Asked by Grant Friesen on Jun 21, 2024
Verified
Suppose you hold a diversified portfolio consisting of a $10,000 investment in each of 12 different common stocks.The portfolio's beta is 1.25.Now suppose you decided to sell one of your stocks that has a beta of 1.00 and use the proceeds to buy a replacement stock with a beta of 1.34.What would be the portfolio's new beta?
A) 1.15
B) 1.21
C) 1.28
D) 1.34
Portfolio Beta
A measure of the volatility, or systematic risk, of a portfolio compared to the market as a whole, indicating how sensitive the portfolio is to market movements.
Diversified Portfolio
An investment strategy that spreads investments across various asset classes to reduce risk and potential volatility.
Replacement Stock
Stock issued in exchange for an existing stock, often used in stock splits, mergers, or acquisitions to adjust shareholder holdings without changing overall equity.
- Calculate portfolio betas and understand the impact of portfolio composition changes on its beta.
Verified Answer
ES
Esteban SuárezJun 25, 2024
Final Answer :
C
Explanation :
The first step is to calculate the current total value of the portfolio, which is:
$10,000 x 12 = $120,000
Next, we need to calculate the current beta of the portfolio. Since all stocks have an equal investment, we can use a simple average of the betas:
(1.25 x 12) / 12 = 1.25
Now, we can calculate the beta of the portfolio after selling the stock with a beta of 1.00 and buying the new one with a beta of 1.34. Since we are only replacing one stock, the total value of the portfolio remains the same at $120,000. The new beta can be calculated as follows:
[ (1.25 x 12) - 1.00 + 1.34 ] / 12 = 1.28
Therefore, the answer is C) 1.28.
$10,000 x 12 = $120,000
Next, we need to calculate the current beta of the portfolio. Since all stocks have an equal investment, we can use a simple average of the betas:
(1.25 x 12) / 12 = 1.25
Now, we can calculate the beta of the portfolio after selling the stock with a beta of 1.00 and buying the new one with a beta of 1.34. Since we are only replacing one stock, the total value of the portfolio remains the same at $120,000. The new beta can be calculated as follows:
[ (1.25 x 12) - 1.00 + 1.34 ] / 12 = 1.28
Therefore, the answer is C) 1.28.
Learning Objectives
- Calculate portfolio betas and understand the impact of portfolio composition changes on its beta.