Forward contracts: payoff for the long and the short
A forward is a private agreement to buy or sell an underlying at a fixed price, F₀(T), on a future date. Nothing is paid upfront. At expiration the buyer (long) gains S_T − F₀(T) and the seller (short) gains F₀(T) − S_T, so one side's gain is the other's loss.
Before this: What a derivative is
On the exam
- Define forward contracts, futures contracts, swaps, options (calls and puts), and credit derivatives and compare their basic characteristics
Define forward contracts and compare them with other derivatives. Expect the payoff at expiration for either side, the value of a forward at inception (zero), the counterparty risk each side carries, and why the payoff is called linear.
How deeply to learn each part
- Know the idea
- Understand it in general. It frames other topics, but you will not calculate with it.
- Use it
- Understand it well enough to solve a question with it. Recognize when it applies.
- Memorize
- Learn it by heart. The exam will not give it to you.
You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.
You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.
What does a forward contract commit you to?
A forward contract is an over-the-counter (OTC) agreement in which one party, the buyer, will purchase an underlying from the other, the seller, on a set future date at a price fixed today. It is a firm commitment: both sides must perform.
Like every firm commitment, it names a contract size, an underlying, a date T for the exchange and the agreed price. The agreed price is the forward price , written F₀(T). The subscript 0 says the price was set today (t = 0), and the T in brackets says the exchange happens at time T. The spot price of the underlying at that date is S_T.
- Forward Memorize OTC, customized, a single exchange at T
- Futures Memorize exchange-traded, standardized, settled daily
- Swap Memorize a series of exchanges, usually fixed for floating
A forward is the most flexible of the three. The parties can tailor the size, the underlying, the date and the credit terms to the exposure they want to hedge, such as an importer locking in the price of foreign currency for a delivery next quarter. The cost of that flexibility is that the contract is private and bilateral.
- The buyer holds the long forward : a position that gains when the underlying rises.
- The seller holds the short forward : a position that gains when the underlying falls.
No cash changes hands at t = 0. F₀(T) is chosen so that the contract is worth nothing to either side when it is agreed, a state called zero value at inception . How that price is found is the subject of the forward pricing module. Here, take F₀(T) as given.
What does each side receive at expiration?
At time T the contract settles on the difference between the spot price and the forward price. It can be settled by physical delivery of the underlying or in cash. Most financial forwards settle in cash.
Because nothing was paid upfront, the payoff is also the profit. The two formulas have opposite signs, so the long’s gain is exactly the short’s loss: a forward is a zero-sum bet between two parties.
- S_T above F₀(T) Memorize long gains, short loses
- S_T below F₀(T) Memorize long loses, short gains
- S_T equal to F₀(T) Use it nothing changes hands
A refiner agrees to buy 40000 barrels under a cash-settled forward at 82.00 a barrel. At expiration the spot price is 87.00. The settlement the refiner receives (a negative number means it pays) is closest to:
40000 × (87.00 − 82.00) = 200,000.00
Gain to the buyer, P200,000.00
- 87−82=×40000=200,000.00
- 87ENTER82−40000×200,000.00
ENTER enter (on the HP, puts the number on the stack)
Try this 0 of 3
- Find the spot price at expiry where neither side gains or loses
- As the long, set the spot at expiry to USD 77 and read the refinery's result
- Switch to the short and find the spot price that pays the dealer USD 200,000
A refinery agrees today to buy crude from a dealer in three months at USD 82 a barrel. Nothing is paid now. Drag the spot price at expiry and read each side's payoff.
A long forward at F₀(T) = USD 82 pays S_T − 82 per barrel: a straight 45-degree line through 82. The short's line is its mirror image. At S_T = USD 87 the long's payoff is +USD 5 a barrel and the short's is −USD 5, so one side's gain is the other's loss.
+USD 5 per barrel × 40,000 = USD 200,000
The refinery (long) gains USD 200,000, and the dealer (short) loses the same. Together: zero.
Show working
Long payoff = S_T − F₀(T) = 87 − 82 = +USD 5 per barrel
Total = 5 × 40,000 = USD 200,000
No premium was paid at the start, so payoff = profit. Cash-settled, only USD 200,000 changes hands.
- 87−82=5 per barrel
- ×40000=200,000
- 87ENTER82−5 per barrel
- 40000×200,000
ENTER enter (on the HP, puts the number on the stack)
Display: 200,000
Each USD 1 move in S_T changes the payoff by exactly USD 1 per barrel, in both directions. That straight-line shape is why forwards, futures and swaps are called linear derivatives .
Exam tip Whatever the long gets, the short loses. If you can do the long’s payoff, flip the sign for the short and you are done.
What risk does each side carry?
Both parties face counterparty credit risk , because a forward is a private promise with no exchange standing behind it. At expiration, the side that is owed money depends on the other side paying. Before expiration the position can have a positive or negative market value, and the side with the positive value is the one exposed.
Dealers often reduce this risk by agreeing collateral terms, similar to the margin on futures. The next lesson shows what a fully standardized, exchange-guaranteed version looks like.
Go deeper Physical delivery or cash settlement?
A forward can specify actual delivery of the underlying or settlement in cash for the difference. Cash settlement is easier when the underlying is an index, a rate or something awkward to deliver. The settlement amount is the same either way: F₀(T) is paid for the underlying that is worth S_T, so the net transfer is the difference. A buyer in the cash market would instead pay S₀ today and earn S_T − S₀, which is a different payoff, because S₀ is not the forward price.
Go deeper Closing a forward early
A forward cannot be sold on an exchange. To get out before T you usually agree an offsetting contract, often with the same dealer, and the two forwards then net against each other. The credit exposure to each counterparty can remain until T, which is one reason some dealers prefer a termination payment instead.
Go deeper Collateral in OTC forwards
Counterparties can sign a credit support annex that requires the side with the negative market value to post collateral. This borrows the margin idea from futures. It cuts counterparty risk but does not remove it, and it is negotiated, not standard.
Memorize this
MemorizeForward payoffs at expiration
| Position | Payoff = profit | Gains when |
|---|---|---|
| Long (buyer) | the underlying rises | |
| Short (seller) | the underlying falls |
Memory hook Long = "what it is worth, minus what I agreed to pay". The short is the mirror image, so the two payoffs always add to zero.
Know it cold Nothing is paid at the start, so payoff = profit, and the value at inception is zero. Use , never today's spot.
MemorizeWhat a forward is
Memory hook Private, tailor-made, one exchange, both must perform.
Know it cold OTC and customized; a firm commitment; linear payoff; both sides carry counterparty credit risk.
- Forward Memorize OTC, customized, a single exchange at T
- Futures Memorize exchange-traded, standardized, settled daily
- Swap Memorize a series of exchanges, usually fixed for floating
- S_T above F₀(T) Memorize long gains, short loses
- S_T below F₀(T) Memorize long loses, short gains
- S_T equal to F₀(T) Use it nothing changes hands
Quick example
Long 1,000 ounces of silver at USD 30.00; spot at expiration USD 33.50. (33.50 − 30.00) × 1,000 = USD 3,500.
- 33.5−30=×1000= 3500
- 33.5ENTER30−1000× 3500
ENTER enter (on the HP, puts the number on the stack)
Quick example
Short 8,000 bushels of wheat at USD 6.40; spot at expiration USD 5.90. (6.40 − 5.90) × 8,000 = USD 4,000.
- 6.4−5.9=×8000= 4000
- 6.4ENTER5.9−8000× 4000
ENTER enter (on the HP, puts the number on the stack)
How it is asked
-
Payoff for a short
Short forward on 5,000 units at 120; the underlying ends at 131. Payoff?
(120 − 131) × 5,000 = −55,000. Trap: the long's sign (+55,000).
-
Value at inception
What is the value of a newly agreed forward to the long?
Zero. F₀(T) is set so neither side pays upfront. Trap: "the buyer gets the asset, so it is worth something".
-
Linear or not
Which describes a forward payoff: linear or non-linear, upfront payment or none?
Linear, no upfront payment. Options are the non-linear ones.
-
Who bears credit risk
Which party to a forward faces counterparty credit risk?
Both, because whichever side is owed money at expiration depends on the other paying.
Exam traps
- Saying the forward buyer pays something at inception. No cash changes hands; F₀(T) is set so the value is zero.
- Using today's spot price instead of F₀(T) in the payoff. The agreed price is F₀(T); today's spot never enters the settlement.
- Thinking only the long faces counterparty risk. Whichever side is owed money at expiration carries it.
- Getting the short's sign wrong. The short's payoff is F₀(T) − S_T, the long's with the sign flipped.
Checkpoint
4 exam-style questions. About 90 seconds each.
1At initiation, the value of a forward contract to the long is most likely:
2An investor is short a forward contract on 10,000 shares at INR 640 per share. At expiration the share price is INR 610. The investor's payoff is closest to:
3Forward contracts are best described as:
4A buyer enters a forward at USD 120 per unit when the spot price is USD 115. At expiration the spot price is USD 118. The buyer's payoff per unit is closest to:
Key takeaways
- A forward is an OTC, customized firm commitment with zero value at inception.
- Long payoff S_T − F₀(T); short payoff F₀(T) − S_T. With no premium, payoff equals profit.
- The long's gain is exactly the short's loss, and the payoff is a straight line in S_T.
- Both sides face counterparty credit risk.
Quick example
Long 1,000 ounces of silver at USD 30.00; spot at expiration USD 33.50. (33.50 − 30.00) × 1,000 = USD 3,500.
- 33.5−30=×1000= 3500
- 33.5ENTER30−1000× 3500
ENTER enter (on the HP, puts the number on the stack)
Quick example
Short 8,000 bushels of wheat at USD 6.40; spot at expiration USD 5.90. (6.40 − 5.90) × 8,000 = USD 4,000.
- 6.4−5.9=×8000= 4000
- 6.4ENTER5.9−8000× 4000
ENTER enter (on the HP, puts the number on the stack)
All Derivatives formulas, every lesson
Practice exam-style questions on Forwards, Futures, Swaps, Options and Credit Derivatives
Questions about this lesson?
Where this comes back
- Futures contracts, daily settlement and margin calls Forwards, Futures, Swaps, Options and Credit Derivatives
- Pricing and Valuing Forward Contracts and FRAs Derivatives
Questions candidates ask
What is the payoff of a long forward contract?
The long forward's payoff at expiration is the spot price minus the forward price, S_T − F₀(T). With a forward at USD 82 and a spot price of USD 87 at expiration, the long gains USD 5 per unit. The short loses the same amount.
Why does a forward contract have zero value at inception?
The forward price is set so that neither party pays anything upfront, which makes the contract fair to both. Value appears later, as the underlying price moves away from F₀(T), and it is positive for one side and negative for the other.
What is the difference between a forward and a futures contract?
A forward is a customized OTC contract settled at expiration, with counterparty risk on both sides. A futures contract is standardized, traded on an exchange and settled every day through margin accounts, which makes counterparty risk small.
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