A hedge fund wants to purchase 100 shares of company X. The bid = $70, offer = $80. They also want to purchase 200 shares of company Y. The bid = $15, offer = $25. 1) What is the proportional bid-offer spread of each company? 2) What is the midmarket total value of each position? 3) What is the cost to the hedge fund to unwind the portfolio? 4) If the bid-offer spreads are normally distributed with mean $10 and standard deviation $3, what is the 99% worst-case cost of unwinding the position in the future?
A hedge fund wants to purchase 100 shares of company X. The bid = $70, offer = $80. They also want to purchase 200 shares of company Y. The bid = $15, offer = $25. 1) What is the proportional bid-offer spread of each company? 2) What is the midmarket total value of each position? 3) What is the cost to the hedge fund to unwind the portfolio? 4) If the bid-offer spreads are normally distributed with mean $10 and standard deviation $3, what is the 99% worst-case cost of unwinding the position in the future?
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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The questions relate to chapters, content and respective lectures of 23, 24, 25, 27, 28, & 29 of the Hull book.
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Transcribed Image Text:**Example Problem on Bid-Offer Spread Analysis**
A hedge fund wants to purchase 100 shares of company X. The bid is $70, and the offer is $80. They also want to purchase 200 shares of company Y. The bid is $15, and the offer is $25.
**Questions:**
1. What is the proportional bid–offer spread of each company?
2. What is the midmarket total value of each position?
3. What is the cost to the hedge fund to unwind the portfolio?
4. If the bid–offer spreads are normally distributed with a mean $10 and standard deviation $3, what is the 99% worst-case cost of unwinding the position in the future?
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### Explanation:
**Question 1: Proportional Bid-Offer Spread**
For Company X:
- The bid price (B) is $70, and the offer price (O) is $80.
- The spread (S) = O - B = $80 - $70 = $10.
- Proportional spread = S / Mid-point of B and O.
- Mid-point = (B + O) / 2 = ($70 + $80) / 2 = $75.
- Proportional spread = $10 / $75 ≈ 0.1333 or 13.33%.
For Company Y:
- The bid price (B) is $15, and the offer price (O) is $25.
- The spread (S) = O - B = $25 - $15 = $10.
- Proportional spread = S / Mid-point of B and O.
- Mid-point = (B + O) / 2 = ($15 + $25) / 2 = $20.
- Proportional spread = $10 / $20 = 0.5 or 50%.
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**Question 2: Midmarket Total Value of Each Position**
For Company X:
- Mid-point price = $75.
- Total value = Mid-point price × Number of shares.
- Total value = $75 × 100 = $7,500.
For Company Y:
- Mid-point price = $20.
- Total value = Mid-point price × Number of shares.
- Total value = $20 × 200 = $4,000.
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**Question 3: Cost to Unwind the Portfolio**
The cost to unwind the portfolio is calculated based on the spread.
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