i.e., a price change of per ounce. If you don’t meet the ...

1 2. Futures and Forward Markets Institutions 1. (Hull ) Suppose that you enter into a short futures contract to sell July silver for $ 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 $3,000. What change in the futures price will lead to a margin call? 5, 000($ F ) = $1, 000. 26, 000 5, 000F = 1, 000. 27,000. F = 5,000. = , a price change of +$ per ounce. What happens if you do not meet the margin call? If you don't meet the margin call, your position gets liquidated. 1. 2. Futures and Forward Markets Institutions 2. (Hull ) An investor enters into two long futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds.

2 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 would lead to a margin call? There is a margin call if $1,500 is lost on one contract. 15, 000(F $ ) = $1, 500. 15, 000F 24, 000 = 1, 500. 22,500. F = 15,000. = This happens if the futures price falls to $ per pound. Under what circumstances could $2,000 be withdrawn from the margin ac- count? $2,000 can be withdrawn from the margin account if the value of one contract rises by $1,000. 15, 000(F $ ) = $1, 000. 15, 000F 24, 000 = 1, 000. F = 25,000. 15,000. = This happens if the futures price rises to $ per pound. 2. 2. Futures and Forward Markets Institutions 3. (Hull ) At the end of one day a clearinghouse member is long 100.

3 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 with the exchange clearinghouse? $36,000. From the clearinghouse to the member: 100 old contracts with ($50,200-$50,000) settlement each. From the member to the clearinghouse: 20 new contracts with $2,000 original margin each. From the member to the clearinghouse: 20 new contracts with ($50,200-$51,000) settlement each. 3. 2. Futures and Forward Markets Institutions 4. (Baby Hull , Papa Hull ) A company enters into a short futures contract to sell 5,000 bushels of wheat for 250 cents per bushel.

4 The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead to a margin call? There is a margin call if $1,000 is lost on the contract. 5, 000( F + $ ) = $1, 000. 5, 000F 12, 500 = 1, 000. 13,500. F = 5,000. = This will happen if the futures price rises to $ per bushel. Under what circumstances could $1,500 be withdrawn from the margin ac- count? 5, 000( F + $ ) = $1, 500. 5, 000F 12, 500 = 1, 500. F = 11,000. 5,000. = $1,500 can be withdrawn if the futures price falls to $ per bushel. 4. 2. Futures and Forward Markets Pricing 1. (Baby Hull , Papa Hull ) A one-year long forward contract on a nondividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 10 percent per annum with continuous compound- ing.

5 (a) What are the forward price and the initial value of the contract? F = SerT. 12. = 12. = f = (F K)e rT. = 0. (b) Six months later, the price of the stock is $45 and the risk-free interest rate is still 10 percent. What are the forward price and the value of the forward contract? F = SerT. 6. = 12. = f= (F K)e rT. 6. = ( )e 12. = 5. 2. Futures and Forward Markets Pricing 2. (Baby Hull , Papa Hull ) Assume that the risk-free interest rate is 9 percent per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In February, May, August, and November, it is 5 percent per annum. In other months, it is 2 percent per annum. Suppose that the value of the index on July 31 is 300. What is the futures price for a contract deliverable on December 31?

6 (5+2+2+5+2). average dividend yield 5. = F = Se(r q)T. 5. = 300e( ) 12. = 6. 2. Futures and Forward Markets Pricing 3. (Baby Hull , Papa Hull ) Estimate the di erence between short- term interest rates in Mexico and the United States on February 4, 2004 from the following information: delivery settle ($/Peso). Mar .08920. June .08812. F = Se(r rf )T. F. = Se(r rf )T (r rf ). T. = F (r rf ). = (r rf ). (r rf ) = 7. 2. Futures and Forward Markets Pricing 4. (Baby Hull , Papa Hull ) A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50. and the risk-free rate of interest is 8 percent per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock.

7 (a) What are the forward price and the initial value of the forward contract? 2 5. I = 1e 12 + 1e 12. = + = F = (S I)erT. 6. = (50 ) 12. = f = (K F )e rT. = 0. (b) Three months later, the price of the stock is $48 and the risk-free rate of interest is still 8 percent per annum. What are the forward price and the value of the short position in the forward contract? 2. I = 1e 12. = F = (S I)erT. 3. = (48 ) 12. = 8. 2. Futures and Forward Markets Pricing 4. (b) (Continued). f= (K F )e rT. 3. = ( )e 12. = 9. 2. Futures and Forward Markets Pricing 5. (Baby Hull , Papa Hull ) A company that is uncertain about the exact date when it will pay or receive a foreign currency may try to negotiate with its bank a forward contract that specifies a period during which delivery can be made.

8 The company wants to reserve the right to choose the exact delivery date to fit in with its own cash flows. Put yourself in the position of the bank. How would you price the product that the company wants? It is likely that the bank will price the product on assumption that the company chooses the delivery date least favorable to the bank. If the foreign interest rate is higher than the domestic interest rate then, 1. The earliest delivery date will be assumed when the company has a long position. 2. The latest delivery date will be assumed when the company has a short position. If the foreign interest rate is lower than the domestic interest rate then, 1. The latest delivery date will be assumed when the company has a long position.

9 2. The earliest delivery date will be assumed when the company has a short position. 10. 2. Futures and Forward Markets Hedging Strategies 1. (Baby Hull , Papa Hull ) The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound). The standard deviation of monthly changes in the futures price of live cattle for the closest contract is The correlation between the futures price changes and the spot price changes is It is now October 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15. The producer wants to use the December live-cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle. What strategy should the beef producer follow?

10 H= FS. = = hNS. N= QF. ,000. = 40,000. = 3. The beef producer should long 3 contracts. 11. 2. Futures and Forward Markets Hedging Strategies 2. (Baby Hull , Papa Hull ) It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is The company would like to use the CME December futures contract on the S&P 500 to change the beta of the portfolio to during the period July 16 to November 16. The index is currently 1000, and each contract is on $250 times the index. (a) What position should the company take? N= ( F ) PA. = ( ) 100,000,000. 250 1000. = 280. The company should short 280 contracts. (b) Suppose that the company changes its mind and decides to increase the beta of the portfolio from to What position in futures contracts should it take?