Data table

​(Click on the following icon 
   
in order to copy its contents into a​ spreadsheet.)

**Portfolio A**

**Portfolio B**

**Probability**

**Return**

**Probability**

 **Return**

0.220.22

negative 4−4​%

0.080.08

66​%

0.460.46

2020​%

0.280.28

88​%

0.320.32

2323​%

0.380.38

1010​%

0.260.26

1616​%Data table

​(Click on the following icon 
   
in order to copy its contents into a​ spreadsheet.)

**Portfolio A**

**Portfolio B**

**Probability**

**Return**

**Probability**

 **Return**

0.220.22

negative 4−4​%

0.080.08

66​%

0.460.46

2020​%

0.280.28

88​%

0.320.32

2323​%

0.380.38

1010​%

0.260.26

1616​%
Question content area top

Part 1

​(Computing **the expected rate of return and**​ risk)**** After a tumultuous period in the stock​ market, 

Logan MorganLogan Morgan 

is considering an investment in one of two portfolios. Given the information in the popup​ window, 

LOADING...

​, 

which investment is​ better, based on risk​ (as measured by the standard​ deviation) and return as measured by the expected rate of​ return?

​(*Hint*​: 

Use at least four decimal places in all​ calculations.)

Question content area bottom

Part 1

**a.** The expected rate of return for portfolio A is 

enter your response here​%. 

 ​(Round to two decimal​ places.)

To calculate the expected rate of return for Portfolio A, we will use the formula for expected return, which is the weighted average of the returns based on their respective probabilities. The formula is:

\[
\text{Expected Return} = \sum (\text{Probability} \times \text{Return})
\]

For Portfolio A, we have the following dataTo calculate the expected rate of return for Portfolio A, we will use the formula for expected return, which is the weighted average of the returns based on their respective probabilities. The formula is:

\[
\text{Expected Return} = \sum (\text{Probability} \times \text{Return})
\]

For Portfolio A, we have the following 

- Probability 1: \( 0.22 \), Return: \( -4\% \)
- Probability 2: \( 0.46 \), Return: \( 20\% \)
- Probability 3: \( 0.32 \), Return: \( 23\% \)

### Step 1: Calculate each term

1. \( 0.22 \times -4 = -0.88\)
2. \( 0.46 \times 20 = 9.20\)
3. \( 0.32 \times 23 = 7.36\)

### Step 2: Sum these values to find the expected return

\[
\text{Expected Return} = -0.88 + 9.20 + 7.36 = 15.68
\]

So, the expected rate of return for Portfolio A is approximately **15.68%**.

Would you like details on calculating the expected return for Portfolio B or the standard deviation for either portfolio?

---

### Related Questions

1. How do you calculate the expected return for Portfolio B?
2. What is the significance of using four decimal places in financial calculations?
3. How do we calculate the standard deviation of a portfolio's returns?
4. Why is standard deviation considered a measure of risk?
5. What other factors might affect the choice between Portfolio A and Portfolio B?

### Tip:
Remember to double-check probabilities add up to 1. This ensures your portfolio analysis is based on a complete distribution.

After a tumultuous period in the stock market, Logan Morgan is considering an investment in one of two portfolios. Given the information in the data table, which investment is better, based on risk (as measured by the standard deviation) and return (as measured by the expected rate of return)?

Analyze Portfolio A and Portfolio B to determine the best investment choice based on expected return and risk, using probability-weighted returns and standard deviation. Detailed calculations for each step with formulas for expected value and standard deviation. Ideal for high school students in Grades 11-12.

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