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Q1. Is a short position of a call option (= writing a call) identical to a long position of a put option (= buying a put)? Please explain.
Q2. Explain the similarities and the differences between a forward contract and a futures contract.
Q3. A company enters into long futures contracts to buy 4,000 bushels of wheat for $3.00 per bushel. The initial margin is $0.60 per bushel. The maintenance margin is $1,000.
a. If futures price becomes $3.30 per bushel (10% increase), calculate the cumulative gain.
b. Calculate the rate of return.
b. What futures price change will trigger a margin call?
Q4. A fund manager has a portfolio worth $20 million with a beta of 1.3. The manager is concerned about the performance of the market over the next two months and plans to use three-month futures contracts on the S&P 500 to hedge the risk. The current index level is 2,000 and one futures contract is on 250 times the index (i.e., the index multiplier is 250). The risk-free rate is 3.0% per annum and assume 0% dividend yield for simplicity. The current three-month futures price is $2,100.
a. What position should the fund manager take to hedge exposure to the market over the next two months? In other words, how many futures contracts does the manager have to buy or sell? Specify whether it’s a long (=buy) or short (=sell) position.
b. Calculate the effect of your strategy on the fund manager’s returns if the index in two months is 1900, 2000, 2100, 2200 and 2300. Assume in 2 months, the one-month futures price will be 0.25% higher than the index level. For example, if the index becomes 2000 two months from now, the index futures price will be 1.0025*2000 = 2005.00.
c. Calculate the standard deviation of stock portfolio values and that of total portfolio (stock + futures) values. Compare the two standard deviations.
d. In 2 months, are the total values (hedged values = stock portfolio plus futures position) always greater than the stock (=unhedged) values, regardless of the index value? If not, does it mean the hedge was unsuccessful? Explain.
Hint: To answer part b, replicate closely the textbook example in pages 65-67. Or review week 1 Excel file as we will be discussing a very similar example. In other words, you need to create a spreadsheet similar to Table 3.4.
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From the Syllabus Addendum
Homework: Each student must submit to “Assignments” in BB. The questions will be announced in the Monday email announcement. You must submit 1 Excel file (no Word file please) showing all the calculations and highlight your final answer. Cover sheet is not necessary.
If you do one of the following, you will receive 0 points for your homework submission.
a. 2 or more students submitting virtually identical Excel files. You may work in groups but each student must prepare and submit his own Excel file. Do not share or copy answers.
b. Typing in numeric answers. For example, if the question asks “what is 123+789?” then you should input in Excel as “=123+789” instead of “912.” Your Excel may display the cell as “912” but when I click it, I need to see your Excel formula “=123+789.”
c. Copying the solutions from previous year homework. Please note that I change all the questions slightly every year.
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