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.As the risk of Megan's portfolio increases, the average annual return on her portfolio .Suppose Megan currently allocates 25% of her portfolio to a diversified group of stocks and 75% of her portfolio to risk-free bonds; that is, she chooses combination B. She wants to increase the average annual return on her portfolio from 3% to 7%. In order to do so, she must do which of the following? Check all that apply.Sell some of her stocks and place the proceeds in a savings accountAccept more riskSell some of her bonds and use the proceeds to purchase stocksSell some of her stocks and use the proceeds to purchase bondsThe 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 5%, 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 . ### Portfolio Management and Risk#### Portfolio Composition and PerformanceThe table below displays various combinations of diversified stocks and their impacts on portfolio performance, including average annual return and risk (standard deviation of portfolio return).| Combination | Fraction of Portfolio in Diversified Stocks (Percent) | Average Annual Return (Percent) | Standard Deviation of Portfolio Return (Risk) (Percent) ||-------------|-------------------------------------------------------|---------------------------------|---------------------------------------------------------|| A | 0 | 1.00 | 0 || B | 25 | 3.00 | 5 || C | 50 | 5.00 | 10 || D | 75 | 7.00 | 15 || E | 100 | 9.00 | 20 |#### Analysis:- As the fraction of diversified stocks in the portfolio increases, both the average annual return and the risk (as measured by standard deviation) increase. #### Investment Decision Scenario:Suppose Megan currently allocates 25% of her portfolio to a diversified group of stocks and 75% to risk-free bonds, choosing combination B (Average Annual Return: 3%, Standard Deviation: 5%). She plans to increase her average annual return from 3% to 7%. To achieve this, she must consider the following options:- [ ] Sell some of her stocks and place the proceeds in a savings account- [ ] Accept more risk- [ ] Sell some of her bonds and use the proceeds to purchase stocks- [ ] Sell some of her stocks and use the proceeds to purchase bonds#### Statistical Note:The table uses standard deviation as a measure of risk. Assuming a normal distribution, a portfolio's return tends to stay within two standard deviations of its average about 95% of the time.**Example Scenario:**Suppose Megan modifies her portfolio to contain 50% in diversified stocks and 50% in risk-free government bonds (Combination C: Average Annual Return: 5%, Standard Deviation: 10%). Typically, 95% of the time the returns will vary within a range given by:\[ Mean \, \text{±} \, 2 \times \text{Standard Deviation} \]Thus, Megan’s return will generally vary from a gain of 3% to a gain of 7%.

Return is the profit expected by the investor on the investment and risk is the probability 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. As the risk of Megan's portfolio increases, the average annual return on her portfolio . Suppose Megan currently allocates 25% of her portfolio to a diversified group of stocks and 75% of her portfolio to risk-free bonds; that is, she chooses combination B. She wants to increase the average annual return on her portfolio from 3% to 7%. In order to do so, she must do which of the following? Check all that apply. Sell some of her stocks and place the proceeds in a savings account Accept more risk Sell some of her bonds and use the proceeds to purchase stocks Sell some of her stocks and use the proceeds to purchase bonds 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 5%, 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

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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.

As the risk of Megan's portfolio increases, the average annual return on her portfolio .
Suppose Megan currently allocates 25% of her portfolio to a diversified group of stocks and 75% of her portfolio to risk-free bonds; that is, she chooses combination B. She wants to increase the average annual return on her portfolio from 3% to 7%. In order to do so, she must do which of the following? Check all that apply.

Sell some of her stocks and place the proceeds in a savings account
Accept more risk
Sell some of her bonds and use the proceeds to purchase stocks
Sell some of her stocks and use the proceeds to purchase bonds
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 5%, 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 .

### Portfolio Management and Risk

#### Portfolio Composition and Performance

The table below displays various combinations of diversified stocks and their impacts on portfolio performance, including average annual return and risk (standard deviation of portfolio return).

| Combination | Fraction of Portfolio in Diversified Stocks (Percent) | Average Annual Return (Percent) | Standard Deviation of Portfolio Return (Risk) (Percent) |
|-------------|-------------------------------------------------------|---------------------------------|---------------------------------------------------------|
| A | 0 | 1.00 | 0 |
| B | 25 | 3.00 | 5 |
| C | 50 | 5.00 | 10 |
| D | 75 | 7.00 | 15 |
| E | 100 | 9.00 | 20 |

#### Analysis:

- As the fraction of diversified stocks in the portfolio increases, both the average annual return and the risk (as measured by standard deviation) increase.

#### Investment Decision Scenario:

Suppose Megan currently allocates 25% of her portfolio to a diversified group of stocks and 75% to risk-free bonds, choosing combination B (Average Annual Return: 3%, Standard Deviation: 5%). She plans to increase her average annual return from 3% to 7%. To achieve this, she must consider the following options:

- [ ] Sell some of her stocks and place the proceeds in a savings account
- [ ] Accept more risk
- [ ] Sell some of her bonds and use the proceeds to purchase stocks
- [ ] Sell some of her stocks and use the proceeds to purchase bonds

#### Statistical Note:

The table uses standard deviation as a measure of risk. Assuming a normal distribution, a portfolio's return tends to stay within two standard deviations of its average about 95% of the time.

**Example Scenario:**

Suppose Megan modifies her portfolio to contain 50% in diversified stocks and 50% in risk-free government bonds (Combination C: Average Annual Return: 5%, Standard Deviation: 10%). Typically, 95% of the time the returns will vary within a range given by:

\[ Mean \, \text{±} \, 2 \times \text{Standard Deviation} \]

Thus, Megan’s return will generally vary from a gain of 3% to a gain of 7%.

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