Question

1. On May 1 a Kansas farmer entered into a short futures contract to sell 200,000 bushels of wheat for 525 cents per bushel by entering into a futures contract that matures on October 3  (5 points each part)  

1. On September 30^th the farmer closed out his contract by taking a long futures position at a price of 450 cents per bushel and sells 200,000 bushels of wheat in the spot market for 450 cents per bushel.  Calculate the effective price paid by the farmer (show the gain or loss on the futures contract plus the amount received in the spot market and combine them to get the effective price).
2. Repeat the question for a closing futures price of 600 cents per bushel and a spot price of 600 cents per bushel.
3. Instead of the outcomes in part a) & b), assume the farmer sells her 200,000 bushels of wheat for 440 cents per bushel on Oct 1, and closes out the futures contract at a price of 425 cents per bushel also on Oct 1.  Calculate the effective price paid by the farmer.
4. Assume that the farmer has a smaller crop than expected and only sells 170,000 bushels of wheat in the spot market on Oct 1. Repeat part c) (she sells the wheat for 440 cents and closes out the futures for 425 cents) calculate the effective price paid by the farmer and explain the two types of basis risk that impacted your answers in parts c and d.

Please explain, I really need to understand instead of just having the answer!

Answer 1

a. Gain from future contract would be difference between short and long position

= (525-450)*200,000 cents = $ 150000 (assuming $1 =100 cents)

Money received from spot market = 450 * (200000) = $ 900000

Effective price = (900000 + 150000)/200000 = $5.25 = 525 cents

b)

Loss from future contract would be difference between short and long position

= (600-525)*200,000 cents = $ 150000 (assuming $1 =100 cents)

Money received from spot market = 600 * (200000) = $ 1200000

Effective price = (1200000 - 150000)/200000 = $5.25 = 525 cents

So basically he is fixing the price at 525 cents by using futures no matter what is the spot price on Oct 1 as long as future and spot prices are close on Oct 1st.

*you coul have ignored quantity if calculation needed per unit.

c) Similarly,

Gain from futures = 525 -425 = 100 cents

and received from spot market = 440 cents

Therefore overall price = 540 cents

Additional gain per unit is coming from the difference in spot and future price as on Oct 1st.

d) Now in this question, Quantity is important

Gained from spot market = 170000 * 440 = $ 748000

Gain from future = (525-425)*200000 = $200000

Total Gain = $948000 < total gain of 1080000 in part c

In part c, difference is coming because of price difference between future and spot while in part d the difference arises because of less quantity produced than expectation.

Overall, farmer is trying to hedge his risk against price fluctuations only by using future contracts