Problem 1. Coal futures trade on the NYMEX. Initial Margin is $3,375; maintenance margin is $2500. Contracts are for 1550 tons of coal. Interest rates are 4%.
a. Coal currently sells in the spot market for $33 per ton. Storage costs are $3 per ton paid in advance. Compute the theoretical price of a 6 month coal futures contract assuming continuous compounding.
b. If the contract is priced at $39 a ton what position could you take to earn an arbitrage profit? Detail all necessary transactions. What profit would you earn on the contract?
Problem 2. The current price of a 12-month coal future is $40 ton. You take a long futures position.
a. At what price will you receive a margin call based on the information in number 1?
b. Do you feel that basis risk is a serious concern for a coal producer? Explain what basis risk is why it exists and why it may or may not be a concern in this instance.
Problem 3. You are a manufacturer who anticipates purchasing 30,000 tons of coal for sale in 8 months. The current price of a 12-month future is $40 per ton. The spot price is $36.
a. What position should you take in the 12-month futures contract?
b. In 8 months you close out your positions. The four month futures price at this time is $45 per ton and the spot price is $39. What is the effective price you pay for coal?
Problem 4. Do you think that it is wise for a coal producer to hedge coal price risk? Support your position with arguments for or against hedging. Be sure to relate the arguments to this specific case – don’t just produce a list of reasons for or against hedging from the reading
Problem 5. The Value Line Stock index currently trades at 2240. Futures contracts are for 10 indexes. The index pays an average dividend of 2%. Current interest rates are 4%. As you undoubtedly remember the VL index consists of 1700 stocks including companies of all sizes.
a. What is the theoretical price of a 9 month futures contract?
b. The 9 month futures contract is trading at 2260. Is there a arbitrage opportunity (if so what position should you take in the index)? Would you expect that most investors can take advantage of this opportunity? Briefly explain.
c. You have $4 million invested in your retirement account. The beta on your portfolio is .9 (relative to the VL index). You would like to decrease the beta to .3. What position should you take in the VL futures market to achieve this result?
Problem 6. The Value Line Index currently trades at 2240. 8-month futures are trading at 2285. Volatility is 20%. Interest rates are 5%. Compute the price of a call on the index future. Exercise price is 2300.
Problem 7. Six-month options on the VL index with exercise price = 2280 are priced as follows (the index itself is currently listed at 2240):
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Call
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Put
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Price:
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134.1281
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117.8347
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Delta (per $):
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0.548682
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-0.45132
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|
Gamma (per $ per $):
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0.00125
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0.00125
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|
Vega (per %):
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6.271818
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6.271818
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Theta (per day):
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-0.49365
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-0.18903
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Rho (per %):
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5.4746
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-5.64393
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You have a portfolio worth $1.5 million. Instead of purchasing VL index securities you decide to enter into fiduciary calls. The continuously compounded interest rate is 5%.
a. What position will you take (amount invested in securities and long/short)?
b. If the VL index is listed at 3500 in 6 months compute your upside capture.
Problem 8. You enter into a break forward on the above option. The exercise price is set to the forward price of the index.
a. Determine the value of your position if the index ends at 2400. Determine the value if the index ends at 3000.
b. Discuss why an investor might want to enter into such a contract.
Problem 9. There are a variety of ways to reduce equity risk.: futures, options, or reducing your equity holdings for example. Contrast these strategies. Provide a rationale why an investor might prefer each of these methods.