Forward contract

 ( Derivatives ) 

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.J.M. Keynes, A Treatise on Money, London: Macmillan, 1930J.R. Hicks, Value and Capital, Oxford: Clarendon Press, 1939 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:

$E(S\_\{T\}-K)\; =\; E(S\_\{T\})\; -\; K$, where $K$ is the delivery price at maturity

Thus, if the speculators expect to profit,

$E(S\_\{T\})\; -\; K\; >\; 0$

$E(S\_\{T\})\; >\; K$

$E(S\_\{T\})\; >\; F\_\{0\}$, as $K\; =\; F\_\{0\}$ when they enter the contract

This market situation, where $E(S\_\{T\})\; >\; F\_\{0\}$, 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 , is referred to as contango. Likewise, contango implies that futures prices for a certain maturity are falling over time. Contango Vs. Normal Backwardation , Investopedia

Having no upfront cashflows is one of the advantages of a forward contract compared to its futures counterpart. Especially when the forward contract is denominated in a foreign currency, not having to post (or receive) daily settlements simplifies cashflow management.

Compared to the futures markets it is very difficult to close out one's position, that is to rescind the forward contract. For instance while being long in a forward contract, entering short into another forward contract might cancel out delivery obligations but adds to credit risk exposure as there are now three parties involved. Closing out a contract almost always involves reaching out to the counterparty.

Compared to their futures counterparts, forwards (especially Forward Rate Agreements) need convexity adjustments, that is a drift term that accounts for future rate changes. In futures contracts, this risk remains constant whereas a forward contract's risk changes when rates change.

Conversely, in markets with easily accessible spot prices or basis rates, in particular the Foreign exchange market and OIS market, forwards are usually quoted using premium points or forward points. That is using the spot price or basis rate as reference forwards are quoted as the difference in pips between the outright price and the spot price for FX, or the difference in between the forward rate and the basis rate for interest rate swaps and forward rate agreements.

Note: The term outright is used in the futures markets in a similar way but is contrasted with futures spreads instead of premium points, which is more than just a quoting convention, and in particular involves the simultaneous transaction in two outright futures.

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

Case 1: Suppose that $F\_\{t,T\}\; >\; S\_t\; e^\{r\; (T-t)\}$. Then an investor can execute the following trades at time $t$:

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

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

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

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

The sum of the inflows in 1.' and 2.' equals $F\_\{t,T\}\; -\; S\_t\; e^\{r\; (T-t)\}$, 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 . Then an investor can do the reverse of what he has done above in case 1. This means selling one unit of the asset, investing this money into a bank account and entering a long forward contract costing 0.

Note: 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.

$F\_\{t,T\}\; =\; S\_t\; e^\{r(T-t)\}\; -\; FV\_T(\backslash text\{all\; cash\; flows\; over\; the\; life\; of\; the\; contract\})$

The cash flows can be in the form of 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:

$F\_\{t,T\}\; =\; (S\_t\; -\; I\_t)\; e^\{r(T-t)\}\; \backslash ,$

Where $I\_t$ is the time t value of all cash flows over the life of the contract.

For more details about pricing, see forward price.

• 988 transaction
• Derivative (finance)
• Forward exchange market
• Forward market
• Forward price
• Futures contract
• Hedging
• Non-deliverable forward
• Option
• Swap (finance)

Other types of trade contracts:

• Spot price
• Spot market

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

• Allaz, B. and Vila, J.-L., Cournot competition, futures markets and efficiency, Journal of Economic Theory 59,297-308.
• Understanding Derivatives: Markets and Infrastructure Federal Reserve Bank of Chicago, Financial Markets Group
• Forward Contract Definition - Investopedia