You have a portfolio that is invested 23 percent in Stock A, 36 percent in Stock B, 41 percent in Stock C, and the remainder in a risk free asset. The betas of the stocks are .68, 1.23,and 1.52, respectively. What is the beta of the portfolio? O1.10 1.14 O122 1.18 O1.38
You have a portfolio that is invested 23 percent in Stock A, 36 percent in Stock B, 41 percent in Stock C, and the remainder in a risk free asset. The betas of the stocks are .68, 1.23,and 1.52, respectively. What is the beta of the portfolio? O1.10 1.14 O122 1.18 O1.38
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
![**Portfolio Beta Calculation**
You have a portfolio that is invested as follows:
- 23% in Stock A with a beta of 0.68
- 36% in Stock B with a beta of 1.23
- 41% in Stock C with a beta of 1.52
- The remainder in a risk-free asset (beta of 0).
**Question:**
What is the beta of the portfolio?
**Options:**
- 1.10
- 1.14
- 1.22
- 1.18
- 1.38
**Explanation:**
To calculate the beta of the portfolio, multiply the percentage of the investment in each stock by its respective beta and then sum up the values. Since the risk-free asset has a beta of 0, it does not influence the portfolio beta.
**Formula:**
\[ \text{Portfolio Beta} = (0.23 \times 0.68) + (0.36 \times 1.23) + (0.41 \times 1.52) \]
**Note:**
The percentages should add up to 100%, confirming that the remaining percentage in the risk-free asset does not affect the overall beta calculation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7d68a3d-74a1-43bb-a00e-227943ec7639%2Fb11fb5fb-4ad7-44cf-8b15-6e17074f6531%2Ft7y97mm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Portfolio Beta Calculation**
You have a portfolio that is invested as follows:
- 23% in Stock A with a beta of 0.68
- 36% in Stock B with a beta of 1.23
- 41% in Stock C with a beta of 1.52
- The remainder in a risk-free asset (beta of 0).
**Question:**
What is the beta of the portfolio?
**Options:**
- 1.10
- 1.14
- 1.22
- 1.18
- 1.38
**Explanation:**
To calculate the beta of the portfolio, multiply the percentage of the investment in each stock by its respective beta and then sum up the values. Since the risk-free asset has a beta of 0, it does not influence the portfolio beta.
**Formula:**
\[ \text{Portfolio Beta} = (0.23 \times 0.68) + (0.36 \times 1.23) + (0.41 \times 1.52) \]
**Note:**
The percentages should add up to 100%, confirming that the remaining percentage in the risk-free asset does not affect the overall beta calculation.
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