short heding and basis risk


New Member
Hi all,

I would like to have this brief exercise on future derivatives and basis risk solved because, although various trials, i cannot find the exact solution.

In February of the year N a farmer expects that his wheat, next July, will be 232,000 bushels.
For the hedge the farmer uses the CME where the wheat futures are traded with volume 5,000 bushels and the closest maturity is August.
Since there is a significant difference between the quality of the wheat in the contract and that produced by the farmer, an optimal hedging ratio has to be used (0.92).
The August future price, when the hedge is started, quotes 6.50/bushel.

HERE THE MAIN POINT: the hail that affected the spring brought about a considerable reduction in the crop that resulted to be 23% lower than expectation.

In July, when the farmer sells his crop and the future contract is closed, the August wheat future price is 7.68 per bushel with a basis 0.18 under (basis = spot price - future price).

Find the effective price per bushel gained by the farmer.

(The number of contract to enter in is the optimal hedging ratio * quantity of asset /volume of future.. Of course the number has to be rounded to the closest integer. It is 43 in this case).

The key is 6.11 but i cannot find the solution in any way. Please help me

Thanks in advance
Last edited:


New Member
Total gain by selling at 6.5$ =232000*.92*6.5= 1387360
Total loss by selling at 7.69 = 232000*.92*.23*7.69= 377511.3
net gain=1009849
net gain per bushel=net gain/(232000*.92*.77)=6.1

I hope I have answered ur query


New Member
Unfortunately this is not correct. What about the basis?

I have mistaken the final future is 7.68 not 7.69. The exact solution is 6.1129

(I am sure that, if the procedure was correct, the key would be exactly this number).

Also by checking in some famous reference books, i don't find this specific case about hedging future. So frustrating


New Member
Hi According to me,
suppose we are buying and selling grains in lots then
toal gain by selling = 43 lots according to ur calcualtion as u have rounded the number * 12.5( this is per tick value of 1 lot of corn , i.e 12.5 $ per tick)* 2600( 1 cent conatins 4 tick and 6.5 $ conntains 2600 tick)=1397500

total los by selling = 10 lot (u can figure it out easily)*12.5*3144 ( 7.68+.18=7.86$ = 3144 ticks)=393000

net gain= 1004500
net gain per bushel = net gain/232000*.77*.92=6.112$