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Forward Contracts
#derivatives

To gain a better understanding of forward contracts, it is necessary to examine their payoffs. As noted, forward contracts—and indeed all derivatives—take (derive) their payoffs from the performance of the underlying asset. To illustrate the payoff of a forward contract, start with the assumption that we are at time t = 0 and that the forward contract expires at a later date, time t = T.5 The spot price of the underlying asset at time 0 is S0 and at time T is ST. Of course, when we initiate the contract at time 0, we do not know what ST will ultimately be. Remember that the two parties, the buyer and the seller, are going long and short, respectively.

At time t = 0, the long and the short agree that the short will deliver the asset to the long at time T for a price of F0(T). The notation F0(T) denotes that this value is established at time 0 and applies to a contract expiring at time T. F0(T) is the forward price. Later, you will learn how the forward price is determined. It turns out that it is quite easy to do, but we do not need to know right now.6

So, let us assume that the buyer enters into the forward contract with the seller for a price of F0(T), with delivery of one unit of the underlying asset to occur at time T. Now, let us roll forward to time T, when the price of the underlying is ST. The long is obligated to pay F0(T), for which he receives an asset worth ST. If ST > F0(T), it is clear that the transaction has worked out well for the long. He paid F0(T) and receives something of greater value. Thus, the contract effectively pays off STF0(T) to the long, which is the value of the contract at expiration. The short has the mirror image of the long. He is required to deliver the asset worth ST and accept a smaller amount, F0(T). The contract has a payoff for him of F0(T) – ST, which is negative. Even if the asset’s value, ST, is less than the forward price, F0(T), the payoffs are still STF0(T) for the long and F0(T) – ST for the short. We can consolidate these results by writing the short’s payoff as the negative of the long’s, –[STF0(T)], which serves as a useful reminder that the long and the short are engaged in a zero-sum game, which is a type of competition in which one participant’s gains are the other’s losses. Although both lose a modest amount in the sense of both having some costs to engage in the transaction, these costs are relatively small and worth ignoring for our purposes at this time. In addition, it is worthwhile to note how derivatives transform the performance of the underlying. The gain from owning the underlying would be STS0, whereas the gain from owning the forward contract would be STF0(T). Both figures are driven by ST, the price of the underlying at expiration, but they are not the same.

Exhibit 1 illustrates the payoffs from both buying and selling a forward contract.

Exhibit 1. Payoffs from a Forward Contract

The long hopes the price of the underlying will rise above the forward price, F0(T), whereas the short hopes the price of the underlying will fall below the forward price. Except in the extremely rare event that the underlying price at T equals the forward price, there will ultimately be a winner and a loser.

An important element of forward contracts is that no money changes hands between parties when the contract is initiated. Unlike in the purchase and sale of an asset, there is no value exchanged at the start. The buyer does not pay the seller some money and obtain something. In fact, forward contracts have zero value at the start. They are neither assets nor liabilities. As you will learn in later readings, their values will deviate from zero later as prices move. Forward contracts will almost always have non-zero values at expiration.

As noted previously, the primary purpose of derivatives is for risk management. Although the uses of forward contracts are covered in depth later in the curriculum, there are a few things to note here about the purposes of forward contracts. It should be apparent that locking in the future buying or selling price of an underlying asset can be extremely attractive for some parties. For example, an airline anticipating the purchase of jet fuel at a later date can enter into a forward contract to buy the fuel at a price agreed upon when the contract is initiated. In so doing, the airline has hedged its cost of fuel. Thus, forward contracts can be structured to create a perfect hedge, providing an assurance that the underlying asset can be bought or sold at a price known when the contract is initiated. Likewise, speculators, who ultimately assume the risk laid off by hedgers, can make bets on the direction of the underlying asset without having to invest the money to purchase the asset itself.

Finally, forward contracts need not specifically settle by delivery of the underlying asset. They can settle by an exchange of cash. These contracts—called non-deliverable forwards(NDFs), cash-settled forwards, or contracts for differences—have the same economic effect as do their delivery-based counterparts. For example, for a physical delivery contract, if the long pays F0(T) and receives an asset worth ST, the contract is worth STF0(T) to the long at expiration. A non-deliverable forward contract would have the short simply pay cash to the long in the amount of STF0(T). The long would not take possession of the underlying asset, but if he wanted the asset, he could purchase it in the market for its current price of ST. Because he received a cash settlement in the amount of STF0(T), in buying the asset the long would have to pay out only ST – [STF0(T)], which equals F0(T). Thus, the long could acquire the asset, effectively paying F0(T), exactly as the contract promised. Transaction costs do make cash settlement different from physical delivery, but this point is relatively minor and can be disregarded for our purposes here.

As previously mentioned, forward contracts are OTC contracts. There is no formal forward contract exchange. Nonetheless, there are exchange-traded variants of forward contracts, which are called futures contracts or just futures.

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