Forward contract

In finance, a forward contract, or simply a forward, is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on in the contract, making it a type of derivative instrument. The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a short position. The price agreed upon is called the delivery price, which is equal to the forward price at the time the contract is entered into.
The price of the underlying instrument, in whatever form, is paid before control of the instrument changes. This is one of the many forms of buy/sell orders where the time and date of trade are not the same as the value date where the securities themselves are exchanged. Forwards, like other derivative securities, can be used to hedge risk, as a means of speculation, or to allow a party to take advantage of a quality of the underlying instrument which is time-sensitive.

Payoffs

The value of a forward position at maturity depends on the relationship between the delivery price and the underlying price at that time.

For a long position this payoff is:
For a short position, it is:

Since the final value of a forward position depends on the spot price which will then be prevailing, this contract can be viewed, from a purely financial point of view, as ''"a bet on the future spot price"''

How a forward contract works

Suppose that Bob wants to buy a house a year from now. At the same time, suppose that Alice currently owns a house that she wishes to sell a year from now. Both parties could enter into a forward contract with each other. Suppose that they both agree on the sale price in one year's time of . Alice and Bob have entered into a forward contract. Bob, because he is buying the underlying, is said to have entered a long forward contract. Conversely, Alice will have the short forward contract.
At the end of one year, suppose that the current market valuation of Alice's house is. Then, because Alice is obliged to sell to Bob for only, Bob will make a profit of. To see why this is so, one needs only to recognize that Bob can buy from Alice for and immediately sell to the market for. Bob has made the difference in profit. In contrast, Alice has made a potential loss of, and an actual profit of.
The similar situation works among currency forwards, in which one party opens a forward contract to buy or sell a currency to expire/settle at a future date, as they do not wish to be exposed to exchange rate/currency risk over a period of time. As the exchange rate between U.S. dollars and Canadian dollars fluctuates between the trade date and the earlier of the date at which the contract is closed or the expiration date, one party gains and the counterparty loses as one currency strengthens against the other. Sometimes, the buy forward is opened because the investor will actually need Canadian dollars at a future date such as to pay a debt owed that is denominated in Canadian dollars. Other times, the party opening a forward does so, not because they need Canadian dollars nor because they are hedging currency risk, but because they are speculating on the currency, expecting the exchange rate to move favorably to generate a gain on closing the contract.
In a currency forward, the notional amounts of currencies are specified. While the notional amount or reference amount may be a large number, the cost or margin requirement to command or open such a contract is considerably less than that amount, which refers to the leverage created, which is typical in derivative contracts.

Example of how forward prices should be agreed upon

Continuing on the example above, suppose now that the initial price of Alice's house is and that Bob enters into a forward contract to buy the house one year from today. But since Alice knows that she can immediately sell for and place the proceeds in the bank, she wants to be compensated for the delayed sale. Suppose that the risk free rate of return R for one year is 4%. Then the money in the bank would grow to, risk free. So Alice would want at least one year from now for the contract to be worthwhile for her – the opportunity cost will be covered.

Spot–forward parity

For liquid assets, spot–forward parity provides the link between the spot market and the forward market. It describes the relationship between the spot and forward price of the underlying asset in a forward contract. While the overall effect can be described as the cost of carry, this effect can be broken down into different components, specifically whether the asset:

pays income, and if so whether this is on a discrete or continuous basis
incurs storage costs
is regarded as
* an investment asset, i.e. an asset held primarily for investment purposes ;
* or a consumption asset, i.e. an asset held primarily for consumption
Investment assets

For an asset that provides no income, the relationship between the current forward and spot prices is
where is the continuously compounded risk free rate of return, and T is the time to maturity. The intuition behind this result is that given you want to own the asset at time T, there should be no difference in a perfect capital market between buying the asset today and holding it and buying the forward contract and taking delivery. Thus, both approaches must cost the same in present value terms. For an arbitrage proof of why this is the case, see Rational pricing below.
For an asset that pays known income, the relationship becomes:

Discrete:
Continuous:

where the present value of the discrete income at time, and is the continuously compounded dividend yield over the life of the contract. The intuition is that when an asset pays income, there is a benefit to holding the asset rather than the forward because you get to receive this income. Hence the income must be subtracted to reflect this benefit. An example of an asset which pays discrete income might be a stock, and an example of an asset which pays a continuous yield might be a foreign currency or a stock index.
For investment assets which are commodities, such as gold and silver, storage costs must also be considered. Storage costs can be treated as 'negative income', and like income can be discrete or continuous. Hence with storage costs, the relationship becomes:

Discrete:
Continuous:

where the present value of the discrete storage cost at time, and is the continuously compounded storage cost where it is proportional to the price of the commodity, and is hence a 'negative yield'. The intuition here is that because storage costs make the final price higher, we have to add them to the spot price.

Consumption assets

Consumption assets are typically raw material commodities which are used as a source of energy or in a production process, for example crude oil or iron ore. Users of these consumption commodities may feel that there is a benefit from physically holding the asset in inventory as opposed to holding a forward on the asset. These benefits include the ability to "profit from" temporary shortages and the ability to keep a production process running, and are referred to as the convenience yield. Thus, for consumption assets, the spot-forward relationship is:

Discrete storage costs:
Continuous storage costs:

where is the convenience yield over the life of the contract. Since the convenience yield provides a benefit to the holder of the asset but not the holder of the forward, it can be modelled as a type of 'dividend yield'. However, it is important to note that the convenience yield is a non cash item, but rather reflects the market's expectations concerning future availability of the commodity. If users have low inventories of the commodity, this implies a greater chance of shortage, which means a higher convenience yield. The opposite is true when high inventories exist.

Cost of carry

The relationship between the spot and forward price of an asset reflects the net cost of holding that asset relative to holding the forward. Thus, all of the costs and benefits above can be summarised as the cost of carry,. Hence,

Discrete:
Continuous:
Relationship between the forward price and the expected future spot price

The market's opinion about what the spot price of an asset will be in the future is the expected future spot price. Hence, a key question is whether or not the current forward price actually predicts the respective spot price in the future. There are a number of different hypotheses which try to explain the relationship between the current forward price, and the expected future spot price,.
The economists John Maynard Keynes and John Hicks argued that in general, the natural hedgers of a commodity are those who wish to sell the commodity at a future point in time. Thus, hedgers will collectively hold a net short position in the forward market. The other side of these contracts are held by speculators, who must therefore hold a net long position. Hedgers are interested in reducing risk, and thus will accept losing money on their forward contracts. Speculators on the other hand, are interested in making a profit, and will hence only enter the contracts if they expect to make money. Thus, if speculators are holding a net long position, it must be the case that the expected future spot price is greater than the forward price.
In other words, the expected payoff to the speculator at maturity is:
Thus, if the speculators expect to profit,
This market situation, where, is referred to as normal backwardation. Forward/futures prices converge with the spot price at maturity, as can be seen from the previous relationships by letting T go to 0 ; then normal backwardation implies that futures prices for a certain maturity are increasing over time. The opposite situation, where, is referred to as contango. Likewise, contango implies that futures prices for a certain maturity are falling over time.