Suppose Megan is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds. Combination A B с D E Fraction of Portfolio in Diversified Stocks (Percent) 0 25 50 75 100 Average Annual Return (Percent) 3.00 5.50 8.00 10.50 13.00 As the risk of Megan's portfolio increases, the average annual return on her portfolio rises Standard Deviation of Portfolio Return (Risk) (Percent) 0 5 10 15 20 Suppose Megan currently allocates 75% of her portfolio to a diversified group of stocks and 25% of her portfolio to risk-free bonds; that is, she chooses combination D. She wants to reduce the level of risk associated with her portfolio from a standard deviation of 15 to a standard deviation of 5. In order to do so, she must do which of the following? Check all that apply. Sell some of her stocks and use the proceeds to purchase bonds Place the entirety of her portfolio in bonds Accept a lower average annual rate of return Sell some of her bonds and use the proceeds to purchase stocks The table uses the standard deviation of the portfolio's return as a measure of risk. A normal random variable, such as a portfolio's return, stays within two standard deviations of its average approximately 95% of the time. Suppose Megan modifies her portfolio to contain 50% diversified stocks and 50% risk-free government bonds; that is, she chooses combination C. The average annual return for this type of portfolio is 8%, but given the standard deviation of 10%, the returns will typically (about 95% of the time) vary from a gain of to a loss of
Suppose Megan is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds. Combination A B с D E Fraction of Portfolio in Diversified Stocks (Percent) 0 25 50 75 100 Average Annual Return (Percent) 3.00 5.50 8.00 10.50 13.00 As the risk of Megan's portfolio increases, the average annual return on her portfolio rises Standard Deviation of Portfolio Return (Risk) (Percent) 0 5 10 15 20 Suppose Megan currently allocates 75% of her portfolio to a diversified group of stocks and 25% of her portfolio to risk-free bonds; that is, she chooses combination D. She wants to reduce the level of risk associated with her portfolio from a standard deviation of 15 to a standard deviation of 5. In order to do so, she must do which of the following? Check all that apply. Sell some of her stocks and use the proceeds to purchase bonds Place the entirety of her portfolio in bonds Accept a lower average annual rate of return Sell some of her bonds and use the proceeds to purchase stocks The table uses the standard deviation of the portfolio's return as a measure of risk. A normal random variable, such as a portfolio's return, stays within two standard deviations of its average approximately 95% of the time. Suppose Megan modifies her portfolio to contain 50% diversified stocks and 50% risk-free government bonds; that is, she chooses combination C. The average annual return for this type of portfolio is 8%, but given the standard deviation of 10%, the returns will typically (about 95% of the time) vary from a gain of to a loss of
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![### Understanding Portfolio Allocation
Suppose Megan is deciding how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table illustrates the risk and return associated with different combinations of stocks and bonds.
#### Portfolio Allocation Table
| Combination | Fraction of Portfolio in Diversified Stocks (Percent) | Average Annual Return (Percent) | Standard Deviation of Portfolio Return (Risk) (Percent) |
|-------------|----------------------------------------------|--------------------------|--------------------------------------------------|
| A | 0 | 3.00 | 0 |
| B | 25 | 5.50 | 5 |
| C | 50 | 8.00 | 10 |
| D | 75 | 10.50 | 15 |
| E | 100 | 13.00 | 20 |
#### Key Insights
- As the risk of Megan’s portfolio increases, the average annual return on her portfolio rises.
#### Example Scenario
Megan currently allocates 75% of her portfolio to a diversified group of stocks and 25% to risk-free bonds, which corresponds to Combination D. She wants to reduce the level of risk (standard deviation) from 15 to 5.
**What should Megan do?**
1. \[ \] Sell some of her stocks and use the proceeds to purchase bonds
2. \[ \] Place the entirety of her portfolio in bonds
3. \[ \] Accept a lower average annual rate of return
4. \[✔️\] Sell some of her bonds and use the proceeds to purchase stocks
#### Calculating Risk and Return
- The table utilizes standard deviation to measure the risk of a portfolio. A portfolio’s return typically stays within two standard deviations of its average about 95% of the time.
#### Further Analysis
Suppose Megan modifies her portfolio to contain 50% diversified stocks and 50% risk-free government bonds, selecting Combination C. The average annual return for this portfolio is 8%. However, with a standard deviation of 10%, returns can vary typically (about 95% of the time) from a gain of ___ to a loss of ___.
This table helps understand how changing the percentage of stocks and bonds in a portfolio affects both expected returns and risks.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2dfbc14-c292-406b-a407-1c08170dae11%2F029cee46-ef8d-4dd4-8c51-2b4c264d2731%2Fh473asg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Portfolio Allocation
Suppose Megan is deciding how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table illustrates the risk and return associated with different combinations of stocks and bonds.
#### Portfolio Allocation Table
| Combination | Fraction of Portfolio in Diversified Stocks (Percent) | Average Annual Return (Percent) | Standard Deviation of Portfolio Return (Risk) (Percent) |
|-------------|----------------------------------------------|--------------------------|--------------------------------------------------|
| A | 0 | 3.00 | 0 |
| B | 25 | 5.50 | 5 |
| C | 50 | 8.00 | 10 |
| D | 75 | 10.50 | 15 |
| E | 100 | 13.00 | 20 |
#### Key Insights
- As the risk of Megan’s portfolio increases, the average annual return on her portfolio rises.
#### Example Scenario
Megan currently allocates 75% of her portfolio to a diversified group of stocks and 25% to risk-free bonds, which corresponds to Combination D. She wants to reduce the level of risk (standard deviation) from 15 to 5.
**What should Megan do?**
1. \[ \] Sell some of her stocks and use the proceeds to purchase bonds
2. \[ \] Place the entirety of her portfolio in bonds
3. \[ \] Accept a lower average annual rate of return
4. \[✔️\] Sell some of her bonds and use the proceeds to purchase stocks
#### Calculating Risk and Return
- The table utilizes standard deviation to measure the risk of a portfolio. A portfolio’s return typically stays within two standard deviations of its average about 95% of the time.
#### Further Analysis
Suppose Megan modifies her portfolio to contain 50% diversified stocks and 50% risk-free government bonds, selecting Combination C. The average annual return for this portfolio is 8%. However, with a standard deviation of 10%, returns can vary typically (about 95% of the time) from a gain of ___ to a loss of ___.
This table helps understand how changing the percentage of stocks and bonds in a portfolio affects both expected returns and risks.
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