FRM Exam Part I · Introduction to Derivatives

Forward Contract Payoff: Long and Short Positions

Updated 11 October 2026 · Fact-checked

A forward contract is an agreement to buy or sell an asset at a fixed delivery price on a set future date. At maturity, the long payoff is S_T − K and the short payoff is K − S_T, where S_T is the spot price and K is the delivery price. The two payoffs sum to zero.

Understand Forward Contracts and Payoffs

A forward contract is a private agreement between two parties to trade an asset at a future date for a price fixed today. That fixed price is the delivery price, written K. The contract is traded over the counter, so its terms (asset, quantity, date) can be customised.

The party who agrees to buy is in the long position. The party who agrees to sell is in the short position. Nothing is usually paid upfront. The forward price is set so the contract has zero value at the start.

At maturity, the long buys at K and could sell at the spot price S_T. If S_T is above K, the long gains. If S_T is below K, the long loses. The short is the mirror image. Every gain for one side is an equal loss for the other, so the contract is a zero-sum game.

The payoff is linear in S_T. It has no cap on the long's gain and no floor on the long's loss (other than S_T = 0). This is different from an option, where the holder can walk away. A forward is an obligation for both sides.

Forwards differ from futures. Futures are standardised, exchange-traded and settled daily through margin, so counterparty risk is low. Forwards are OTC and usually settle only at maturity, so each side carries the other's default risk. Payoffs at maturity look the same in both.

Key formulas to remember

Long forward payoff at maturity: Payoff (long) = S_T − K; Per unit of the asset. Multiply by the contract size for the total.
Short forward payoff at maturity: Payoff (short) = K − S_T; Exactly the negative of the long payoff.
Zero-sum check: Payoff (long) + Payoff (short) = 0; Ignores credit default and transaction costs.
Total payoff: Total = (S_T − K) × contract size for the long; Use the opposite sign for the short.

How to solve Forward Contracts and Payoffs questions

Use this routine for any question on forward payoffs, whatever the asset or currency.

1Identify which side you are asked about: long (buyer) or short (seller).
2Write down the delivery price K and the spot price S_T at maturity. Make sure both are in the same units and currency.
3Check the contract size, such as 1,000 barrels or 100 ounces, and note the number of contracts.
4Compute S_T − K for the long, or K − S_T for the short.
5Multiply by the contract size and number of contracts.
6Check the sign: a gain is positive, a loss is negative. Confirm the other party has the opposite result.
7If the question asks about value before maturity, stop: that needs the forward pricing formulas, not the payoff.

Quickest way: Direction check, then subtract

When to use it: Use when several options look close and you have little time.

Ask: did spot end above or below K?
If spot is above K, the long wins and the short loses. If below, the reverse.
Compute the absolute gap |S_T − K|, then apply the sign from the direction.
Multiply by the total quantity and match to the option.

Common mistakes in Forward Contracts and Payoffs

Using K − S_T for the long position.
Students mix up the long and short formulas under pressure.
Fix: Remember that the long profits when prices rise, so the long payoff is S_T − K.
Treating the forward payoff like an option payoff with max(S_T − K, 0).
Option payoffs are learned first and feel familiar.
Fix: A forward is an obligation. The payoff can be negative with no floor at zero.
Forgetting to multiply by the contract size.
The per-unit answer looks like a finished answer.
Fix: Reread the question for units and size before you choose an option.
Assuming the forward costs money to enter.
Students confuse forwards with options, which carry a premium.
Fix: A forward is normally entered at zero cost because the forward price is set to give zero initial value.
Saying forwards and futures have identical risks.
Their maturity payoffs look alike.
Fix: Futures are exchange-traded with daily margining. Forwards are OTC and carry counterparty credit risk.

Worked examples

Example 1

A company enters a long forward to buy 5,000 barrels of oil at a delivery price of USD 80 per barrel. At maturity the spot price is USD 86. What is the payoff to the long position?

Show the solution

Long payoff per barrel = S_T − K = 86 − 80 = USD 6.
Total payoff = 6 × 5,000 = USD 30,000.

Answer: The long gains USD 30,000.

Example 2

A bank is short a forward contract to sell EUR 2,000,000 at a delivery rate of USD 1.10 per EUR. At maturity the spot rate is USD 1.13 per EUR. What is the bank's payoff?

Show the solution

Short payoff per EUR = K − S_T = 1.10 − 1.13 = −USD 0.03.
Total payoff = −0.03 × 2,000,000 = −USD 60,000.
The counterparty (long) gains USD 60,000.

Answer: The short position loses USD 60,000.

Exam tips

Write S_T − K for the long and K − S_T for the short at the top of your scratch sheet before you read the options.
Read whether the question asks for payoff at maturity or value before maturity. They use different formulas.
Check the currency quote. A rate of USD per EUR and EUR per USD are opposite, and mixing them flips the answer.
Expect conceptual questions on forward versus futures: OTC versus exchange, customised versus standard, credit risk versus margining.

Practice questions from Introduction to Derivatives

Forward Contracts and Payoffs in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Forward Contracts and Payoffs: frequently asked questions

What is the payoff of a long forward contract?

At maturity it is S_T − K per unit, where S_T is the spot price and K is the delivery price. The long gains if spot is above K and loses if spot is below K.

What is the difference between forward and futures contracts?

Forwards are private OTC contracts, customised, and normally settled at maturity. Futures are standardised, exchange-traded and marked to market daily with margin. This makes counterparty risk much lower in futures.

Can a forward contract payoff be negative?

Yes. Both sides are obligated to trade, so either party can lose. There is no premium paid and no right to walk away, unlike an option.

Is the payoff the same as the value of a forward?

No. The payoff applies at maturity only. Before maturity, the forward has a value that depends on the current spot price, interest rates and time left.