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 1.32 and the total portfolio is equally 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, e.g., 32.16.)

You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.32 and the total portfolio is equally 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, e.g., 32.16.)

Explanation / Answer

Since the portfolio is equally invested, each component has a weightage of 33.33%, i.e., equally weighted.

The risk free asset is given a Beta of 0.

Portfolio Beta= Asset1 Weightage * Asset1 Beta + Asset2 Weightage * Asset2 Beta + Asset3 Weightage * Asset3 Beta.

Asset3 Weightage * Asset3 Beta.= 0, since Beta of riskfree asset =0.

Market Beta is Always 1 & so Portfolio Beta = 1.

Thus, 1 = 0.33 * Asset1 Beta + 0.33 * 1.32

1 = 0.33 * Asset1 Beta + 0.4356

1-0.4356 = 0.33 * Asset1 Beta

Asset1 Beta = 0.5644/0.33

= 1.71

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