A fund manages a $3.6 billion equity portfolio with a beta of 0.6. If the S&P contract multiplier is $50 and the index is currently at 2,400, how many contracts should the fund sell to make its overall position market neutral? Number of contracts
A fund manages a $3.6 billion equity portfolio with a beta of 0.6. If the S&P contract multiplier is $50 and the index is currently at 2,400, how many contracts should the fund sell to make its overall position market neutral? Number of contracts
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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![**Market Neutral Position Calculation for a Fund**
A fund manages a $3.6 billion equity portfolio with a beta of 0.6. If the S&P contract multiplier is $50 and the index is currently at 2,400, how many contracts should the fund sell to make its overall position market neutral?
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**Number of Contracts Calculation:**
A table is presented showing "Number of contracts" with a field for input or calculation, suggesting the need to determine how many contracts to sell for achieving market neutrality.
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**Explanation:**
To calculate the number of contracts needed to make the fund's position market neutral, use the formula:
\[ \text{Number of Contracts} = \frac{\text{Portfolio Value} \times \text{Beta}}{\text{Index Value} \times \text{Multiplier}} \]
Plug in the given values:
- Portfolio Value = $3.6 billion
- Beta = 0.6
- Index Value = 2,400
- Multiplier = $50
\[ \text{Number of Contracts} = \frac{3,600,000,000 \times 0.6}{2,400 \times 50} \]
This formula calculates the number of S&P futures contracts needed to hedge the portfolio entirely, considering its market sensitivity (beta).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce31b907-ccde-4608-9095-702f0fde7fce%2F902d5155-0e14-4e28-8136-064988c73716%2F4hfrddk_processed.png&w=3840&q=75)
Transcribed Image Text:**Market Neutral Position Calculation for a Fund**
A fund manages a $3.6 billion equity portfolio with a beta of 0.6. If the S&P contract multiplier is $50 and the index is currently at 2,400, how many contracts should the fund sell to make its overall position market neutral?
---
**Number of Contracts Calculation:**
A table is presented showing "Number of contracts" with a field for input or calculation, suggesting the need to determine how many contracts to sell for achieving market neutrality.
---
**Explanation:**
To calculate the number of contracts needed to make the fund's position market neutral, use the formula:
\[ \text{Number of Contracts} = \frac{\text{Portfolio Value} \times \text{Beta}}{\text{Index Value} \times \text{Multiplier}} \]
Plug in the given values:
- Portfolio Value = $3.6 billion
- Beta = 0.6
- Index Value = 2,400
- Multiplier = $50
\[ \text{Number of Contracts} = \frac{3,600,000,000 \times 0.6}{2,400 \times 50} \]
This formula calculates the number of S&P futures contracts needed to hedge the portfolio entirely, considering its market sensitivity (beta).
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