Now here's an important concept,"Fair Value In Futures Contract". It's a little bit like the forward interest parity that we talked about in forward rate. What should the futures price be? Well, let's consider a physical delivery futures contract where the grain is in storage and there's a percent storage cost per unit of time. Let's say per year. So 's' is the percent of the value of the commodity that it would cost you to store it for one year. That's something that is quoted to you by a warehouse. A warehouse will tell you, I'll store it for you for one year by such and such an amount in dollars. You divide that by the value of it today and that's the storage cost as a percent. 'r' is the interest rate for the same interval of time. So we're talking now about a futures contract, let's say one year ahead. Or it could be any other year ahead, times ahead, but we have to adjust. If it's one month ahead, then we mark a one month interest rate and the one month storage cost. The fair value equation, the famous equation says, the price of the future is equal to the price of the spot times 1 plus r plus s. Which says that normally because r and s are normally positive, futures contracts are generally in contango. They're generally upward sloping because the longer in the future that the contract is dated, the higher r is. Remember this is r per month, if it's one month in the future. It's r per year if it's one year in the future, which would be 12 times bigger. So you can see that it makes for an upward sloping futures contract normally. Except at harvest time maybe. At harvest time you could say this doesn't apply any more. You can put it in a different way. One way is saying it doesn't apply any more because nobody is storing any more. But of course somebody is storing and you've got to store it somewhere. But maybe it's gotten kind of rare. Another thought, some people say that we can end up in backwardation if the storage cost becomes negative. Now that's a way of thinking. How can the storage cost be negative? Well, it can be. Here's how it can happen. Go to a manufacturer of breakfast cereals. This guy feels it's very important that we ship so many cartons of breakfast cereal every month. And there's uncertainty about shipments and deliveries, so the guy there wants to keep a store of grain, let's say wheat, in the factory warehouse. Because if you don't - suppose you're the maker of Wheaties and you suddenly run out of wheat, then your employees all show up one morning to make Wheaties and there's no wheat. So you have to pay them for the day's work and they didn't do anything, so you're losing money. So you want to have wheat in storage at all times. So suppose wheat is getting really scarce. It's the end of the season and the harvest is not in yet, so you can't buy it from the farmers. You might actually quote a negative storage cost to someone who wants to store wheat right. You'd say, look, I don't want to risk my factory shutting down. So I'll just charge you -2% if you let me store the wheat. So that's in effect what happens in backwardation. Or another way of saying it is that if the commodity is not in storage, then it is possible that the future - if you want to count this as a normal storage cost, the price of the future can be less than fair value. So it sometimes happens.
