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Queensland wheat, also known as Pacific wheat, is used as livestock feed, in industrial products, or to make processed foods. Queensland wheat is distinguished by a hard outer shell and kernels with a range of colors from white to red. Queensland wheat is usually harvested only once a year usually in the month of September.

A Queensland wheat farmer from Indiana expects, on April 1, 2022 to harvest 6,000,000 bushels of wheat on September 30, 2022. In order start preparing for the harvest (e.g., to pay for the seed and equipments) the farmer had to withdraw and spend $11,500,000 from his saving account on January 1, 2022. He had to withdraw and spend $4,000,000 on April 1, 2022 to meet planting expenses and fund purchase of fertilizers. He also had to withdraw and spend $3,000,000 on September 1, 2022 to meet harvesting and transporta- tion expenses.

Our farmer can borrow/lend money at the risk free rate which is 5.8% on continuously compounded basis and is fixed for all loan/deposit maturities.

The farmer is worried about fluctuations in the wheat price during the harvest time and wishes to hedge the position in April. Currently (April 1, 2022) Queensland wheat spot price is 321.5 cents/bushel.

Only two contracts on Queensland wheat (exact variety that the farmer produces) are traded on the Chicago exchange:

September 30 deliver FS cents/bushel December 31 delivery FD cents/bushel

Prices are in cents per bushel, and wheat futures contracts are per 5,000 bushels. For simplicity, we assume that each futures contract expires on the last day of the delivery month.

(6 points) Please find the algebraic expressions for FS and FD using all relevant information.

(6 points) Initially, assume storage is not possible. Construct the perfect hedge for the farmer, using September futures contracts. Assume all wheat are harvested as well as delivered (or sold in the spot market) on September 30, 2022 without tailing adjustment. How many contracts should the farmer buy (long) or sell (short)? As- sume two possible scenarios on September 30, 2022:

Realized ST = 310 cents/bushel of Queensland wheat; or

Realized ST = 350 cents/bushel of Queensland wheat.

Demonstrate that your hedge is indeed eective by comparing hedged and unhedged value of the farmers earnings for each of these two scenarios.

(5 points) Still assume storage is not possible. Is there any arbitrage opportunity if a September futures contract is quoted in the market for 375 cents/bushel? Is there any arbitrage opportunity if a September futures contract is quoted in the market for 300 cents/bushel? Clearly show your strategies and profits for each of these two scenarios.

(5 points) Now suppose that the farmer can store any quantity up to 6 million bushels of wheat paying a fixed warehouse rental of $500,000 per month. Assume that all wheats are harvested on September 30, 2022 and storage costs starts from October 1, 2022 and rental agreement is required until December 31, 2022. Also, assume that rents are paid at the beginning of each month as advance. How should the farmers hedging strategy change, if at all?

(3 points) Now suppose that the farmer owns a warehouse which is not much in demand lately (not earned any rentals for the past few years). He can store up to 2 million bushels of wheat in his own warehouse. Also, note that outside rental of warehouse is unaected by the reduced quantity; i.e., to store additional 4,000,000 bushels of wheat in outside storage, the farmer still has to pay $500,000 per month as warehouse rental. How should the farmers hedging strategy change, if at all? (Caution: explanation of the result is more important than the numerical part of the result.)

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