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Futuresbeginner

Futures Payoff

The futures payoff is the cumulative profit or loss realised between entering the contract at price F0F_0 and the settlement price STS_T. For a long position the payoff is Πlong=ST−F0\Pi_{\text{long}} = S_T - F_0, and for a short it is Πshort=F0−ST\Pi_{\text{short}} = F_0 - S_T. The payoff diagram is a straight line with unit slope crossing zero at ST=F0S_T = F_0, with no premium and no embedded option, which makes futures the simplest linear derivative.

Why it matters

Plot profit on the vertical axis and the realised price STS_T on the horizontal axis. For a long, draw a 45-degree line passing through (F0,0)(F_0, 0). Every dollar above F0F_0 is a dollar of profit, every dollar below F0F_0 is a dollar of loss. The short's diagram is the mirror image across the horizontal axis. There is no kink, no curvature, and no entry cost beyond posting margin, which is why futures payoffs are often called linear while option payoffs are called hockey stick.

Formulas

Long payoff per unit
Πlong=ST−F0\Pi_{\text{long}} = S_T - F_0
Short payoff per unit
Πshort=F0−ST\Pi_{\text{short}} = F_0 - S_T
Total dollar profit
Π$=(ST−F0)×multiplier×N\Pi_{\$} = (S_T - F_0) \times \text{multiplier} \times N
NN is contracts held. Sign flips for the short side. Hull (2022) §1.3 gives the same expression.

Worked examples

Scenario

A trader is long one ASX SPI 200 futures contract at F0=7,500F_0 = 7{,}500. Multiplier is A$25. At final settlement ST=7,380S_T = 7{,}380.

Solution

Per index point payoff =7,380−7,500=−120= 7{,}380 - 7{,}500 = -120, so total profit =−120×25=−= -120 \times 25 = -A$3,000. The short side gains exactly A$3,000. The payoff is realised over the holding period through daily variation margin, not as one lump sum at expiry.

Scenario

A trader sells one CME E-mini S&P 500 futures contract at F0=5,200F_0 = 5{,}200, multiplier US$50. The contract settles at ST=5,120S_T = 5{,}120.

Solution

Short payoff per point =5,200−5,120=80= 5{,}200 - 5{,}120 = 80, total profit =80×50== 80 \times 50 = US$4,000. If the trader had been long the same contract, the realised loss would also be US$4,000, illustrating the zero-sum symmetry.

Common mistakes

  • ✗Futures payoffs include a premium like options. They do not. There is no upfront cost beyond posting initial margin, which is a refundable performance bond, so the payoff line crosses zero at F0F_0.
  • ✗Realising the payoff requires holding to delivery. The daily mark-to-market flow already pays out the cumulative profit St−F0S_t - F_0 as the price moves, so closing out before expiry yields the same economic outcome as holding to settlement at that day's price.
  • ✗Losses cannot exceed the initial margin. They can. Margin is replenished through margin calls to fund losses that exceed the original deposit, which is the central credit-risk mechanism of the clearing house.

Revision bullets

  • •Linear payoff with no premium and no floor or cap
  • •Long payoff Π=ST−F0\Pi = S_T - F_0, short payoff Π=F0−ST\Pi = F_0 - S_T
  • •Zero-sum between long and short counterparties
  • •Payoff diagram is a straight 45-degree line through (F0,0)(F_0, 0)
  • •Realised continuously through variation margin, not at expiry

Quick check

The payoff diagram for a long futures position is:

An investor is short two ASX SPI 200 futures at 7,300. The final settlement price is 7,420. Multiplier is A$25. Total profit or loss is:

Connected topics

Long/ShortMark-to-Mkt

In learning paths

Futures Path

Sources

  1. Hull (2022), §1.3 and Fig. 1.1
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Standard textbook payoff diagrams and formulas for long and short futures positions, including the linear shape and zero-sum interpretation.
  2. CME Group, Futures Payoff Profiles
    CME Group. Calculating P&L on a Futures Trade. CME Group Education, 2024.
    Step-by-step worked examples of computing payoffs with contract multipliers on benchmark US futures.
  3. ASX SPI 200 Brochure
    Australian Securities Exchange. ASX SPI 200 and Mini SPI 200 Brochure. ASX, 2023.
    Provides the A$25 per index point multiplier used in the worked SPI 200 examples.
How to cite this page
Dr. Phil's Quant Lab. (2026). Futures Payoff. Derivatives Atlas. https://phucnguyenvan.com/concept/futures-payoff
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