An individual has $15,000 invested in a stock with a beta of 0.6 and another $80,000 invested in a stock with a beta of 1.5. If these are the only two investments in her portfolio, what is her portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.
An individual has $15,000 invested in a stock with a beta of 0.6 and another $80,000 invested in a stock with a beta of 1.5. If these are the only two investments in her portfolio, what is her portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.
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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Question
![### Calculating the Portfolio Beta
An individual has $15,000 invested in a stock with a beta of 0.6 and another $80,000 invested in a stock with a beta of 1.5. If these are the only two investments in her portfolio, what is her portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.
To solve this problem, you need to calculate the weighted average beta of the portfolio. The formula for the portfolio beta (\( \beta_p \)) is given by:
\[
\beta_p = \frac{\sum{(w_i \cdot \beta_i)}}{\sum{w_i}}
\]
Where:
- \( w_i \) is the value of each investment
- \( \beta_i \) is the beta of each investment
Steps to Solve:
1. **Calculate the total investment**:
\[
\text{Total Investment} = \$15,000 + \$80,000 = \$95,000
\]
2. **Calculate the weight of each investment**:
- For the first investment:
\[
w_1 = \frac{\$15,000}{\$95,000}
\]
- For the second investment:
\[
w_2 = \frac{\$80,000}{\$95,000}
\]
3. **Calculate the portfolio beta**:
\[
\beta_p = w_1 \cdot 0.6 + w_2 \cdot 1.5
\]
Perform the calculations without intermediate rounding to ensure precision and provide the final answer rounded to two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00e39c23-5382-4320-a2d9-cf042c74097f%2F0bbca524-3a0a-49b1-8df1-59b1201aa1af%2Fokrz0a7g_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculating the Portfolio Beta
An individual has $15,000 invested in a stock with a beta of 0.6 and another $80,000 invested in a stock with a beta of 1.5. If these are the only two investments in her portfolio, what is her portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.
To solve this problem, you need to calculate the weighted average beta of the portfolio. The formula for the portfolio beta (\( \beta_p \)) is given by:
\[
\beta_p = \frac{\sum{(w_i \cdot \beta_i)}}{\sum{w_i}}
\]
Where:
- \( w_i \) is the value of each investment
- \( \beta_i \) is the beta of each investment
Steps to Solve:
1. **Calculate the total investment**:
\[
\text{Total Investment} = \$15,000 + \$80,000 = \$95,000
\]
2. **Calculate the weight of each investment**:
- For the first investment:
\[
w_1 = \frac{\$15,000}{\$95,000}
\]
- For the second investment:
\[
w_2 = \frac{\$80,000}{\$95,000}
\]
3. **Calculate the portfolio beta**:
\[
\beta_p = w_1 \cdot 0.6 + w_2 \cdot 1.5
\]
Perform the calculations without intermediate rounding to ensure precision and provide the final answer rounded to two decimal places.
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