futures forwards and swaps


Suppose you bought four five-year gold futures contracts when the five-year futures price of gold was $395 per ounce, and closed the position at the end of the sixth trading day. The initial margin requirement is $2,000 per contract, and the maintenance margin requirement is $1,500 per contract. One contract is for 100 ounces of gold. The daily prices on the intervening trading days are shown in the following table.


Settlement Price

Mark-to-Market ($)


Account Balance ($)

















Assume that you deposit the initial margin and do not withdraw the excess on any given day. Whenever a margin call occurs, you would make a deposit to bring the balance up to meet the initial margin requirement. Fill the appropriate numbers in the blank cells. (Hint: Refer to Table 8.2 in the textbook on p. 272.)

(10 marks)


Suppose that you enter into a long futures contract to buy May gasoline for $0.80 per gallon on the New York Commodity Exchange. The size of the contract is 42,000 gallons. The initial margin requirement is $2,000, and the maintenance margin is $1,500. What change in the futures price will lead to a margin call?

(10 marks)


Consider the three-month futures on stock BBM. Currently, the price of stock BBM is $100. The stock is expected to pay a dividend of $2.00 in two months. Assume that the simple interest rate is 6% per year. Determine the price of the futures assuming no arbitrage opportunites are present.

(10 marks)


Suppose that the market price of gold is $370 per ounce. The risk-free interest rate is 10% per year, compounded monthly, for all terms. Gold can be stored for $0.05 per month per ounce, paid at the end of the month. According to the cost of carry model, what should be the price of a gold futures contract, if expiration is six months away? What is the cost of carry?

(10 marks)


Suppose you entered a long position in a forward contract to buy 100 ounces of silver for $5.80 per ounce in December. Currently, the spot price of silver is $5.50, the December forward price of silver is $6.20, and the price of a T-bill expired in December with a face value of $100,000 is $96,500. What is the value of the forward contract you hold?

(6 marks)


Suppose the spot price and the six-month futures price of soybeans are $4.80 and $5.20 per bushel, respectively. One futures contract is for buying 5,000 bushels. The six-month risk-free interest is 6% per year. The storage cost for soybeans is $0.05 per bushel for six months, paid in advance. Could you make an arbitrage profit in the soybean market? How?

(15 marks)


It is March 15, 2005. Suppose you are a dealer in canola holding 80 tonnes of canola worth $380 per tonne. You consider using September 2005 canola futures to hedge. The price of the futures contract is $397 per tonne. Each contract is for 20 tonnes.


Determine the original basis.

(3 marks)


How many contracts will you use? Long or short?

(3 marks)


If you close your position on July 10, 2005, when the basis is -12, what would be the profit from a hedge?


(4 marks)


A coffee trader holds a current inventory of coffee worth $1 million at the present price of $1,250 per ton. The standard deviation of the value for the inventory is 0.27. She is considering a minimum-variance hedge of her inventory using the six-month coffee futures contract. The contract size is 10 tons. The volatility (i.e., standard deviation) of the futures is 0.33. For the particular grade of coffee in her inventory, the correlation between the futures and spot coffee is 0.85.


Compute the minimum-variance hedge ratio.

(7 marks)


How many contracts she should trade? Long or short?

(7 marks)


You manage a $4 million portfolio, currently all invested in Canadian equities. The beta of the portfolio is 1.25. You believe that the market is on the verge of a big but short-lived downturn. You would move your portfolio temporarily into T-bills, but you do not want to incur the transaction costs of liquidating and reestablishing your equity position. Instead, you decide to hedge your portfolio with three-month S&P/TSX 60 index futures contracts for one month. Currently, the level of the S&P/TSX 60 index is 425, the three-month futures price of the S&P/TSX 60 is 428, and one contract is for $200 times the index. The annual risk-free rate is 3%.


How many futures contracts should you use? Long or short?

(5 marks)


Suppose the return on the S&P/TSX 60 index is -5% in one month, and the S&P/TSX index futures price falls to 405 in one month. Calculate your gain or loss.

(10 marks)



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