Problem 11-12 Calculating Portfolio Betas [LO 3] You own a portfolio equally inv

Question

Problem 11-12 Calculating Portfolio Betas [LO 3]

You own a portfolio equally invested in a risk-free asset and two stocks. One of the stocks has a beta of 1.3 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. One of the stocks has a beta of 1.3 and the total portfolio is equally as risky as the market.

Explanation / Answer

The beta of the entire market is equal to 1

So if the beta of one stock is 1.3

Let the beta of the other stock be = beta2

Since they are equally invested, the proporions of the two stocks is 0.5

Hence, we solve for beta2 as per the below equation:

1.3*0.5 + beta2*0.5 = 1

0.65 +0.5beta2 = 1

beta 2 = 0.7

Hence beta of the other stock in your portfolio = 0.7

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