You hold a diversified portfolio consisting of a $10,000 investment in each of 15 different common stocks (i.e., your total investment is $150,000). The portfolio beta is equal to 1.1 . You have decided to sell one of your stocks which has a beta equal to 0.9 for $10,000. You plan to use the proceeds to purchase another stock which has a beta equal to 0.9 . What will be the beta of the new portfolio? Show your answer to 2 decimal places.

Question

You hold a diversified portfolio consisting of a $10,000 investment in each of 15 different common stocks (i.e., your total investment is $150,000). The portfolio beta is equal to 1.1 . You have decided to sell one of your stocks which has a beta equal to 0.9 for $10,000. You plan to use the proceeds to purchase another stock which has a beta equal to 0.9 . What will be the beta of the new portfolio? Show your answer to 2 decimal places.

Answer 1

To calculate the beta of the new portfolio after selling one stock and purchasing another stock, you need to consider the current composition of the portfolio and the beta of the stocks involved.

Here are the steps to calculate the beta of the new portfolio:

1. Calculate the total value of the portfolio before the sale:
- The total investment in each stock is $10,000, and there are 15 different stocks.
- Therefore, the total value of the portfolio before the sale is 15 * $10,000 = $150,000.

2. Determine the beta-weighted value for the stock being sold:
- The stock being sold has a beta of 0.9 and a value of $10,000.
- Multiply the beta of the stock by its value: 0.9 * $10,000 = $9,000.

3. Determine the beta-weighted value for the new stock to be purchased:
- The new stock has a beta of 0.9 and a value of $10,000.
- Multiply the beta of the stock by its value: 0.9 * $10,000 = $9,000.

4. Calculate the new total portfolio value:
- Subtract the beta-weighted value for the stock being sold from the total value of the portfolio before the sale: $150,000 - $9,000 = $141,000.
- Add the beta-weighted value for the new stock to the new total portfolio value: $141,000 + $9,000 = $150,000.

5. Calculate the new beta of the portfolio:
- Divide the beta-weighted value of the stock being sold by the new total portfolio value: $9,000 / $150,000 = 0.06.
- Divide the beta-weighted value of the new stock by the new total portfolio value: $9,000 / $150,000 = 0.06.
- Sum the results to get the new portfolio beta: 0.06 + 0.06 = 0.12.

Therefore, the beta of the new portfolio after selling one stock and purchasing another stock will be 0.12.

0.98

To calculate the beta of the new portfolio after selling one stock and purchasing another stock, you need to consider the current composition of the portfolio and the beta of the stocks involved.