You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.11 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?

Problem 13-12 Calculating Portfolio Betas [LO4]

You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.11 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.)

  

Portfolio beta

 

Explanation:

The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. If the portfolio is as risky as the market, it must have the same beta as the market. Since the beta of the market is one, we know the beta of our portfolio is one. We also need to remember that the beta of the risk-free asset is zero. It has to be zero since the asset has no risk. Setting up the equation for the beta of our portfolio, we get:

βP = 1.0 = 1/3(0) + 1/3(1.11) + 1/3(βX)

  

Solving for the beta of Stock X, we get:

    

βX = 1.89