Carson Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population, not a sample.) Do not round your intermediate calculations. Economic Conditions Strong Normal Weak O a. 17.49% O b. 12.36% O c. 22.49% O d. 10.10% O e. 18.36% Prob. 30% 40% 30% Return 27.0% 13.0% -17.0%
Carson Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population, not a sample.) Do not round your intermediate calculations. Economic Conditions Strong Normal Weak O a. 17.49% O b. 12.36% O c. 22.49% O d. 10.10% O e. 18.36% Prob. 30% 40% 30% Return 27.0% 13.0% -17.0%
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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![### Economic Conditions and Standard Deviation of Returns
Carson Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below.
#### Question:
What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population, not a sample.) Do not round your intermediate calculations.
#### Economic Conditions Probability Distribution:
| **Economic Conditions** | **Prob.** | **Return** |
|--------------------------|-----------|------------|
| Strong | 30% | 27.0% |
| Normal | 40% | 13.0% |
| Weak | 30% | -17.0% |
#### Answer Choices:
- a. 17.49%
- b. 12.36%
- c. 22.49%
- d. 10.10%
- e. 18.36%
#### Explanation:
To find the standard deviation of the returns, we use the formula for standard deviation of a population. Here are the steps:
1. **Calculate the Expected Return (Mean)**:
\[ E(R) = \sum (P_i \times R_i) \]
Where \( P_i \) is the probability of each economic condition, and \( R_i \) is the return.
2. **Compute the Variance**:
\[ \sigma^2 = \sum [P_i \times (R_i - E(R))^2] \]
3. **Find the Standard Deviation**:
\[ \sigma = \sqrt{\sigma^2} \]
Use these steps to calculate the actual standard deviation based on the given probabilities and returns.
----------
This problem illustrates the concept of standard deviation in the context of varying economic conditions and expected returns, a crucial topic in financial management and investment analysis. Understanding how to calculate and interpret standard deviation helps in assessing risk and making better-informed financial decisions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F136a9916-8a5d-490b-a1c4-57e644d5608a%2Fa7bfb008-c7e2-4b89-82e1-c14b5113fcc6%2Fdv9qf9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Economic Conditions and Standard Deviation of Returns
Carson Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below.
#### Question:
What's the standard deviation of the estimated returns? (Hint: Use the formula for the standard deviation of a population, not a sample.) Do not round your intermediate calculations.
#### Economic Conditions Probability Distribution:
| **Economic Conditions** | **Prob.** | **Return** |
|--------------------------|-----------|------------|
| Strong | 30% | 27.0% |
| Normal | 40% | 13.0% |
| Weak | 30% | -17.0% |
#### Answer Choices:
- a. 17.49%
- b. 12.36%
- c. 22.49%
- d. 10.10%
- e. 18.36%
#### Explanation:
To find the standard deviation of the returns, we use the formula for standard deviation of a population. Here are the steps:
1. **Calculate the Expected Return (Mean)**:
\[ E(R) = \sum (P_i \times R_i) \]
Where \( P_i \) is the probability of each economic condition, and \( R_i \) is the return.
2. **Compute the Variance**:
\[ \sigma^2 = \sum [P_i \times (R_i - E(R))^2] \]
3. **Find the Standard Deviation**:
\[ \sigma = \sqrt{\sigma^2} \]
Use these steps to calculate the actual standard deviation based on the given probabilities and returns.
----------
This problem illustrates the concept of standard deviation in the context of varying economic conditions and expected returns, a crucial topic in financial management and investment analysis. Understanding how to calculate and interpret standard deviation helps in assessing risk and making better-informed financial decisions.
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