What is the expected return of the optimal stock portfolio?

EBK CONTEMPORARY FINANCIAL MANAGEMENT
14th Edition
ISBN:9781337514835
Author:MOYER
Publisher:MOYER
Chapter8: Analysis Of Risk And Return
Section: Chapter Questions
Problem 13QTD
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### Multiple Choice Question Example

#### Instructions: 
Select the correct percentage from the options provided below:

1. 17.9%
2. 15.1%
3. 19.5%
4. 16.4%
5. 17.2%

#### Sidebar Menu
- **Skipped**: Indicates the questions or sections that have been skipped.
- **eBook**: Provides access to the electronic version of the textbook or related study materials.
- **References**: Access to the reference materials and additional resources for further reading and study.

### Description of Options:
The screen shows a multiple choice question with five percentage options presented as follows:

- **Option 1**: 17.9%
- **Option 2**: 15.1%
- **Option 3**: 19.5%
- **Option 4**: 16.4%
- **Option 5**: 17.2%

Each option is accompanied by a radio button to indicate the selection choice. The interface allows the user to select only one correct option out of the given alternatives.

Feel free to consult the eBook or References if you are unsure about the correct answer.
Transcribed Image Text:### Multiple Choice Question Example #### Instructions: Select the correct percentage from the options provided below: 1. 17.9% 2. 15.1% 3. 19.5% 4. 16.4% 5. 17.2% #### Sidebar Menu - **Skipped**: Indicates the questions or sections that have been skipped. - **eBook**: Provides access to the electronic version of the textbook or related study materials. - **References**: Access to the reference materials and additional resources for further reading and study. ### Description of Options: The screen shows a multiple choice question with five percentage options presented as follows: - **Option 1**: 17.9% - **Option 2**: 15.1% - **Option 3**: 19.5% - **Option 4**: 16.4% - **Option 5**: 17.2% Each option is accompanied by a radio button to indicate the selection choice. The interface allows the user to select only one correct option out of the given alternatives. Feel free to consult the eBook or References if you are unsure about the correct answer.
### Portfolio Allocation Analysis

**Question 19**

A portfolio analyst has been asked to allocate investment funds among three different stocks. The relevant data for the stocks is shown in the following table. The goal is to maximize return while maintaining risk within acceptable bounds (in this case, a portfolio standard deviation of no more than 20%). Find the proper allocation of the funds to each stock.

#### Data Table:
| Stock | Return (%) | Risk (Standard Deviation) (%) | Pair of Stocks | Joint Risk (Covariance) |
|-------|------------|-------------------------------|----------------|-------------------------|
| A     | 20%        | 25%                           | A to B         | 0.6                     |
| B     | 15%        | 15%                           | A to C         | 0.05                    |
| C     | 12%        | 12%                           | B to C         | -0.05                   |

What is the expected return of the optimal stock portfolio?

#### Multiple Choice:
- [ ] 17%
- [ ] 15.1%
- [ ] 16%
- [ ] 18.4%

The task involves understanding the risk-return characteristics of each stock individually and their combined effect when blended into a portfolio. By doing so, the analyst can find an optimal allocation that maximizes returns while ensuring the overall portfolio risk does not exceed 20%. 

#### Explanation of Joint Risk (Covariance):
- **Covariance** between stocks A and B: 0.6
- **Covariance** between stocks A and C: 0.05
- **Covariance** between stocks B and C: -0.05

Covariance helps in determining how the stocks move together. A positive covariance indicates that the stocks move in the same direction, while a negative covariance indicates they move in opposite directions.

By analyzing these figures, one would theoretically calculate the weights of each stock in the portfolio to find the highest expected return while constraining the portfolio’s standard deviation to 20%.
Transcribed Image Text:### Portfolio Allocation Analysis **Question 19** A portfolio analyst has been asked to allocate investment funds among three different stocks. The relevant data for the stocks is shown in the following table. The goal is to maximize return while maintaining risk within acceptable bounds (in this case, a portfolio standard deviation of no more than 20%). Find the proper allocation of the funds to each stock. #### Data Table: | Stock | Return (%) | Risk (Standard Deviation) (%) | Pair of Stocks | Joint Risk (Covariance) | |-------|------------|-------------------------------|----------------|-------------------------| | A | 20% | 25% | A to B | 0.6 | | B | 15% | 15% | A to C | 0.05 | | C | 12% | 12% | B to C | -0.05 | What is the expected return of the optimal stock portfolio? #### Multiple Choice: - [ ] 17% - [ ] 15.1% - [ ] 16% - [ ] 18.4% The task involves understanding the risk-return characteristics of each stock individually and their combined effect when blended into a portfolio. By doing so, the analyst can find an optimal allocation that maximizes returns while ensuring the overall portfolio risk does not exceed 20%. #### Explanation of Joint Risk (Covariance): - **Covariance** between stocks A and B: 0.6 - **Covariance** between stocks A and C: 0.05 - **Covariance** between stocks B and C: -0.05 Covariance helps in determining how the stocks move together. A positive covariance indicates that the stocks move in the same direction, while a negative covariance indicates they move in opposite directions. By analyzing these figures, one would theoretically calculate the weights of each stock in the portfolio to find the highest expected return while constraining the portfolio’s standard deviation to 20%.
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