1. A company enters into a short futures contract to sell 5,000 bushels of wheat for $4.50 per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead to a margin call? Under what circumstances could $1,500 be withdrawn from the margin account? (Any amount in excess of the initial margin can be withdrawn from a margin account.)
2. On January 1, farmer Jones agrees to sell forward to a grain elevator company an expected 10,000 bushel crop of soybeans for $5.75 per bushel. The delivery date is August 31. On February 1, the same farmer, now expecting higher soybean prices this summer, begins to regret the decision. Jones decides to buy forward a neighboring farm’s expected 10,000 bushel crop of soybeans. The forward price for this new contract is $6.00 per bushel for August 31 delivery. What is the net payout at delivery of the combined short and long forward contracts?
3. Suppose that February platinum futures were actively traded today, and settled at $800 per oz, based on the price of the last trade of the day. What settlement price would you recommend that the clearing house use for the May contract, which did not trade at all today? Assume that the continuously compounded risk-free interest rate is 5%.
4. You enter 20 short gold futures contracts at the end of day 1 (at the settlement price for that day). You close out your position at the end of day 4 by entering 20 long futures contracts at the settlement price for that day. Determine the daily mark-to-market gains (losses), margin balance, and margin calls (if any) for your position based on the below hypothetical futures prices. Each contract represents 100 ounces and suppose the per-contract margins (whether long or short) are $4,400 initial and $4,000 maintenance.
Day Futures settlement Mark-to-market gains/losses Margin Margin call
1 $1,003
2 1,013
3 1,025
4 1,020
5. (old exam) Suppose a stock is trading for $50/share and a forward contract for delivery in 6 months is also trading for $50. The stock is not expected to pay a dividend between now and expiration. The continuously compounded interest rate is 5%. What is the arbitrage strategy? (Be precise.)
6. The spot price of gold is $1,284.00 per troy ounce and futures price for delivery in six months is $1,286.10 per troy ounce (1/23/15 settlement prices). What is the continuously compounded interest rate? (This is commonly referred to as the implied repo rate for this futures contract.)
7. The party with a short position in futures contracts sometimes has options as to the precise asset that will be delivered, where delivery will take place, when delivery will take place, and so on. Do these options increase or decrease the futures price? Explain.
8. Suppose the (cash) spot price of a 10% coupon Treasury bond is $115 (per $100 par). The bond matures on February 15, 2021; it therefore pays coupons of $5 (per $100 par) every February 15 and August 15. Suppose today is January 15. Find the forward price (per $100 par) for delivery of the bond on May 15 (4 months from now). Assume a continuously compounded repo rate of 2%.
9. Suppose a futures contract on a stock index begins trading today. At 10am, trader A goes long 5 contracts with trader B, who shorts 5 contracts, at a price of $200. At 2pm, trader A shorts 2 contracts with trader C, who goes long 2, at a price of $210. The settlement price of the day, set by the clearing house, is $205.
a) What is the volume of trades for the day??b) What is the open interest at the end of the day?
c) What are the mark-to-market gains (losses) for each trader after settlement? Assume a multiplier of 10.