A stock has a beta of 1.38 and an expected return of 13.6 percent. If the risk-free rate is 4.7 percent, 1)what is the expected return on a portfolio that is equally invested in the two assets? 2. if a portfolio of the assets has a beta of 0.98, what are the portfolio weights? 3. if a portfolio of the two assets has an expected return of 12.8 percent, what is its beta? 4. If a portfolio of the two assets has a beta of 2.58, what are the portfolio weights?
A stock has a beta of 1.38 and an expected return of 13.6 percent. If the risk-free rate is 4.7 percent, 1)what is the expected return on a portfolio that is equally invested in the two assets? 2. if a portfolio of the assets has a beta of 0.98, what are the portfolio weights? 3. if a portfolio of the two assets has an expected return of 12.8 percent, what is its beta? 4. If a portfolio of the two assets has a beta of 2.58, what are the portfolio weights?
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
![### Understanding Portfolio Investments and Beta
#### Problem Statement:
A stock has a beta of 1.38 and an expected return of 13.6 percent. The risk-free rate is 4.7 percent. Based on this information, we have the following questions:
1. What is the expected return on a portfolio that is equally invested in two assets?
2. If a portfolio of the assets has a beta of 0.98, what are the portfolio weights?
3. If a portfolio of the two assets has an expected return of 12.8 percent, what is its beta?
4. If a portfolio of the two assets has a beta of 2.58, what are the portfolio weights?
#### Understanding the Concepts:
1. **Expected Return with Equal Investment**:
To find the expected return on a portfolio equally invested in two assets, we need to consider the formula for the expected return of a portfolio:
\[
E(R_p) = w_1 \cdot E(R_1) + w_2 \cdot E(R_2)
\]
Where:
- \(E(R_p)\) is the expected return of the portfolio.
- \(w_1\) and \(w_2\) are the weights of the investments in the two assets.
- \(E(R_1)\) and \(E(R_2)\) are the expected returns of the two assets.
If the investment is equal in both assets, \(w_1 = w_2 = 0.5\).
2. **Portfolio Weights Based on Beta**:
To determine the portfolio weights when given a specific portfolio beta, we use the following relationship:
\[
\beta_p = w_1 \cdot \beta_1 + w_2 \cdot \beta_2
\]
Where:
- \(\beta_p\) is the portfolio beta.
- \(w_1\) and \(w_2\) are the weights of the investments in the two assets.
- \(\beta_1\) and \(\beta_2\) are the betas of the two assets.
3. **Portfolio Beta Based on Expected Return**:
The Capital Asset Pricing Model (CAPM) helps us to relate the expected return to the beta:
\[
E(R_i) = R_f](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce618159-930e-4ade-8eed-109751c2dc39%2Fc0bb3596-7dfa-4ec2-a6da-b210b70510af%2Ffm8xyg.png&w=3840&q=75)
Transcribed Image Text:### Understanding Portfolio Investments and Beta
#### Problem Statement:
A stock has a beta of 1.38 and an expected return of 13.6 percent. The risk-free rate is 4.7 percent. Based on this information, we have the following questions:
1. What is the expected return on a portfolio that is equally invested in two assets?
2. If a portfolio of the assets has a beta of 0.98, what are the portfolio weights?
3. If a portfolio of the two assets has an expected return of 12.8 percent, what is its beta?
4. If a portfolio of the two assets has a beta of 2.58, what are the portfolio weights?
#### Understanding the Concepts:
1. **Expected Return with Equal Investment**:
To find the expected return on a portfolio equally invested in two assets, we need to consider the formula for the expected return of a portfolio:
\[
E(R_p) = w_1 \cdot E(R_1) + w_2 \cdot E(R_2)
\]
Where:
- \(E(R_p)\) is the expected return of the portfolio.
- \(w_1\) and \(w_2\) are the weights of the investments in the two assets.
- \(E(R_1)\) and \(E(R_2)\) are the expected returns of the two assets.
If the investment is equal in both assets, \(w_1 = w_2 = 0.5\).
2. **Portfolio Weights Based on Beta**:
To determine the portfolio weights when given a specific portfolio beta, we use the following relationship:
\[
\beta_p = w_1 \cdot \beta_1 + w_2 \cdot \beta_2
\]
Where:
- \(\beta_p\) is the portfolio beta.
- \(w_1\) and \(w_2\) are the weights of the investments in the two assets.
- \(\beta_1\) and \(\beta_2\) are the betas of the two assets.
3. **Portfolio Beta Based on Expected Return**:
The Capital Asset Pricing Model (CAPM) helps us to relate the expected return to the beta:
\[
E(R_i) = R_f
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