You are an investor in common stock, and you currently hold a well-diversified portfolio which has an expected return of 12 percent, a beta of 1.2, and a total value of $9,000.You plan to increase your portfolio by buying 100 shares of AT&E at $10 a share.AT&E has an expected return of 20 percent with a beta of 2.0.What will be the expected return and the beta of your portfolio after you purchase the new stock? A) = 20.0%; β_p = 2.00 B) = 12.8%; β_p = 1.28 C) = 12.0%; β_p = 1.20 D) = 13.2%; β_p = 1.40 E) = 14.0%; β_p = 1.32

Question

Quizplus · Accepted Answer

To calculate the expected return and beta of the portfolio after buying the new stock, we use the following formula:

Rp = (W1 x R1) + (W2 x R2)
βp = (W1 x β1) + (W2 x β2)

Where:
Rp = expected return of the portfolio
βp = beta of the portfolio
W1 = proportion of the current portfolio's value
W2 = proportion of the new stock's value
R1 = expected return of the current portfolio
R2 = expected return of the new stock
β1 = beta of the current portfolio
β2 = beta of the new stock

Plugging in the numbers from the question, we get:

Rp = (0.9 x 0.12) + (0.1 x 0.20) = 0.128 or 12.8%
βp = (0.9 x 1.2) + (0.1 x 2.0) = 1.28

Therefore, the expected return of the portfolio after buying the new stock is 12.8%, and the beta of the portfolio is 1.28. Choice B is the correct answer.

You Are an Investor in Common Stock, and You Currently