Assignment
You are a farmer in south-central Pennsylvania producing wheat for the cash grain market. You have planted 100 acres of winter wheat in the fall of 2016 and you are wondering whether you should hedge your output. You expect a yield of at least 50 bushels per acre. Below is a table listing the range of the wheat basis in your area based on recent history.
|
South-central PA Wheat basis (cents per bushel)
|
|
Month
|
Average
|
|
JAN
|
43
|
|
FEB
|
41
|
|
MAR
|
40
|
|
APR
|
39
|
|
MAY
|
36
|
|
JUN
|
22
|
|
JUL
|
16
|
|
AUG
|
19
|
|
SEP
|
25
|
|
OCT
|
30
|
|
NOV
|
34
|
|
DEC
|
39
|
|
YEAR
|
32
|
You plan to sell your wheat in July 2017. The July 2017 futures price in Chicago as you prepare to plant the wheat is $5.00.
1. What is the price you would expect in your local area if the futures price is an accurate forecast of the Chicago price for when you plan to sell your wheat? What is your expected total revenue? Please show and explain your work.
2. If you want to use the futures market to hedge what would you do? Explain in detail what you would do and when.
3. It is now July 152017. The price of the July contract in Chicago is $5.50. The price offered by your local flour mill is $5.70. Your actual production is 5,500 bushels. You are ready to harvest and sell your wheat. Please explain exactly what you will do? Assuming a commission of 1 cent per bushel calculate how your hedge worked out? Please explain the result and show your work.
4. How does your total revenue with the hedge compare to what you would have received if you had not hedged your expected production? Explain what accounts for the difference.
SOURCES
At planting time
Suppose you are a farmer trying to decide in May whether to plant corn to be harvested and sold in October. The price of corn for delivery in October is $5 per bushel in the futures market in Chicago. You track futures prices and local prices closely and you know that in October, on average, the basis is $0.25 - so if things work out you could expect to receive a local price for your corn of:
$5 + $0.25 = $5.25 per bushel.
If you want to use a broker to sell a futures contract for you in Chicago for delivery of corn in October, you will have to pay a commission of $0.01 per bushel for her/his services - after all, brokers have to make money to pay their bills. So this means that, per bushel on the sale of the contract, that you could expect to make:
$5.25 - $0.01 = $5.24 per bushel.
You figure that given the costs of planting, cultivating, and harvesting the corn, you can make a profit at that price.
On the basis of your calculation, you decide you are going to plant the corn. Before you start the tractor you call your broker and instruct her/him so sell a futures contract on your behalf in Chicago. Let's assume that the size of that contract (5,000 bushels) is roughly the amount of corn you expect to have for sale in October.
At harvest time
It's now October and you are harvesting your corn. You call your broker again and tell her/him to purchase a futures contract for delivery of corn this month regardless of the price. You need to do this, because you would otherwise be obligated to deliver your corn to Chicago to the person who owns the contract you sold in May. You might want to visit Chicago someday, but you certainly don't want to have to do this with 5,000 bushels of corn for company!
Your broker follows your instructions and informs you that the price of the contract was $4.50 per bushel. Clearly market conditions have changed since you sold your contract in May - perhaps the demand for corn is lower than expected or supplies are larger than expected, so the price of the October contract has fallen.
The purchase of a futures contact that entitles you to take delivery of 5,000 bushels of corn this month offsets the contract that you sold to deliver 5,000 bushels this month, so you don't have to move any corn to or from Chicago to where you live. The two contracts cancel each other out. You sold a contract to deliver 5,000 bushels but you bought an offsetting contract for the delivery of 5,000 bushels, so you don't have to deliver any corn to Chicago.
Selling locally
You now sell your crop locally. This will minimize the costs of transportation and, as implied by the law of one price, give you the highest price that you can obtain for your corn.
Let's suppose that your local feed mill (this is where you usually sell your corn) gives you a price of $4.70 per bushel. This price is lower than the $5.25 that you estimated you would receive when you planted in May. It has fallen in line with the fall in prices in Chicago - remember it's the law of one price in action again!
The Bottom Line
Let's do the calculations to see how this hedge worked out financially.
Based on the Chicago price, the sale of the futures contract in May was:
$5.00 - $0.01 = $4.99 per bushel.
Recall that $0.01 per bushel is what you have to pay your broker for trading futures contracts in Chicago on your behalf.
If your purchase of the futures contract in October was $4.50 per bushel, your futures market transactions (hedge) yielded a gain of:
$4.99 - $4.50 = $0.49 per bushel.
Your local sale gave you $4.70 per bushel, so your net sales price (local price + gain on the hedge) is:
$4.70 + $0.49 = $5.19 per bushel.
You have come very close to the price you estimated when you decided to plant corn in May. You were estimating a price of $5.24 at that time and your actual price is just 5 cents per bushel less. This is because the local price has fallen by a little more than the Chicago price at the time you harvested and sold your crop, perhaps because the corn crop in your area has increased by more than the national average.
Why Hedging Makes Sense
Let us discuss what hedging has done for you in this case. The change in the price of the October futures contract between May and October was in your favor, and the gain that you made on the hedge offset to a large extent the fall in the local price of corn. If you had not hedged, rather than a price of $5.19 per bushel for your corn, you would be looking at a price of $4.70; the difference of $0.49 between these could be the difference between profit and loss for the current season. So the hedge has allowed you to limit the risk of fluctuating corn prices and provided some financial stability for your business.
Before we leave this example, think about how things would play out if instead of a fall in the futures contract price for October between May and October, prices had risen.
You would then end up paying more for that October contract than the value of your contract that you sold in May. You would now make a loss on the hedge. But the law of one price would say that your local price in October would also have increased, so in this case the higher local price would offset the loss on the hedge and again you would have come out with a price close to the one you had estimated when you decided to plant.
Hedging Purchases
How does hedging work for someone who wants to buy corn in the future, for example, a livestock farmer who needs feed?
In that case, this is how hedging works:
1. At the time you want to lock in a price for the future, purchase a futures contract.
2. When you are ready to buy your corn, sell an equivalent futures contract.
3. Purchase your corn locally.
As in the case of the corn producer, price changes in the futures market and locally should cancel each other out to a large extent thereby reducing price risk.
Note that if you use the futures market to hedge price risk, basis risk still exists. The price that you end up receiving as a corn producer (or paying as a corn user) may still differ significantly from what you were expecting because the basis turned out to be significantly different from the average when you needed to sell or buy locally. In the example above basis risk resulted in the farmer obtaining a price that was 5 cents lower than he/she expected when planting corn.