Pay-off Profile for Futures Contracts
The sub‑topic "Pay‑off Profile for Futures Contracts" explains how profit or loss is determined for both long and short positions in commodity futures. Understanding the payoff helps candidates answer exam questions on profit‑loss calculations, break‑even analysis, and risk characteristics. This concept links directly to the broader chapter on Commodity Futures and is a high‑frequency topic in NISM Series XVI.
Learning Objectives
- 1Define the payoff formula for long and short futures positions.
- 2Interpret profit‑loss diagrams and identify break‑even points.
- 3Explain the impact of daily mark‑to‑market settlement on cash flows.
- 4Compare the risk‑reward profile of long versus short futures.
Understanding Futures Pay‑off
A futures contract is a standardized agreement to buy or sell a specified quantity of a commodity at a predetermined price (the futures price, F₀) on a future date. Unlike forward contracts, futures are traded on exchanges and are subject to daily mark‑to‑market (MTM) settlement, which means gains and losses are realised each trading day.
The pay‑off of a futures contract is the net amount that the holder receives (or pays) at contract expiry, based solely on the difference between the spot price at expiry (S_T) and the original futures price (F₀). No premium is paid upfront like in options, so the entire exposure is captured by this price difference.
For the NISM exam, candidates must be able to write the payoff expressions, calculate profit or loss for given spot prices, and quickly determine the break‑even level (which is simply F₀). The exam often presents tables of spot prices; recognising the sign (+/–) for long and short positions is critical to avoid common mistakes.
- Long position benefits when the spot price at expiry is higher than the futures price.
- Short position benefits when the spot price at expiry is lower than the futures price.
Many candidates forget that a long futures payoff is <em>S_T – F₀</em> (positive when price rises) while a short payoff is <em>F₀ – S_T</em>. Reversing the sign leads to a wrong answer even if the arithmetic is correct.
Long Position Pay‑off
A trader who takes a long position agrees to buy the commodity at the futures price F₀. At expiry, the trader will actually purchase the commodity at the prevailing spot price S_T. The cash outcome is the difference S_T – F₀. If S_T exceeds F₀, the trader gains; if it is lower, the trader incurs a loss.
Because futures are settled daily, the trader’s margin account is adjusted each day by the change in the contract’s mark‑to‑market value. However, the final payoff at expiry still follows the same simple formula, irrespective of the intermediate cash flows.
In exam questions, you will often be given the entry futures price and a set of possible expiry spot prices. Apply the formula directly to each spot price to obtain the profit or loss for the long position.
Where:
S_T= Spot price of the commodity at expiry (₹ per unit)F_0= Initial futures price at which the contract was entered (₹ per unit)Worked Example
Given F_0 = 4,500 and S_T = 4,700: Step 1: Payoff = 4,700 - 4,500 Step 2: Payoff = 200 Verification: 4,700 - 4,500 = 200.
Short Position Pay‑off
A trader who takes a short position agrees to sell the commodity at the futures price F₀. At expiry, the trader must deliver the commodity at the prevailing spot price S_T. The cash outcome is the reverse of the long position: F₀ – S_T. The short gains when the spot price falls below the futures price.
Just like the long, the short’s margin account is adjusted daily through MTM. The cumulative effect of these adjustments equals the final payoff computed by the same formula.
Exam candidates should remember that the short payoff is the negative of the long payoff for the same spot price, which makes it easy to cross‑check answers.
Where:
F_0= Initial futures price (₹ per unit)S_T= Spot price at expiry (₹ per unit)Worked Example
Given F_0 = 4,500 and S_T = 4,700: Step 1: Payoff = 4,500 - 4,700 Step 2: Payoff = -200 Verification: 4,500 - 4,700 = -200.
Combined Pay‑off Diagram
The graphical representation of futures pay‑off is a straight line with a slope of +1 for the long and –1 for the short. The line crosses the horizontal axis at the futures price F₀, which is the break‑even point. To the right of F₀, the long line is positive (profit) and the short line is negative (loss). To the left, the situation reverses.
This linearity is a key differentiator from options, whose pay‑off curves are non‑linear because of the premium paid. For futures, the absence of an upfront premium means the maximum loss can be unlimited for both long and short positions, depending on price movement.
In the exam, you may be asked to sketch the diagram or to identify the profit zone for a given position. Remember the slope signs and the break‑even at F₀ – they are quick mental cues.
Pay‑off Comparison for Long vs Short Futures
Mark‑to‑Market and Settlement
SEBI‑regulated commodity futures are settled on a daily MTM basis. At the end of each trading day, the exchange calculates the difference between the previous day's settlement price and the current day's settlement price. This difference is credited or debited to the trader’s margin account.
If the account balance falls below the required maintenance margin, the trader receives a margin call and must top‑up the account. Conversely, a positive MTM results in a cash credit, reducing the amount of capital that must be held.
For the NISM exam, you may be asked to compute the cumulative cash flow after several days of price changes. The final payoff at expiry will always equal the sum of daily MTM adjustments, reinforcing the importance of monitoring margin requirements.
Students sometimes calculate only the expiry payoff and forget that daily MTM cash flows affect the effective profit. The total profit is the sum of all MTM credits/debits plus the final settlement.
Comparative Summary
Key Differences Between Long and Short Futures Positions
| Feature | Long Position | Short Position |
|---|---|---|
| Pay‑off Formula | S_T - F_0 | F_0 - S_T |
| Profit When Price | Rises (S_T > F_0) | Falls (S_T < F_0) |
| Loss When Price | Falls (S_T < F_0) | Rises (S_T > F_0) |
| Risk Profile | Unlimited loss if price falls sharply | Unlimited loss if price rises sharply |
| Typical User | Commodity producer hedging future purchase | Commodity trader/speculator betting on price fall |
Scenario
An Indian distributor enters a long futures contract for 10 grams of gold at a futures price of ₹45,000 per 10 g. The contract expires in 3 months. At expiry the spot price of gold is ₹48,000 per 10 g. The initial margin requirement was ₹5,000 and the daily MTM resulted in a net credit of ₹1,200 over the life of the contract.
Solution
Step 1: Compute expiry payoff using the long formula: Payoff = 48,000 – 45,000 = ₹3,000. Step 2: Add the cumulative MTM credit: Total profit = ₹3,000 + ₹1,200 = ₹4,200. Step 3: Subtract the initial margin (which was returned at expiry): Net cash received = ₹4,200 (the margin is merely a performance bond, not a cost). Thus the distributor earns a net profit of ₹4,200 on the contract.
Conclusion
The example shows how the final profit combines the price differential with daily MTM adjustments, a pattern frequently tested in NISM questions.
Practical Exam Tips
Memorise the two payoff formulas as mirror images; a quick way is to think "Long = Spot – Futures, Short = Futures – Spot". This helps you write the answer instantly.
When a question provides a table of possible spot prices, calculate the payoff for the first price, then add or subtract the same difference for subsequent prices – the slope is always ±1.
Always check whether the question asks for "profit" (positive only) or "pay‑off" (which can be negative). If profit is required, report the absolute value and indicate the direction (gain/loss).
Watch out for units: futures contracts are quoted per unit (e.g., per kilogram of wheat). Multiply the per‑unit payoff by the contract size to obtain the total profit or loss.
⭐Exam Takeaways
- Long futures payoff = Spot price at expiry (S_T) minus the initial futures price (F₀).
- Short futures payoff = F₀ minus S_T; it is the negative of the long payoff for the same spot price.
- Break‑even occurs exactly at S_T = F₀; profit zones are to the right for longs and to the left for shorts.
- Daily mark‑to‑market settles gains and losses; total profit equals the sum of MTM credits/debits plus the final payoff.
- Both long and short positions have unlimited loss potential; the risk profile is linear with slope +1 (long) or –1 (short).
- Remember to multiply per‑unit payoff by contract size and to include any MTM cash flows when the question asks for total profit.
- Typical exam traps: reversing sign conventions and ignoring MTM adjustments.
Practice Questions
8 questions on Pay-off Profile for Futures Contracts
What is the payoff formula for a long futures position?
At which spot price does a futures contract break even?
A short futures position is entered at F₀ = ₹4,500. At expiry the spot price S_T is ₹4,700. What is the payoff for the short position?
In the combined payoff diagram, what is the slope of the long futures payoff line?
A trader goes long a futures contract at F₀ = ₹4,400 per unit. Daily MTM over the life results in a net debit of ₹800. At expiry the spot price is ₹4,600. What is the total profit (including MTM) ignoring margin?
Which statement correctly describes the loss potential of futures positions?
Which of the following is a typical user of a short futures position?
What is the daily process called that settles gains and losses in SEBI‑regulated commodity futures?