Forward contract

Forward contract is a derivative contract in which two parties agree to buy or sell an underlying asset, financial instrument, or other reference at a predetermined price on a specified future date.

The predetermined price is commonly called the forward price. Unlike an option, a forward contract generally creates an obligation for both parties to complete the transaction according to the contractual terms.

Forward contracts are commonly used for hedging, risk management, and speculation. They are generally negotiated over the counter and can be customized according to the requirements of the counterparties.

Concept

A simplified forward contract can be represented as:

$t_0\to t_T$

where:

• $t_0$ = date on which the forward contract is entered into;
• $t_T$ = contractual settlement date.

At maturity, the buyer agrees to purchase the underlying at the predetermined forward price $K$.

A simplified long-forward payoff is:

${\text{Payoff}}_{\text{Long}}=S_T-K$

where:

• $S_T$ = market price of the underlying asset at maturity;
• $K$ = agreed forward price.

The payoff of a short-forward position is:

${\text{Payoff}}_{\text{Short}}=K-S_T$

Long and short positions

The party agreeing to buy the underlying asset is said to hold a long forward position.

The party agreeing to sell the underlying asset is said to hold a short forward position.

The basic relationship is:

$\text{Long Forward}\to \text{Buy at }K$

$\text{Short Forward}\to \text{Sell at }K$

If the market price at maturity is greater than the agreed forward price, the long position has a positive payoff.

If the market price at maturity is below the agreed forward price, the short position has a positive payoff.

Forward price

The forward price is the price agreed at the beginning of the contract for the future transaction.

For a simplified non-income-producing asset under continuous compounding, the theoretical forward price can be represented as:

$F_0=S_0{e}^{rT}$

where:

• $F_0$ = theoretical forward price;
• $S_0$ = current spot price;
• $r$ = continuously compounded risk-free interest rate;
• $T$ = time to maturity.

The precise forward-pricing relationship depends on factors such as income, dividends, storage costs, convenience yield, financing costs, and the characteristics of the underlying asset.

Forward pricing with income

For an asset providing a continuous income yield $q$, a simplified forward-price relationship is:

$F_0=S_0{e}^{(r-q)T}$

where:

• $q$ = continuous income or dividend yield.

For physical commodities, the pricing relationship may also incorporate storage costs and convenience yield.

Value of a forward contract

At inception, a fairly priced forward contract generally has a value close to zero before consideration of transaction costs, credit effects, and other adjustments.

After the contract has been entered into, changes in the underlying asset price and other market variables can cause the contract to have positive or negative value.

For a simplified long forward:

$V_T=S_T-K$

at maturity.

Before maturity, the value depends on the present value of the expected future payoff.

A simplified representation is:

$V_t=PV(S_T-K)$

where $PV$ represents present value.

Example

Suppose a company expects to purchase 10,000 units of a commodity in six months and is concerned that the price may increase.

The company enters into a forward contract agreeing to purchase the commodity at $100 per unit.

The contractual value of the purchase is:

$10,000\times 100=\mathrm{\$}1,000,000$

If the market price at maturity is $120 per unit, the economic benefit of the long forward is:

$10,000\times (120-100)=\mathrm{\$}200,000$

The company can therefore acquire the commodity at the contracted price rather than the higher prevailing market price, subject to the contractual settlement structure.

If the market price instead falls to $90 per unit:

$10,000\times (90-100)=-\mathrm{\$}100,000$

The long forward position has a negative economic payoff relative to the market price.

Currency forward

A foreign-exchange forward is a forward contract in which two parties agree to exchange currencies at a predetermined exchange rate on a future date.

A simplified currency-forward payoff can be represented as:

$\text{Payoff}=N(S_T-K)$

where:

• $N$ = relevant foreign-currency amount;
• $S_T$ = spot exchange rate at maturity;
• $K$ = contracted forward exchange rate.

Currency forwards are commonly used by companies and investors to manage exposure to future exchange-rate movements.

Interest-rate forward

Forward contracts can also be used to establish an interest rate for a future period.

A Forward rate agreement (FRA) is an example of an interest-rate derivative in which counterparties agree on an interest rate applicable to a specified future period and notional amount.

A simplified settlement amount can be represented as:

$\text{Settlement}=N\times (r_{\text{Reference}}-r_{\text{Agreed}})\times t$

subject to the specific settlement and discounting provisions of the contract.

Commodity forwards

Commodity forwards allow producers, consumers, traders, and other market participants to agree on a future price for a commodity.

For example:

• an oil producer may sell oil forward;
• an airline may purchase fuel forward;
• an agricultural producer may sell future production forward;
• a manufacturer may purchase a commodity forward.

The purpose may be to reduce uncertainty about future revenues or costs.

Hedging with forward contracts

Forward contracts are widely used for hedging.

A company expecting to receive foreign currency in the future may sell that currency forward.

A simplified hedged exposure is:

$\text{Hedged Position}=\text{Underlying Exposure}+\text{Forward Contract}$

The objective is to reduce the effect of adverse movements in the underlying price or exchange rate.

For example, an exporter expecting to receive foreign currency may enter into a short currency forward to lock in the domestic-currency value of the expected receipt.

Speculation

Forward contracts can also be used to take directional positions on future prices.

An investor expecting an asset's price to rise may enter into a long forward.

An investor expecting the price to fall may enter into a short forward.

Unlike an option buyer, a forward participant generally does not pay an option premium to obtain the contractual right. Instead, both parties undertake contractual obligations.

Forward contracts and options

Forward contracts and options are both derivatives, but their contractual structures differ.

A forward generally creates an obligation for both parties:

$\text{Forward}\to \text{Obligation to Transact}$

An option gives the buyer a right without creating the same obligation for the option buyer:

$\text{Option}\to \text{Right but Not Obligation}$

An option buyer generally pays a premium for this right.

Forward contracts and futures

Forward contracts and futures contracts are similar because both can establish a future transaction price.

However, important differences exist.

Forward contracts are generally:

• privately negotiated;
• traded over the counter;
• customizable;
• subject to bilateral contractual arrangements.

Futures contracts are generally:

• standardized;
• traded on organized exchanges;
• centrally cleared;
• subject to standardized margin requirements.

A simplified comparison is:

$\text{Forward}=\text{Customized OTC Contract}$

$\text{Future}=\text{Standardized Exchange-Traded Contract}$

Settlement

Forward contracts can be settled through physical delivery or cash settlement, depending on the contractual terms.

Physical settlement requires delivery of the underlying asset or instrument.

Cash settlement involves payment of the difference between the agreed price and the relevant settlement price.

A simplified cash settlement for a long position is:

$\text{Cash Settlement}=Q(S_T-K)$

where:

• $Q$ = contract quantity;
• $S_T$ = settlement price;
• $K$ = contracted forward price.

Notional amount

The notional amount represents the quantity or reference value used to determine the economic exposure of the contract.

For a forward involving an asset quantity $Q$:

$\text{Notional Value}=Q\times F_0$

The notional value does not necessarily represent an amount exchanged when the contract is entered into.

Counterparty risk

Because forward contracts are generally negotiated directly between counterparties, they can involve counterparty credit risk.

One party may fail to fulfill its contractual obligation at maturity.

The risk is particularly relevant when the forward contract has substantial positive value to one counterparty.

Collateral arrangements, credit limits, netting agreements, and other risk-management mechanisms may be used to reduce counterparty exposure.

Liquidity risk

Forward contracts can involve liquidity risk because customized OTC contracts may not have an active secondary market.

A party seeking to terminate a forward before maturity may need to negotiate with the counterparty or enter into an offsetting transaction.

The cost of terminating the contract can therefore depend on prevailing market conditions.

Basis risk

Basis risk occurs when the forward contract does not perfectly offset the underlying exposure.

For example, a company may hedge an expected commodity purchase with a forward contract referencing a related but different commodity or delivery location.

A simplified residual exposure is:

$\text{Residual Exposure}=\text{Underlying Price Change}-\text{Forward Price Change}$

The residual amount represents the portion of the original risk that remains after the hedge.

Advantages

Potential advantages of forward contracts include:

• customized contract terms;
• flexibility in maturity dates;
• flexibility in contract size;
• direct management of specific exposures;
• ability to lock in future prices or exchange rates;
• usefulness for corporate risk management.

Disadvantages

Potential disadvantages include:

• counterparty risk;
• limited secondary-market liquidity;
• basis risk;
• valuation complexity;
• potential opportunity cost;
• contractual obligations for both parties;
• termination risk;
• collateral or credit-support requirements in some arrangements.

A forward contract can protect against an adverse price movement while also preventing the hedging party from fully benefiting from a favorable price movement.

Risk management

The effectiveness of a forward hedge depends on the relationship between the underlying exposure and the forward contract.

A simplified hedge ratio is:

$h=\frac{\text{Forward Position}}{\text{Underlying Exposure}}$

The appropriate hedge ratio depends on the size and characteristics of the underlying exposure and the objectives of the hedging strategy.

Importance

Forward contracts are important instruments in financial risk management because they allow counterparties to establish prices, exchange rates, or other contractual terms for future transactions. They are particularly useful when the underlying exposure is known in advance and the parties require a customized hedge.

However, because forward contracts are generally privately negotiated and create obligations for both parties, they involve counterparty, liquidity, basis, and market risks. Their use therefore requires consideration of the underlying exposure, contractual terms, creditworthiness of the counterparties, and applicable settlement arrangements.

See also

• Derivative (finance)
• Hedging
• Futures contract
• Option (finance)
• Swap (finance)
• Forward rate agreement
• Foreign exchange
• Currency swap
• Basis risk
• Counterparty risk
• Liquidity risk
• Risk management
• Over-the-counter
• Financial risk
• Commodity
• Interest rate