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You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.08 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?

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Answer: 0.92

Explanation:

Beta is a measure of riskiness and Market beta is always 1.

The total portfolio therefore has a beta of 1.

Portfolio Beta is weighted average of the betas of the composite stocks.

The stocks are equally invested in so their weights are 0.5.

Assume the beta needed is x.

(0.5 * 1.08) + (0.5 * x) = 1

0.54 + 0.5x = 1

0.5x = 1 - 0.54

x = 0.46/0.5

= 0.92