A forward contract is a contract between two individuals, you might call them counter-parties, to deliver at a future date called the exercise date or maturity date. Historically, forward contracts preceded futures contracts. A futures contract is a more sophisticated idea. So for example, what was happening in Dojima before the 1670s, rice farmers would make a deal to sell their rice to a warehouser. Now they could just wait until the harvest is in and then bring it to Dojima and see what price they could get, but they have an alternative of establishing the price earlier and locking it in. Farmers like to do this because they don't know what the price will be when they sell it. So you put in a lot of expense to produce the product, and it might not pay you back all of your expenses, so you don't like that. So they typically like to lock in the price. That's called, if you do it directly and typically you would sell it to a warehouse or a grain elevator as they're called. There would be a local grain, I don't know about rice, wheat or corn or any of these. In the countryside, there's a local grain elevator, and you can go to that person and say, "I'm planning to harvest rice at such and such a month. Will you buy it and can you give me a price today?" Most farmers don't hedge in the futures market. It's too complicated and sophisticated. But the grain elevator or the warehouser I think they almost always hedge because they're going to be storing. The hedging, the storage business is a tight margin business. It's very competitive. You could store a lot of grain or promise to buy grain at a price that turns out to be unprofitable for you. So what happens is these stores of grain are the hedgers and they will quote prices to farmers as a forward price. There's other kinds... It's not just grain. Grains are historically the origin of forwards and futures, but let's talk about other things. You can also make a forward contract to exchange pounds for yen or dollars for yen or any number of combinations. If I make a forward contract, both sides are locked into the contract, so they have no liquidity. Why do they do it? Well, they do it because they don't want to fit into one of those standard contracts that are offered at the exchange. They might want a different delivery location, they might want a different date, they might want a different quality, and so they make forward contracts are big. But the problem with forward contracts is you can't get out of them and you don't necessarily trust the counterparty. What if the farmer just doesn't, he gets drunk and doesn't plant and you're standing on the other side of the contract? So you're out of luck. The advantage of futures contract is that you don't have to worry because your counterparty is the futures exchange. It's not between the producer of wheat and the manufacturer of breakfast cereals. The producer of wheat deals with the futures exchange, and so does the manufacturer of breakfast cereals who might be taking effectively the other side. So they have to... If you're going to go with forwards, you have to worry about your counterparty, and you have to check the counterparty out, and you need to establish that the counterparty has good credit so they're inherently limited. Futures markets. You want to trade? You can call up a broker tomorrow and trade. The broker will do it with anyone who posts margin. But let me come back to that. Forward exchange futures, a forward exchange contract, FX forwards can be thought of as a pair of zero coupon bonds stapled together in two different currencies. Suppose I'm selling goods. I'm a Japanese producer of goods which I'm selling in the United States. I'm going to sell them for dollars of course, Americans pay dollars. And then I want to repatriate the money to Japan, so I'm going to exchange it into yen. But I want to have a forward contract which locks in the price today. I don't have to go through the forward market. I can borrow the money today in dollars, exchange it at the spot exchange rate today into yen, take the yen back to Japan and put them in some interest bearing account in Japan earning the Japanese interest rate. So I'm going to be charged the dollar interest rate but I'm going to be credited the Japanese interest rate. And so I have an amount left at the end equal to the product of the spot exchange rate times 1 plus r yen divided by 1 plus r dollars. So that's what I could do without entering the forward exchange market, just by trading currency, by borrowing and then investing in Japan. So this number should equal the forward exchange rate by arbitrage, because it's two different ways of doing the same thing and so they should be the same number. So that means that the forward exchange rate, yen dollar exchange rate is not as interesting a number as you might think. You might think that the forward exchange rate is some prediction of the spot exchange rate. Well, maybe it is, but it's also just this. It reflects the relative interest rates in the two countries. If you look at forward exchange rates and compare them with spot exchange rates and check out this formula, it works pretty well explaining the forward interest rate. So that's called forward interest parity. Forward rate agreements use a formula which looks a little, it's not exactly what I just showed you. They typically actually just have a settlement which is the actual interest rate on the contract date minus the contract rate times the days in the contract period times the contract amount divided by B, which is depending on the convention either 360 or 365 days. We're in leap year this year, so we have 366 days so that you know the formula won't be exact because it's either... They went back to 360 days for formulas like this because people couldn't divide. They wanted a round number. So that's an old tradition and 366 doesn't appeal to anybody but that's the settlement formula.