Q28. 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 transportation 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.

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

information.

(b) (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)? Assume 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.

(c) (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.

(d) (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?

(e) (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.)