Question

You currently hold a diversified stock portfolio that is exactly as risky as the market. You are considering adding another stock, with a Beta of 1.40, to your portfolio. Assuming you do add the stock to your portfolio, which of the following statements is/are likely to be true? (Choose all that apply.)

The beta of your portfolio will increase.

The beta of your portfolio will be between 1 and 1.40

The stock's reward-to-risk ratio is less than that of the market.

The new stock is overpriced.

The expected return on your portfolio will decrease.

Answer 1

Solution:

We currently have a diversified stock portfolio that is as risky as the market. It means that the beta of the portfolio is 1. We are adding one stock that has a beta of 1.40.

We calculate the portfolio beta by taking the sum of the weight of the asset * beta of that asset

Eg. $100 value has beta = 1, $10 value has beta = 1.40

Portfolio beta = 100 * 1 / 110 + 10 *1.4 /110 =  0.9090 + 0.1272 = 1.0362

Correct option is The beta of your portfolio will be between 1 and 1.40