Question

ou own a portfolio equally invested in a risk-free asset and two stocks. If one of the tocks has a beta of 1.34 and the total portfolio is equally as risky as the market, what nust the beta be for the other stock in your portfolio? (Do not round intermediate alculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

To ensure the portfolio is as risky as the market, the beta of the other stock in the portfolio must be 0.66 if the portfolio includes a risk-free asset and another stock with a beta of 1.34.

Step-by-step explanation:

The question asks for the beta of the other stock in a portfolio that includes a risk-free asset and two stocks, one with a known beta of 1.34. To determine the beta of the other stock, we need to understand that the beta of the entire portfolio should be equal to the market's beta, which is 1 since the portfolio is equally as risky as the market.

The formula for the beta of a portfolio (βportfolio) is the weighted average of the betas of the individual assets, where weights are the proportions of the investment in each asset. For a two-asset portfolio with a risk-free asset (which has a beta of 0), the calculation would be:

βportfolio = (0.5 * βstock1) + (0.5 * βstock2)

Given the portfolio's beta is 1 (equal to the market) and one of the stocks has a beta of 1.34, we can set up the equation:

1 = (0.5 * 1.34) + (0.5 * βstock2)

By solving for βstock2, we find the beta for the other stock.

1 = 0.67 + (0.5 * βstock2)
βstock2 = (1 - 0.67) / 0.5
βstock2 = 0.66

Therefore, the beta for the other stock must be 0.66 to ensure the portfolio has the same risk level as the market.

Answer 2

The beta of the second stock must be 1.66 for the portfolio, which includes a risk-free asset and two stocks, to have the same level of risk as the market.

Step-by-step explanation:

The student's question pertains to finding the required beta of the second stock in a portfolio that is as risky as the market. Since the portfolio's risk level is equal to that of the market, the portfolio's beta is 1. The portfolio consists of a risk-free asset, which has a beta of 0, and two stocks. The beta of the portfolio is the average of the betas of its components. Given that one stock has a beta of 1.34 and assuming that the risk-free asset and the two stocks are equally weighted, the beta of the second stock can be calculated using the following formula:

Portfolio Beta = (Beta of Stock 1 + Beta of Stock 2 + Beta of Risk-Free Asset) / 3

Setting the Portfolio Beta to 1, as it is as risky as the market, and solving for Beta of Stock 2 gives:

1 = (1.34 + Beta of Stock 2 + 0) / 3

Multiplying through by 3 and rearranging the terms, we get:

Beta of Stock 2 = 3 - 1.34

Beta of Stock 2 = 1.66

Therefore, the other stock must have a beta of 1.66 for the portfolio to have the same level of risk as the market.