Question

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 1.32 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?

Answer 1

To calculate the beta of the other stock in a portfolio, you can use the formula for the beta of a portfolio and given weights and betas of the stocks. In this case, the beta of the other stock is determined to be 0.34.

Step-by-step explanation:

To calculate the beta of the other stock in your portfolio, we need to use the formula for the beta of a portfolio:

Beta of Portfolio = Weight of Stock1 * Beta of Stock1 + Weight of Stock2 * Beta of Stock2

Since your portfolio is equally invested in a risk-free asset and two stocks, the weights of the stocks are both 0.5. Since the portfolio is equally as risky as the market, the beta of the portfolio should also be 1. To solve for the beta of the other stock, we can rearrange the formula as:

Beta of Stock2 = (Beta of Portfolio - Weight of Stock1 * Beta of Stock1) / Weight of Stock2

Substituting the given values, we get:

Beta of Stock2 = (1 - 0.5 * 1.32) / 0.5 = 0.34

Therefore, the beta of the other stock in your portfolio must be 0.34.