# Forward contract

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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 at the time of conclusion of the contract, making it a type of derivative instrument. [1] [2] 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.

In finance, a derivative is a contract that derives its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements for speculation or getting access to otherwise hard-to-trade assets or markets. Some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the New York Stock Exchange, while most insurance contracts have developed into a separate industry. In the United States, after the financial crisis of 2007–2009, there has been increased pressure to move derivatives to trade on exchanges. Derivatives are one of the three main categories of financial instruments, the other two being stocks and debt. The oldest example of a derivative in history, attested to by Aristotle, is thought to be a contract transaction of olives, entered into by ancient Greek philosopher Thales, who made a profit in the exchange. Bucket shops, outlawed a century ago, are a more recent historical example.

The forward price is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, we can express the forward price in terms of the spot price and any dividends. For forwards on non-tradeables, pricing the forward may be a complex task.

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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 is not the same as the value date where the securities themselves are exchanged. Forwards, like other derivative securities, can be used to hedge risk (typically currency or exchange rate 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.

Value date, in finance, is the date when the value of an asset that fluctuates in price is determined. The value date is used when there is a possibility for discrepancies due to differences in the timing of asset valuation. It usually applies to forward currency contracts, options and other derivatives, interest payable or receivable.

A hedge is an investment position intended to offset potential losses or gains that may be incurred by a companion investment. A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, gambles, many types of over-the-counter and derivative products, and futures contracts.

Speculation is the purchase of an asset with the hope that it will become more valuable in the near future. In finance, speculation is also the practice of engaging in risky financial transactions in an attempt to profit from short term fluctuations in the market value of a tradable financial instrument—rather than attempting to profit from the underlying financial attributes embodied in the instrument such as capital gains, dividends, or interest.

A closely related contract is a futures contract; they differ in certain respects. Forward contracts are very similar to futures contracts, except they are not exchange-traded, or defined on standardized assets. [3] Forwards also typically have no interim partial settlements or "true-ups" in margin requirements like futures – such that the parties do not exchange additional property securing the party at gain and the entire unrealized gain or loss builds up while the contract is open. However, being traded over the counter (OTC), forward contracts specification can be customized and may include mark-to-market and daily margin calls. Hence, a forward contract arrangement might call for the loss party to pledge collateral or additional collateral to better secure the party at gain.[ clarification needed ] In other words, the terms of the forward contract will determine the collateral calls based upon certain "trigger" events relevant to a particular counterparty such as among other things, credit ratings, value of assets under management or redemptions over a specific time frame, e.g., quarterly, annually, etc.

In finance, a futures contract is a standardized forward contract, a legal agreement to buy or sell something at a predetermined price at a specified time in the future, between parties not known to each other. The asset transacted is usually a commodity or financial instrument. The predetermined price the parties agree to buy and sell the asset for is known as the forward price. The specified time in the future—which is when delivery and payment occur—is known as the delivery date. Because it is a function of an underlying asset, a futures contract is a derivative product.

Over-the-counter (OTC) or off-exchange trading is done directly between two parties, without the supervision of an exchange. It is contrasted with exchange trading, which occurs via exchanges. A stock exchange has the benefit of facilitating liquidity, providing transparency, and maintaining the current market price. In an OTC trade, the price is not necessarily publicly disclosed.

## Payoffs

The value of a forward position at maturity depends on the relationship between the delivery price (${\displaystyle K}$) and the underlying price (${\displaystyle S_{T}}$) at that time.

• For a long position this payoff is: ${\displaystyle f_{T}=S_{T}-K}$
• For a short position, it is: ${\displaystyle f_{T}=K-S_{T}}$

Since the final value (at maturity) 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" [4]

## How a forward contract works

Suppose that Bob wants to buy a house a year from now. At the same time, suppose that Andy currently owns a $100,000 house that he 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$104,000 (more below on why the sale price should be this amount). Andy 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, Andy will have the short forward contract.

## Spot–forward parity

For liquid assets ("tradeables"), 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:

In business, economics or investment, market liquidity is a market's feature whereby an individual or firm can quickly purchase or sell an asset without causing a drastic change in the asset's price. Liquidity is about how big the trade-off is between the speed of the sale and the price it can be sold for. In a liquid market, the trade-off is mild: selling quickly will not reduce the price much. In a relatively illiquid market, selling it quickly will require cutting its price by some amount.

• 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 (e.g. gold, financial securities);
• or a consumption asset, i.e. an asset held primarily for consumption (e.g. oil, iron ore etc.)

### Investment assets

For an asset that provides no income, the relationship between the current forward (${\displaystyle F_{0}}$) and spot (${\displaystyle S_{0}}$) prices is

${\displaystyle F_{0}=S_{0}e^{rT}}$

where ${\displaystyle r}$ 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: ${\displaystyle F_{0}=(S_{0}-I)e^{rT}}$
• Continuous: ${\displaystyle F_{0}=S_{0}e^{(r-q)T}}$

where ${\displaystyle I=}$ the present value of the discrete income at time ${\displaystyle t_{0}, and ${\displaystyle q\%p.a.}$ 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 (${\displaystyle I}$ or ${\displaystyle q}$) 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: ${\displaystyle F_{0}=(S_{0}+U)e^{rT}}$
• Continuous: ${\displaystyle F_{0}=S_{0}e^{(r+u)T}}$

where ${\displaystyle U=}$ the present value of the discrete storage cost at time ${\displaystyle t_{0}, and ${\displaystyle u\%p.a.}$ 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" (hedge against) temporary shortages and the ability to keep a production process running, [1] and are referred to as the convenience yield. Thus, for consumption assets, the spot-forward relationship is:

• Discrete storage costs: ${\displaystyle F_{0}=(S_{0}+U)e^{(r-y)T}}$
• Continuous storage costs: ${\displaystyle F_{0}=S_{0}e^{(r+u-y)T}}$

where ${\displaystyle y\%p.a.}$ 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. [1]

### Cost of carry

The relationship between the spot and forward price of an asset reflects the net cost of holding (or carrying) that asset relative to holding the forward. Thus, all of the costs and benefits above can be summarised as the cost of carry, ${\displaystyle c}$. Hence,

• Discrete: ${\displaystyle F_{0}=(S_{0}+U-I)e^{(r-y)T}}$
• Continuous: ${\displaystyle F_{0}=S_{0}e^{cT},{\text{ where }}c=r-q+u-y.}$

## 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. [1] 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, ${\displaystyle F_{0}}$ and the expected future spot price, ${\displaystyle E(S_{T})}$.

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. [5] [6] 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:

${\displaystyle E(S_{T}-K)=E(S_{T})-K}$, where ${\displaystyle K}$ is the delivery price at maturity

Thus, if the speculators expect to profit,

${\displaystyle E(S_{T})-K>0}$
${\displaystyle E(S_{T})>K}$
${\displaystyle E(S_{T})>F_{0}}$, as ${\displaystyle K=F_{0}}$ when they enter the contract

This market situation, where ${\displaystyle E(S_{T})>F_{0}}$, 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 (see also basis); then normal backwardation implies that futures prices for a certain maturity are increasing over time. The opposite situation, where ${\displaystyle E(S_{T}), is referred to as contango. Likewise, contango implies that futures prices for a certain maturity are falling over time. [7]

## Rational pricing

If ${\displaystyle S_{t}}$ is the spot price of an asset at time ${\displaystyle t}$, and ${\displaystyle r}$ is the continuously compounded rate, then the forward price at a future time ${\displaystyle T}$ must satisfy ${\displaystyle F_{t,T}=S_{t}e^{r(T-t)}}$.

To prove this, suppose not. Then we have two possible cases.

Case 1: Suppose that ${\displaystyle F_{t,T}>S_{t}e^{r(T-t)}}$. Then an investor can execute the following trades at time ${\displaystyle t}$:

1. go to the bank and get a loan with amount ${\displaystyle S_{t}}$ at the continuously compounded rate r;
2. with this money from the bank, buy one unit of asset for ${\displaystyle S_{t}}$;
3. enter into one short forward contract costing 0. A short forward contract means that the investor owes the counterparty the asset at time ${\displaystyle T}$.

The initial cost of the trades at the initial time sum to zero.

At time ${\displaystyle T}$ the investor can reverse the trades that were executed at time ${\displaystyle t}$. Specifically, and mirroring the trades 1., 2. and 3. the investor

1. ' repays the loan to the bank. The inflow to the investor is ${\displaystyle -S_{t}e^{r(T-t)}}$;
2. ' settles the short forward contract by selling the asset for ${\displaystyle F_{t,T}}$. The cash inflow to the investor is now ${\displaystyle F_{t,T}}$ because the buyer receives ${\displaystyle S_{T}}$ from the investor.

The sum of the inflows in 1.' and 2.' equals ${\displaystyle F_{t,T}-S_{t}e^{r(T-t)}}$, which by hypothesis, is positive. This is an arbitrage profit. Consequently, and assuming that the non-arbitrage condition holds, we have a contradiction. This is called a cash and carry arbitrage because you "carry" the asset until maturity.

Case 2: Suppose that ${\displaystyle F_{t,T}. Then an investor can do the reverse of what he has done above in case 1. But if you look at the convenience yield page, you will see that if there are finite assets/inventory, the reverse cash and carry arbitrage is not always possible. It would depend on the elasticity of demand for forward contracts and such like.

### Extensions to the forward pricing formula

Suppose that ${\displaystyle FV_{T}(X)}$ is the time value of cash flows X at the contract expiration time ${\displaystyle T}$. The forward price is then given by the formula:

${\displaystyle F_{t,T}=S_{t}e^{r(T-t)}-FV_{T}({\text{all cash flows over the life of the contract}})}$

The cash flows can be in the form of dividends from the asset, or costs of maintaining the asset.

If these price relationships do not hold, there is an arbitrage opportunity for a riskless profit similar to that discussed above. One implication of this is that the presence of a forward market will force spot prices to reflect current expectations of future prices. As a result, the forward price for nonperishable commodities, securities or currency is no more a predictor of future price than the spot price is - the relationship between forward and spot prices is driven by interest rates. For perishable commodities, arbitrage does not have this

The above forward pricing formula can also be written as:

${\displaystyle F_{t,T}=(S_{t}-I_{t})e^{r(T-t)}\,}$

Where ${\displaystyle I_{t}}$ is the time t value of all cash flows over the life of the contract.

For more details about pricing, see forward price.

## Theories of why a forward contract exists

Allaz and Vila (1993) suggest that there is also a strategic reason (in an imperfect competitive environment) for the existence of forward trading, that is, forward trading can be used even in a world without uncertainty. This is due to firms having Stackelberg incentives to anticipate their production through forward contracts.

## Footnotes

1. John C Hull, Options, Futures and Other Derivatives (6th edition), Prentice Hall: New Jersey, USA, 2006, 3
2. Understanding Derivatives: Markets and Infrastructure, Federal Reserve Bank of Chicago
3. Gorton, Gary; Rouwenhorst, K. Geert (2006). "Facts and Fantasies about Commodity Futures" (PDF). Financial Analysts Journal. 62 (2): 47–68. doi:10.2469/faj.v62.n2.4083.
4. J.M. Keynes, A Treatise on Money, London: Macmillan, 1930
5. J.R. Hicks, Value and Capital, Oxford: Clarendon Press, 1939
6. Contango Vs. Normal Backwardation, Investopedia

## Related Research Articles

Normal backwardation, also sometimes called backwardation, is the market condition wherein the price of a commodities' forward or futures contract is trading below the expected spot price at contract maturity. The resulting futures or forward curve would typically be downward sloping, since contracts for further dates would typically trade at even lower prices. In practice, the expected future spot price is unknown, and the term "backwardation" may be used to refer to "positive basis", which occurs when the current spot price exceeds the price of the future.

Contango, also sometimes called forwardation, is a situation where the futures price of a commodity is higher than the anticipated spot price at maturity of the futures contract. In a contango situation, arbitrageurs/speculators, are "willing to pay more [now] for a commodity [to be received] at some point in the future than the actual expected price of the commodity [at that future point]. This may be due to people's desire to pay a premium to have the commodity in the future rather than paying the costs of storage and carry costs of buying the commodity today." On the other side of the trade, hedgers are happy to sell futures contracts and accept the higher-than-expected returns. A contango market is also known as a normal market, or carrying-cost market.

The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price regardless of the risk of the security and its expected return. The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. It is widely used, although often with some adjustments, by options market participants.

In financial mathematics, put–call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to a single forward contract at this strike price and expiry. This is because if the price at expiry is above the strike price, the call will be exercised, while if it is below, the put will be exercised, and thus in either case one unit of the asset will be purchased for the strike price, exactly as in a forward contract.

In finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options—as well as others where the payoff is calculated similarly—are referred to as "vanilla options". Options where the payoff is calculated differently are categorized as "exotic options". Exotic options can pose challenging problems in valuation and hedging.

The Black model is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond options, Interest rate cap and floors, and swaptions. It was first presented in a paper written by Fischer Black in 1976.

In mathematical finance, a risk-neutral measure is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure. This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure. Such a measure exists if and only if the market is arbitrage-free.

In finance, a spot contract, spot transaction, or simply spot, is a contract of buying or selling a commodity, security or currency for immediate settlement on the spot date, which is normally two business days after the trade date. The settlement price is called spot price. A spot contract is in contrast with a forward contract or futures contract where contract terms are agreed now but delivery and payment will occur at a future date.

A swap is a derivative in which two counterparties exchange cash flows of one party's financial instrument for those of the other party's financial instrument. The benefits in question depend on the type of financial instruments involved. For example, in the case of a swap involving two bonds, the benefits in question can be the periodic interest (coupon) payments associated with such bonds. Specifically, two counterparties agree to exchange one stream of cash flows against another stream. These streams are called the legs of the swap. The swap agreement defines the dates when the cash flows are to be paid and the way they are accrued and calculated. Usually at the time when the contract is initiated, at least one of these series of cash flows is determined by an uncertain variable such as a floating interest rate, foreign exchange rate, equity price, or commodity price.

Rational pricing is the assumption in financial economics that asset prices will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.

In finance, a foreign exchange option is a derivative financial instrument that gives the right but not the obligation to exchange money denominated in one currency into another currency at a pre-agreed exchange rate on a specified date. See Foreign exchange derivative.

In finance, a single-stock future (SSF) is a type of futures contract between two parties to exchange a specified number of stocks in a company for a price agreed today with delivery occurring at a specified future date, the delivery date. The contracts are traded on a futures exchange. The party agreeing to take delivery of the underlying stock in the future, the "buyer" of the contract, is said to be "long", and the party agreeing to deliver the stock in the future, the "seller" of the contract, is said to be "short". The terminology reflects the expectations of the parties - the buyer hopes or expects that the stock price is going to increase, while the seller hopes or expects that it will decrease. Note that the contract itself costs nothing to enter; the buy/sell terminology is a linguistic convenience reflecting the position each party is taking?

The cost of carry or carrying charge is cost of storing a physical commodity, such as grain or metals, over a period of time. The carrying charge includes insurance, storage and interest on the invested funds as well as other incidental costs. In interest rate futures markets, it refers to the differential between the yield on a cash instrument and the cost of the funds necessary to buy the instrument.

Interest rate parity is a no-arbitrage condition representing an equilibrium state under which investors will be indifferent to interest rates available on bank deposits in two countries. The fact that this condition does not always hold allows for potential opportunities to earn riskless profits from covered interest arbitrage. Two assumptions central to interest rate parity are capital mobility and perfect substitutability of domestic and foreign assets. Given foreign exchange market equilibrium, the interest rate parity condition implies that the expected return on domestic assets will equal the exchange rate-adjusted expected return on foreign currency assets. Investors then cannot earn arbitrage profits by borrowing in a country with a lower interest rate, exchanging for foreign currency, and investing in a foreign country with a higher interest rate, due to gains or losses from exchanging back to their domestic currency at maturity. Interest rate parity takes on two distinctive forms: uncovered interest rate parity refers to the parity condition in which exposure to foreign exchange risk is uninhibited, whereas covered interest rate parity refers to the condition in which a forward contract has been used to cover exchange rate risk. Each form of the parity condition demonstrates a unique relationship with implications for the forecasting of future exchange rates: the forward exchange rate and the future spot exchange rate.

A convenience yield is an implied return on holding inventories. It is an adjustment to the cost of carry in the non-arbitrage pricing formula for forward prices in markets with trading constraints.

The forward exchange rate is the exchange rate at which a bank agrees to exchange one currency for another at a future date when it enters into a forward contract with an investor. Multinational corporations, banks, and other financial institutions enter into forward contracts to take advantage of the forward rate for hedging purposes. The forward exchange rate is determined by a parity relationship among the spot exchange rate and differences in interest rates between two countries, which reflects an economic equilibrium in the foreign exchange market under which arbitrage opportunities are eliminated. When in equilibrium, and when interest rates vary across two countries, the parity condition implies that the forward rate includes a premium or discount reflecting the interest rate differential. Forward exchange rates have important theoretical implications for forecasting future spot exchange rates. Financial economists have put forth a hypothesis that the forward rate accurately predicts the future spot rate, for which empirical evidence is mixed.

Spot–future parity is a parity condition whereby, if an asset can be purchased today and held until the exercise of a futures contract, the value of the future should equal the current spot price adjusted for the cost of money, dividends, "convenience yield" and any carrying costs. That is, if a person can purchase a good for price S and conclude a contract to sell it one month later at a price of F, the price difference should be no greater than the cost of using money less any expenses from holding the asset; if the difference is greater, the person has an opportunity to buy and sell the "spots" and "futures" for a risk-free profit, i.e. an arbitrage. Spot–future parity is an application of the law of one price; see also Rational pricing and #Futures.

## References

• John C. Hull, (2000), Options, Futures and other Derivatives, Prentice-Hall.
• Keith Redhead, (31 October 1996), Financial Derivatives: An Introduction to Futures, Forwards, Options and Swaps, Prentice-Hall
• Abraham Lioui & Patrice Poncet, (March 30, 2005), Dynamic Asset Allocation with Forwards and Futures, Springer
• Forward Contract on Wikinvest