In this module, we're going to introduce you to futures, why futures are needed, how one can hedge using futures and in later module we're going to introduce you to the mechanics of the margin account associated with the futures. Recall that, we had introduced these contracts called forwards a couple of modules ago. Forwards were contracts that gave the buyer the right and the obligation to purchase a certain amount of an underlying asset at a specified price at a specified time. The problem with these forward contracts were that they are a multitude of prices here. As a result of that, they cannot be organized through an exchange. So what do I mean by multitude of prices? So, let's say that there is a expiration time capital T. If you construct a forward contract at time t equal to 0, associated with that particular contract would be a forward price F_0. If you construct it at some other time t equal to k there'll be a different forward price F_k. If you construct something at t equal to u, there'll be another price F_u. So all of these contracts are expiring at the same time capital T, and they have different prices depending upon when they were struck. So in every other respect these contracts are similar except for the price. Because of that, it's very difficult to set these contracts up to an exchange. Because they are not set up through an exchange, there is no price transparency. Recall that price transparency is very important to make sure that supply and demand sets fair prices or no arbitrage prices. If there is no price transparency, one would not be able to construct arbitrage prices. That is, supply and demand would not equilibriate when arbitrage free prices. Because there is no price transparency and these contracts are not organized through an exchange, there is something called double-coincidence-of-wants. When you construct these forward contract, you have to have somebody take the opposite side. In order to find that counter party you have to go look for it and that might lead to problems where certain forward contracts cannot be written because the counter party is not available. There's also default risk of the counter party. We talked about this in the context of swaps. If you take on a forward contract with a counter party and the counter party is not willing to make the payments when the time comes or is bankrupt, then you expose yourself to unnecessary risk. So one needs a contract that works like a forward contract, that's able to fix prices sometime in the future, but is able to solve these other problems associated with forward contracts. That is, it's organized through an exchange, there is price transparency, you can get in and get out of this contract very easily, there is no counter party with which you are contracting, you are contracting through brokers who are organized in an exchange. One such contract is called the futures contracts. It solves the problem of the multitude of prices for the same maturity by marking-to-market. It just gives the profits and losses at the end of the day. So there's a single price for a single maturity. There aren't any more prices based on when the contract was set. The contracts, because of the fact that these multitude of prices don't exist, they can be organized through an exchange. They can be written on any underlying security which has a settlement price. You can write it on commodities, you can write it on broad-based indices such as the S&P 500, the Russel 2000, etc. You can even write it for the volatility of the market. For example, VIX futures. There are a whole number of different assets that are available and I would encourage you to go to this website by the CME group to look at the various kinds of commodities, indices, and other measurable quantities on which forward future contracts are written. So here are how a future contract work. An individual opens a margin account with a broker, it enters into a certain number of futures contracts with a certain price F_0, so this is the futures price that is available at time t equal to zero and in order to enter into these futures contracts, you have to set up an initial margin that depends on whether you're a hedger or a speculator and so on, and it typically is around 5-10 percent of the total contract value. All the profits and losses are settled using a margin account. If there are profits which means that the futures price goes up and you are having a long position, then the profit that you make is credited to your margin account, if the price goes down, then the losses are also settled through the margin account. If the margin account becomes below a certain margin called a maintenance margin, then there is a margin call. That is, the broker asks you to put more money in and you have to make it back up to the initial margin. I've given a snapshot of a particular worksheet of a workbook that I'm going to be working through in a later module that gives you how this margin account works and how the mechanics of the futures work out. In this particular module, we will be looking at some of the more theoretical results associated with the futures. In the later module on Excel, I will walk you through how the mechanics work out. So what are some pros and cons of futures? Well, the pros are, you can have high leverage. You only put 5-10 percent of the total notional amount of the contract in the margin account. As a result, you can control very large sums of money by putting very small amount of money up front. So you can get yourself very high profit. Futures accounts are very liquid. So you can take exposure to many different kinds of assets very easily. It can be written on a wide variety of underlying assets. So if you want to hedge or speculate, you can speculate on a very wide range of assets. The cons are quite related to the pros. The high leverage means that you expose yourself to higher risk as well. Futures prices are approximately linear function of the underlying. So only linear payoffs can be hedged. So if you have a cash flow that is a non-linear function of some underlying asset price or some underlying market indicator, then you cannot hedge them using futures prices because futures prices are linear functions of the underlying. Futures may not be completely flexible. Futures are organized through exchanges which means that they mature at a specified date, they're written for a specified quantity, they're only written for certain commodities and so on. So if you want to hedge something which doesn't quite fit the specifications of futures contracts, you might have to construct a one-off forward contract. You might have to go back to the broker and construct a one-off forward contract or take on something called basis risk, which is going to come later on in this module. What about pricing futures? So in order to price futures, we need something called a martingale pricing formalism. This comes because in its full generality, the interest rates are random or stochastic, and when you have stochastic interest rates, we cannot use the simple arbitrage arguments that we have constructed so far to construct a price for a future. If on the other hand the interest rates are deterministic, then we know that forward price is equal to the futures price, we know how to construct the forward price using our arbitrage arguments and therefore we know how to price the futures price. One thing that we do know is that at maturity, the futures price F_T is equal to the price of the underlying S_T. This is what we are going to be using in the next few slides to make some hedging arguments.
