1. (10 marks) Suppose you bought two one-year gold futures contracts when the one-year futures price of gold was $1650 per ounce, and closed the position at the end of the sixth trading day. The initial margin requirement is $8,000 per contract, and the maintenance margin requirement is $7,000 per contract. One contract is for 100 ounces of gold. The daily prices on the intervening trading days are shown in the following table.

Day

Settlement Price

Mark-to-Market ($)

Other Entries

Account Balance ($)

Explanation

0

1650.00

—

—

1

1660.00

2

1640.00

3

1630.00

4

1660.00

5

1650.00

6

1640.00

Closed

—

—

—

—

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 on p. 272 of the textbook.)

2. (12 marks) A soybean oil futures contract of CBOT covers 60,000 pounds of soybean oil. The initial margin is $2,025 and the maintenance margin is $1,500. Suppose you are going to short five August soybean futures contracts for the price of $0.32 per pound.

a. How much margin deposit do you need to put up? (2 marks)

b. At what price would there be a margin call? (5 marks)

c. If the futures price rises by 5% next day, what would be your loss and margin variation? (3 marks)

d. How can you close your position in May? (2 marks)

3. (8 marks) Suppose you have a short position in a forward contract for 500 troy ounces of gold at $920. The contract has 10 months to expire. Currently, the spot price of gold is $922, and the risk-free rate and the rate of storage cost are 8% and 3% per annum, respectively. Both rates are continuously compounded. What is the value of the contract to you?

4. (10 marks) Consider the 90-day futures on stock ABC. Currently, the share price of ABC is $80 per share. The stock is expected to pay a dividend of $1.50 in one month’s time. Assume that the simple interest rate is 8% per year, and that there are 30 days in a month. Determine the price of the futures and the dollar cost of carry, assuming no arbitrage opportunities are present.

5. (8 marks) You buy 500 shares of stock ABC at $60 per share and short five September futures contracts at $62 per share. One contract is for 100 shares. If you close your position on June 1 when the basis is $5, how much money can you get?

6. (10 marks) Currently, the spot price of silver is $9 per ounce and the one-year futures price of silver is $11. The storage costs are $0.24 per ounce per year payable at the end of the year. Assume the simple interest rate is 10% per annum.

What is the “fair” one-year futures price of silver? What is the cost of carry? (4 marks)

How can you make an arbitrage profit? Show your transactions in details using a numerical example. (6 marks)

7. (12 marks) Today is February 15. Suppose you are an oil dealer and hold a position of 200,000 barrels of crude oil. You hedge by trading May crude oil futures, each of which is on 10,000 barrels. The hedge will be on until April 15. The current spot price and the May futures price are $20.50 and $20.00 per barrel, respectively. For simplicity, a hedge ratio of 1 is used.

How many contracts will you use? Long or short? (3 marks)

What is the basis today? (3 marks)

If the basis on April 15 is 20% higher than today’s basis, what is your gain or loss? (3 marks)

If the basis on April 15 is 0.05 lower than today’s basis, what is your gain or loss? (3 marks)

8. (12 marks) Chococo Inc., a producer of powdered hot chocolate, has just received a large order that will require the purchase of 750 metric tons of cocoa in 3 months. The current spot price of cocoa is $2,645 per metric ton. The standard deviation of the value for the inventory is 0.15. Mr. Dulce, the CFO of the Chococo, is considering a minimum-variance hedge of this future cocoa purchase using the three-month cocoa futures contract. The contract size is 10 metric tons. The volatility of the futures is 0.2. The covariance between the change in the spot and futures cocoa price is 0.027.

a. Compute the minimum-variance hedge ratio. (5 marks)

b. How many contracts she should trade? Long or short? (3 marks)

c. What is the estimated effectiveness of this minimum variance hedge? (2 marks)

d. What is the correlation of the change in the spot and futures cocoa price? (2 marks)

9. (15 marks) You manage a portfolio that is currently all invested in equities in companies in five major Canadian industries. The market value involved and beta for each industry are shown in the table below.

Industry

MV

Beta

Oil and Gas

$1,000,000

1.2

Technology

600,000

1.5

Utilities

1,500,000

0.8

Financial

800,000

1.3

Pharmaceutical

1,300,000

1.1

You believe that the Canadian equity 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 678.68, the three-month futures price of the S&P/TSX 60 is 665.60, and one contract is for $200 times the index. The annual simple risk-free rate of return is 1%.

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 620 in one month. Calculate your net gain or loss on your hedged portfolio in part (a). (10 marks)

10. (3 marks)

Define contango and normal contango, and describe the difference(s) between the two. (1 mark)

Define backwardation and normal backwardation, and describe the difference(s) between the two. (1 mark)

Is it possible for normal contango and backwardation to occur at the same time? (1 mark)

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