Financial Derivatives Futures and Forwards

Mechanics of futures markets 1° Suppose that you enter into a short futures contract to sell July silver for $10.20 per ounce on the New York Commodity Exchange. The size of the contract is 5,000 ounces. The initial margin is $4,000, and the maintenance margin is $3,000. What change in the futures price will lead to a margin call? What happens if you do not meet the margin call? 2° Suppose that in September 2009 a company takes a long position in a contract on May 2010 crude oil futures. It closes out its position in March 2010. The futures price when it enters into the contract is $68.3 per barrel, and $70.5 when it closes out its position. One contract is for the delivery of 1,000 barrels. What is the company’s total profit? 3° A trader buys two July futures contracts on orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound. The initial margin is $6,000 per contract, and the maintenance margin is $4,500 per contract. What price change will lead to a margin call? Under what circumstances could the trader withdraw $2,000 from his margin account? 4° At the end of one day, a clearinghouse member is long 100 contracts, and the settlement price is $50,000 per contract. The original margin is $2,000 per contract. On the following day, the member becomes responsible for clearing an additional 20 long contracts, entered into at a price of $51,000 per contract. The settlement price at the end of this day is $50,200. How much does the member have to add to its margin account? 5° You sell three December gold futures contracts when the futures price is $410 per ounce. Each contract is on 100 ounces of gold and the initial margin per contract is $2,000. The maintenance margin per contract is $1,500. During the next seven days the futures price rises slowly to $412 per ounce. What is the balance of your margin account at the end of the seven days? 6° On July 1, 2009, a Japanese company enters into a forward contract to buy $10 million on January 1, 2010. On September 1, 2009, it enters into a forward contract to sell $10 million on January 1, 2010. Describe the profit or loss the company will make in yen as a function of the forward exchange rates on July 1, 2009, and September 1, 2009. 7° Suppose that, on October 24, 2009, a company sells one April 2010 live cattle futures contract. It closes out its position on January 21, 2010. The futures price is 91.2 cents per pound when it enters into the contract, 88.3 cents when it closes out its position. One contract is for the delivery of 40,000 pounds of cattle. What is the total profit?

Hedging strategies using futures 1° Under what circumstances are a) a short hedge and b) a long hedge appropriate for a firm? 2° Explain what is meant by “basis risk”. 3° What is a “perfect hedge”? Is it easy to find? Is it always better than an imperfect hedge or no hedge at all? Explain. 4° Suppose the standard deviation of quarterly changes in the price of a commodity is €0.75, the standard deviation of quarterly changes in the future price in an other but similar commodity is €0.85 and the correlation between the two changes is 0.8. What is the optimal hedge ratio for a 3-month contract? What does it mean? 5° A company has a €20 million portfolio with a beta of 1.2. It would like to use futures contracts on the CAC40 to hedge its risk. The index futures price is currently standing at 3,240, and each contract is for delivery of €10 times the index. What is the hedge that minimizes risk? What should the company do if it wants to reduce the beta of the portfolio to 0.8? 6° “If the minimum variance hedge ratio is calculated to be 1.0 then the hedge must be perfect”. Is that sentence true? Explain. 7° The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.2. The standard deviation of monthly changes in the future price of live cattle for the closest contract is 1.4. The correlation between the futures price changes and the spot price changes is 0.7. If we are now October 15 and a beef producer is committed to purchasing 600,000 pounds of live cattle on November 15, knowing that December futures contracts are available and each is for the delivery of 40,000 pounds of cattle, what strategy should the beef producer follow? 8° Suppose that the standard deviation of monthly changes in the price of commodity A is €2. The standard deviation of monthly changes in a futures price for a contract on commodity B (which is similar to commodity A) is €3. The correlation between the futures price and the commodity price is 0.9. What hedge ratio should be used when hedging a one month exposure to the price of commodity A? 9° A company has a $36 million portfolio with a beta of 1.2. The S&P index is currently standing at 900. Futures contracts on $250 times the index can be traded. What trade is necessary to achieve the following. (Indicate the number of contracts that should be traded and whether the position is long or short.) (i) Eliminate all systematic risk in the portfolio (ii) Reduce the beta to 0.9 (iii) Increase beta to 1.8

Determination of forward and futures prices 1° What is the difference between the forward price and the value of a forward contract? 2° Suppose you enter in a 4-month forward contract on a stock that does not pay any dividends. The stock price is now €35 and the (continuously compounded) risk free rate is 5% per annum. What is the forward price? 3° A stock index currently stands at 350, the continuously compounded risk free rate is 8% p.a. and the dividend yield on this index is 4% p.a. What should the futures price for a 6-month contract be? 4° A one year long forward contract on a non-dividend paying stock is entered into when the stock price is €20 and the risk free rate is 8% p.a. (continuously compounded) a) What are the forward price and the initial value of the contract? b) Six months later the price of the stock has moved to €23 while the risk free rate has remained unchanged. What are the forward price and the value of the forward contract? 5° The risk free rate of interest is 7% per annum with continuous compounding, and the dividend yield on a stock index is 3.2% per annum. The current value of the index is 150. What is the 6-month futures price? 6° Assume that the risk free rate is 9% p.a. (continuous compounding) and that the dividend yield on a stock index varies throughout the year. In February, May, August and November, dividends are paid at a rate of 5% p.a. In other months, dividends are paid at a rate of 2% p.a. Suppose that the value of this index on 31/07/2009 is 300, what is the future price for a contract maturing on 31/12/2009? 7° Suppose the risk free rate is 10% p.a. (continuous) and the dividend yield on a stock index is 4% p.a. The index stands at 400 and the future price for a contract deliverable in four month is 405. Does this creates arbitrage opportunities, and, if there are, how can we exploit them? 8° The 2-month interest rate in Switzerland and the United States are, respectively, 2% and 5% p.a. (continuous compounding). The spot price of the Swiss Franc is $0.8000. The futures price of a contract deliverable in 2 months is $0.8100. What arbitrage opportunities does this create? 9° The spot price of silver is $9 per ounce. The storage costs are $0.24 per ounce per year payable quarterly in advance. Assuming that interest rates are 10% p.a. for all maturities, calculate the futures price of silver for delivery in 9 months. 10° An exchange rate is 0.7000 and the six-month forward rate is 0.6930. if the six-month domestic risk-free interest rates is 5% (expressed with continuous compounding), what is the six-month foreign risk-free interest rate?