free asset and two stocks. If one

Question

You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.26, and the total portfolio is exactly as risky as the market, what must the beta be for the other stock in your portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.26, and the total portfolio is exactly as risky as the market, what must the beta be for the other stock in your portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation / Answer

Let the amount invested in Risk free asset is 1/3 = 0.33

The amount invested in Stock 1 = 1/3 = 0.33

The amount invested in Stock 2 = 1/3 = 0.33

Portfolio Beta = (weight asset 1 * Beta 1) + (weight asset 2 * Beta 2) + (weight risk free asset * Beta risk free asset)

Beta of Risk free asset is always 0

Beta of Portfolio is 1

therefore, 1 = (0.33* 1.26) + (0.33 * beta of Stock 2 ) + 0

1 = 0.4158 + (0.33 * beta of Stock 2 )

0.5842 = 0.33 * Beta of Stock 2

Beta of Stock 2 = 1.77

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