A futures contract is an agreement to deliver a specific amount of a commodity  5,000 bushels of wheat, say  on a certain date in the future. Such contracts are important hedging tools for farmers, grain elevators, commodity processors and anyone with a stake in future grain prices. A futures contract that calls for delivery of wheat in July may trade for more or less for each bushel than today’s cash market price. But as each day goes by, its price should move a bit closer to that day’s cash price. And on expiration day, when the bushels of wheat covered by that futures contract are due for delivery, their price should very nearly match the price in the cash market, allowing for a little market friction or major delivery disruptions like Hurricane Katrina.

But on dozens of occasions since early 2006, the futures contracts for corn, wheat and soybeans have expired at a price that was much higher than that day’s cash price for those grains.

For example, soybean futures contracts expired in July at a price of $9.13 a bushel, which was 80 cents higher than the cash price that day, Professor Irwin said. In August, the futures expired at $8.62, or 68 cents above the cash price, and in September, the expiration price was $9.43, or 78 cents above the cash price.

Corn has been similarly eccentric. A corn futures contract expired last September at $3.36, which was a remarkable 55 cents above the cash price, but the contract that expired in March 2007 was roughly even with the cash price.

“As far as I know, nothing like this has ever happened in the corn market,” said Professor Irwin.

Wheat futures had been especially prone to this phenomenon, going back several years. Indeed, the 2007 study by Professor Irwin and his colleagues concluded that wheat price distortions reflected a “failure to accomplish one of the fundamental tasks of a futures market.”

And while the situation improved sharply for wheat futures in Chicago late last year, it deteriorated for futures traded in Kansas City. And it has gotten worse for corn and soybeans, Professor Irwin said. Many people have a theory about why this is happening, but none of them seem to cover all the available facts.

Mary Haffenberg, a spokeswoman for the CME Group, which owns the Chicago Board of Trade, where these contracts trade, said the anomalies might be a temporary result of “a lot of shocks to the system,” including sharp increases in worldwide food demand, uncertainty about supplies and surging commodity investments.