Forward Contracts

A forward contract is an agreement to buy or sell an asset at a certain future time for a certain price. It can be contrasted with a spot contract, which is an agreement to buy or sell an asset today. A forward contract is traded in the over-the-counter market, usually between two financial institutions or between a financial institution and one of its clients.

One of the parties to a forward contract assumes a long position and agrees to buy the underlying asset on a certain specified future date for a certain specified price. The other party assumes a short position and agrees to sell the asset on the same date for the same price. The price in a forward contract is known as the delivery price.

Forward contracts are commonly used to hedge foreign currency risk. Suppose it is June 10 of a certain year and the treasurer of a U.S. corporation knows that the corporation will receive 5 million pounds sterling in six months (on December 10) and wants to hedge against exchange rate moves. The treasurer could contact a bank, find out that exchange rate for a six-month forward contract on sterling is 1.5500, and agree to sell 5 million pounds. The corporation then has a short forward contract on sterling. It has agreed that on December 10 it will sell 5 million pounds sterling to the bank for $7.75 million. The bank has a long forward contract on sterling. It has agreed that on December 10 it will buy 5 million pounds sterling for $7.75 million. Both sides have made a binding commitment.

Forward Price

The forward price for a particular forward contract at a particular time is the delivery price that would apply if the contract were entered at that time. Thus, on June 10 in our example, 1.5500 is the forward price for a forward contract that involves the delivery of sterling on December 10.

It is important to distinguish between the forward price and the delivery price. The two are the same when the contract is first entered into but are likely to be different at a later time. In our foreign exchange example, the forward price and the delivery price are both 1.5500 on June 10 for a contract with a delivery date on December 10. However, consider the situation on August 10 when the forward contract has been in existence for two months. The delivery price in the forward contract is still 1.5500. The forward price is the price of sterling on August 10 for a (four-month) forward contract with a delivery date December 10. In general, this will not be 1.5500. If the sterling exchange rate has increased between June 10 and August 10, it will be tend to be greater than 1.5500. If the sterling exchange rate has decreased between June 10 and August 10, it will tend to be less than 1.5500.

Payoffs from forward Contracts

Consider a trader who enters into a long forward contract on February 10, 2013, to buy £5 million in three months at an exchange rate of 1.6625. What are the possible outcomes? The contract would obligate the trader to buy £5 million for U.S.$ 8,312,500 (5 million x 1.6625) . If the spot exchange rate rose to say, 1.6825, at the end of the three months, the trader would gain $100,000 (=$8,412,500 – $8,312,500) because the pound, as soon as they have been purchased, can be sold for $8,412,500 (5million x 1.6825). Similarly, if the spot exchange rate fell to 1.6325 at the end of the three month, the trader would lose $150,000 because the forward contract would lead to the trader paying U.S.$ 150,000 more than the market price for the sterling which would be $8,162,500 (5 million x 1.6325).

In general, the payoff from a long position in a forward contract on one unit of an asset is:

St-K

Where K is the delivery price and ST is the spot price of the asset at maturity of the contract. This is because the holder of the contract is obligated to buy an asset worth ST for K. Similarly, the payoff from a short position in a forward contract on one unit of an asset is:

K-St

These payoffs from forward contracts can be positive or negative. They are illustrated in below pictures.

 payoffs-onestopbrokers

Forward prices and Spot Prices

The following example illustrates the reason why spot and forward prices are related by considering forward contract on gold. We assume that there are no storage costs associated with gold.

Suppose that the spot price of gold is $400 per ounce and the risk-free interest rate for investments lasting one year is 5% per annum. What is a reasonable value for the one-year forward price of gold?

Suppose first that the one-year forward price is $450 per ounce. A trader can immediately take the following actions:

  1. Borrow $400 at 5% for one year.
  2. Buy one ounce of gold.
  3. Enter into a short forward contract to sell the gold for $450 in one year.

The interest on the $400 that is borrowed (assuming annual compounding) is $20. The trader can, therefore, use $420 of the $450 that is obtained for the gold in one year to repay the loan. The remaining $30 is profit. Any one-year forward price greater than $420 will lead to this arbitrage trading strategy being profitable.

Suppose next that the forward price is $400. An investor who has a portfolio that includes gold can:

  1. Sell the gold for $400 per ounce.
  2. Invest the proceeds at 5%.
  3. Enter into a long forward contract to repurchase the gold in one year for $400 per ounce.

When this strategy is compared with the alternative strategy of keeping the gold in the portfolio for one-year we see that the investor is better off by $20 per ounce. In any situation where the forward price is less than $420, investor holding gold have an incentive to sell the gold and enter into a long forward contract in the way that has been described.

The first strategy is profitable when the one-year forward price of gold is greater than $420. As more traders attempt to take advantage of this strategy, the demand for short forward contracts will increase and the one-year forward price of gold will fall.

The second strategy is profitable for all investors who hold gold in their portfolios when the one-year forward price of gold is less than $420. As these investors attempt to take advantage of this strategy, the demand for long forward contracts will increase and the one-year forward price of gold will rise. Assuming that individuals are always willing to take advantage of arbitrage opportunities when they arise, we can conclude that the activities of trader should cause the one-year forward price of gold to be exactly $420. Any other price leads to an arbitrage opportunity.

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