Payoff Charts for Futures contracts
This sub‑topic explains how payoff charts illustrate the profit or loss of futures contracts. Understanding these charts helps you visualise the impact of spot price movements on long and short positions, a key requirement for the NISM Series VIII exam. The content links the mathematical payoff formulas to their graphical representation and highlights common exam pitfalls.
Learning Objectives
- 1Define the payoff of a futures contract for long and short positions.
- 2Apply the standard payoff formulas using contract size.
- 3Interpret payoff charts and identify break‑even points.
- 4Avoid typical mistakes related to directionality and contract multiplier.
Understanding Futures Payoff
A futures contract is an agreement to buy or sell an underlying asset at a predetermined price (the futures price) on a specified future date. Unlike forwards, futures are standardized, exchange‑traded, and settled daily through mark‑to‑market. For exam purposes, the key outcome of a futures position is the profit or loss realized when the contract is closed or at expiry.
The profit or loss, often called the payoff, depends on two variables: the spot price of the underlying at expiry (S_T) and the futures price at the time the position was entered (F_0). Because each futures contract represents a fixed number of units of the underlying (the contract size Q), the monetary payoff is the price difference multiplied by Q.
In the NISM syllabus, candidates are expected to compute payoff, plot it against possible spot prices, and read the chart to answer multiple‑choice questions. Remember that the shape of the payoff line is linear, and the slope changes sign when you switch from a long to a short position.
Many candidates calculate (S_T ‑ F_0) correctly but omit multiplying by the contract size Q. The exam will mark the answer wrong because the monetary payoff is expressed in rupees, not in price points.
Payoff Formula for a Long Futures Position
Where:
S_{T}= Spot price of the underlying at expiry (₹ per unit)F_{0}= Futures price at contract initiation (₹ per unit)Q= Contract size – number of units covered by one futures contractWorked Example
Given F_{0}=1,500, S_{T}=1,600, Q=500: Step 1: Difference = 1,600 - 1,500 = 100 Step 2: Payoff = 100 \times 500 = 50,000 Verification: (1,600 - 1,500) \times 500 = 50,000.
The formula shows that a long futures holder benefits when the spot price at expiry exceeds the futures price paid. The payoff is positive (profit) if S_T > F_0, zero at the break‑even point (S_T = F_0), and negative (loss) when the market moves opposite to the position.
Because the payoff is linear, each one‑point movement in the spot price changes the monetary outcome by Q rupees. For a contract size of 500 shares, a 1‑point rise yields a ₹500 gain, and a 1‑point fall yields a ₹500 loss.
Exam questions often present a range of possible spot prices. You can quickly compute the payoff at each price by plugging the values into the formula, then plot the points to draw the straight‑line chart.
Payoff Formula for a Short Futures Position
Where:
F_{0}= Futures price at contract initiation (₹ per unit)S_{T}= Spot price of the underlying at expiry (₹ per unit)Q= Contract size – number of units covered by one futures contractWorked Example
Given F_{0}=1,500, S_{T}=1,600, Q=500: Step 1: Difference = 1,500 - 1,600 = -100 Step 2: Payoff = -100 \times 500 = -50,000 Verification: (1,500 - 1,600) \times 500 = -50,000.
A short futures position profits when the spot price falls below the futures price originally sold. The payoff becomes positive when S_T < F_0, zero at the break‑even point, and negative when the market rises.
Just as with the long side, the slope of the payoff line is constant but opposite in sign. For each one‑point increase in the spot price, the short holder loses Q rupees; each one‑point decrease yields a gain of Q rupees.
In the exam, you may be asked to identify whether a chart represents a long or short position. Look at the slope: upward‑sloping lines indicate long positions, while downward‑sloping lines indicate short positions.
Payoff Charts – Visual Representation
A payoff chart plots the monetary payoff on the vertical axis against possible spot prices on the horizontal axis. The chart for a long futures contract is a straight line with a positive slope, crossing the horizontal axis at the futures price (F_0). The short contract chart is a mirror image with a negative slope.
The break‑even point, where payoff equals zero, always occurs at S_T = F_0. The distance from the break‑even point to any spot price multiplied by the contract size gives the exact rupee amount shown on the vertical axis.
Examiners use these charts to test your ability to read and interpret linear relationships. You may be given a partially drawn chart and asked to fill in missing values, or you may need to select the correct chart for a described position.
Payoff Profiles for Long and Short Futures (Q = 500)
Comparative Summary – Long vs Short Futures
Key differences between long and short futures payoff characteristics
| Position | Payoff Formula | Break‑Even Spot (S_T) | Risk Direction | Reward Direction |
|---|---|---|---|---|
| Long | (S_T - F_0) \times Q | S_T = F_0 | Loss when spot falls | Gain when spot rises |
| Short | (F_0 - S_T) \times Q | S_T = F_0 | Loss when spot rises | Gain when spot falls |
If the chart slopes upward to the right, it is a long position; if it slopes downward, it is a short position. Confusing the two is a frequent cause of lost marks.
Scenario
Rohan enters a long NIFTY futures contract when the index futures price is 15,000 points. Each contract represents 75 index points (Q = 75). At expiry, the NIFTY spot index closes at 15,250 points.
Solution
Step 1: Compute price difference = 15,250 - 15,000 = 250 points.\nStep 2: Multiply by contract size = 250 \times 75 = 18,750.\nStep 3: Since Rohan is long, the payoff is +₹18,750.\nStep 4: Break‑even spot = 15,000 points (where payoff would be zero).\nStep 5: If the spot had been 14,800, payoff would be (14,800 - 15,000) \times 75 = -200 \times 75 = -₹15,000, indicating a loss.
Conclusion
The example shows how a simple linear calculation yields the monetary outcome. Remember to always multiply the price difference by the contract size and to check the direction of the position before assigning the sign.
⭐Exam Takeaways
- Long futures payoff = (Spot at expiry – Futures price) × Contract size; short payoff = (Futures price – Spot at expiry) × Contract size.
- The break‑even spot price is always equal to the futures price at contract initiation (S_T = F_0).
- Payoff charts are straight lines: upward slope for long, downward slope for short.
- Never forget to multiply the price difference by the contract multiplier Q; the exam often tests this explicitly.
- Identify the slope direction to determine whether the chart represents a long or short position.
- For each one‑point move in the underlying, the monetary impact equals Q rupees.
- Use the formula to fill missing values on a partially drawn chart – a common NISM multiple‑choice format.
Practice Questions
8 questions on Payoff Charts for Futures contracts
What is the payoff formula for a long futures position?
At what spot price does a futures contract break even?
A trader enters a short futures contract with F_0 = ₹1,200, Q = 400 units. If the spot price at expiry is S_T = ₹1,150, what is the monetary payoff?
On a payoff chart, which slope indicates a long futures position?
For a futures contract with Q = 500, the payoff chart shows a long position payoff of ₹50,000 at a spot price of ₹1,600. What would be the payoff at a spot price of ₹1,650?
Rohan buys a long NIFTY futures contract at F_0 = 15,000 points with Q = 75. If the spot index at expiry is 15,250 points, what is his payoff?
A common exam mistake is to compute (S_T - F_0) without multiplying by Q. If S_T = 1,600, F_0 = 1,500 and Q = 500, what error in rupees would result from this omission?
Which statement correctly describes the risk direction for a short futures position?