Pay-off
Also written Payoff · Pay-off profile · Pay-off diagram
The profit or loss on a position at expiry, stated as a function of the settlement price — positive when the trade makes money, negative when it loses.
In plain language
A pay-off is just the answer to one question: at each possible expiry price, how much do I end up with?
Drawn as a graph, it is a pay-off diagram, and the shape of that graph is the single clearest way to tell instruments apart. A futures pay-off is a straight line — every rupee the commodity moves is a rupee to you, in either direction, and the buyer's line is the exact mirror of the seller's.
An option pay-off has a kink. Below the strike a long call earns nothing more however far the price falls, because the buyer simply walks away; above it the line rises one-for-one. That bend is the optionality, and it is what the premium buys.
How it works
For futures the arithmetic is two subtractions and nothing else. Buy at Rs 100, and at an expiry price of Rs 110 you gain Rs 10; at Rs 90 you lose Rs 10. The seller's numbers are the same with the signs reversed, because one side's gain is always the other side's loss.
Options break that symmetry, and the workbook's risk-reward table is the examinable summary:
| Position | Maximum risk | Maximum reward |
|---|---|---|
| Long call | Limited to premium | Unlimited |
| Short call | Unlimited | Limited to premium |
| Long put | Limited to premium | Strike price less premium |
| Short put | Strike price less premium | Limited to premium |
The put rows are the ones candidates get wrong. A long put cannot earn without limit, because the commodity cannot fall below zero — the most it can deliver is the strike, less what was paid for it.
The formula
Long futures pay-off = ST - F
Short futures pay-off = F - ST
where ST is the spot price at expiry and F the price at which the futures contract was traded.
For options, at expiry:
Long call = max(ST - X, 0) - premium
Long put = max(X - ST, 0) - premium
A worked example
Futures, the linear case. A trader expects gold to rise and in April buys one 1 kilogram gold futures contract at Rs 50,000 per 10 grams — a contract value of Rs 50,00,000. In May the June futures reach Rs 55,000 per 10 grams and he squares off.
Pay-off = (55,000 - 50,000) x 100 units of 10 g = Rs 5,00,000
Had gold fallen to Rs 45,000 instead, the pay-off would have been minus Rs 5,00,000. Same size, opposite sign — that is what linear means.
Options, the kinked case. Zinc, strike Rs 180, call premium Rs 10, put premium Rs 8, on the workbook's zinc lot of 5 MT = 5,000 kilograms:
| Expiry price | Call buyer, per kg | Call buyer, per lot |
|---|---|---|
| Rs 140 | −10 | −Rs 50,000 |
| Rs 160 | −10 | −Rs 50,000 |
| Rs 180 | −10 | −Rs 50,000 |
| Rs 200 | +10 | +Rs 50,000 |
| Rs 220 | +30 | +Rs 1,50,000 |
Below Rs 180 the loss stops dead at the premium — Rs 50,000 on the lot, whether zinc lands at Rs 160 or at Rs 40. Above Rs 190 it runs. The call seller's column is this one inverted, and his upside stops at the Rs 50,000 he collected.
Why NISM asks about it
Chapter 3 (Commodity Futures), section 3.8, for the long and short futures pay-off formulae and their tables, and Chapter 4 (Commodity Options), section 4.3, for the option pay-off profiles and the risk-reward table. Expect to be handed a strike, a premium and a settlement price and asked for the net position of one of the four parties, and expect "maximum loss to the buyer of an option is ____" (the premium).
Common exam traps
- A long put is not unlimited upside. Its ceiling is the strike price less the premium, because the underlying cannot go below zero.
- Pay-off is measured against the settlement price, not the last traded price. The workbook is careful that LTP and DSP/FSP are different numbers.
- Premium is sunk. The buyer of a call that expires worthless loses the premium regardless of how far out of the money it finished; the workbook's zinc table shows the same −Rs 10 at 160 and at 140.
- Futures pay-offs are symmetric; option pay-offs are not. A question that says "the return would fall by the same amount for the same fall in price" is describing a future, not an option.
- The option buyer's gain equals the option seller's loss in every cash-settled case — the workbook says so twice in the same table.
- Adding CTT, brokerage and GST turns a small positive pay-off negative. That is exactly why a contrary instruction exists.
Check yourself
1.A trader sells (shorts) a commodity futures contract at Rs 100. If the spot price on maturity is Rs 90, what is the pay-off?
- a)A loss of Rs 10
- b)A profit of Rs 10
- c)No profit or loss
- d)A profit of Rs 90
Show the answer
Answer: (b) A profit of Rs 10
Short pay-off = F − ST = 100 − 90 = a profit of Rs 10.
The workbook explains the mechanics rather than just the formula: the short seller can buy at Rs 90 in the spot market on the expiry day and immediately deliver it to the futures buyer and receive Rs 100 from the futures buyer, thereby making a profit of Rs 10.
Spot at expiry Short pay-off (sold at 100) 60 +40 90 +10 100 0 110 −10 140 −40 The lower the price of the underlying at expiry, the higher the profit made by the seller of the futures contract.
Option (a) is the answer to the long version of the same question — and the two are always exact mirror images, because the profits and losses for the short futures position will be exactly opposite of the long futures position. It is a zero-sum transfer between the two sides.
2.Why does the workbook warn against selective hedging?
- a)Because SEBI prohibits partial hedging of commodity exposures
- b)Because choosing when to hedge and when not to is as good as speculation, with pay-offs on both sides
- c)Because partial hedges attract higher margins than full hedges
- d)Because basis risk only arises when a hedge is partial
Show the answer
Answer: (b) Because choosing when to hedge and when not to is as good as speculation, with pay-offs on both sides
This is the most practically important sentence in the chapter. The moment a company decides when prices "look high", it has stopped hedging and started trading the commodity — with the operating business as collateral. The bet has simply moved from the price level to the timing of the decision.
And it explains a pattern that puzzles many boards: a hedging desk showing cumulative losses over three years is not evidence that hedging fails. If the desk was hedging selectively, it was speculating, and speculation loses about as often as it wins. A systematic hedge is not expected to make money at all — its output is certainty, not profit.
The other four limitations: price risk cannot be fully eliminated · basis risk continues to remain · transaction cost is to be incurred · margin is to be maintained, leading to cash flow pressures.
Where this is taught
- Series IV · Chapter 3: Exchange Traded Interest Rate Futuresintroduced here
- Series XVI · Chapter 3: Commodity Futuresintroduced here
Related terms
- Intrinsic valueWhat an asset is actually worth — the present value of the cash it will generate over its remaining life, as against whatever price the market is quoting today.
- Futures contractA standardised forward traded on an exchange, where the exchange fixes every term except the price and the clearing corporation guarantees settlement, so neither side carries the other's default risk.
- MoneynessWhether exercising an option right now would give the buyer a positive, zero or negative cash flow — classifying it as in the money, at the money or out of the money.
- OptionA contract giving the buyer the right, but not the obligation, to buy or sell the underlying at a stated price on or before a stated date, in exchange for a premium paid to the writer.
- Option premiumThe price an option buyer pays the seller for the right the contract carries — non-refundable, and made up of intrinsic value plus time value.
- Long speculatorA trader who buys first and expects the price to rise — a long futures or option position taken with no corresponding short position in the spot market and no intention of using the commodity.
- Short speculatorA speculator who sells a commodity futures contract first, expecting to buy it back later at a lower price — profiting from a price fall with no intention of ever taking or giving physical delivery.
- Asymmetric risk exposureThe defining pay-off feature of options: gains when the underlying moves one way differ sharply from losses when it moves the other way. Futures, by contrast, have symmetric exposure.