Pay off Charts of Futures Contract

This sub‑topic explains Pay‑off Charts of Futures Contracts, a visual tool that shows profit or loss at contract expiry for different spot price scenarios. Understanding these charts is essential for NISM Series I because exam questions frequently ask you to interpret or construct them. The content links the chart to the underlying payoff formulas, contract specifications, and exam‑style calculations.

Learning Objectives

1Define a payoff chart and identify its axes.
2Derive the payoff formulas for long and short currency futures.
3Construct a payoff chart using contract size and strike price.
4Analyse common exam traps related to payoff charts.

What is a Pay‑off Chart?

A payoff chart is a graphical representation that plots the profit or loss of a futures position against the spot price of the underlying currency at contract expiry. The horizontal axis (X‑axis) shows the spot price (in INR per unit of foreign currency) while the vertical axis (Y‑axis) shows the monetary payoff (in rupees) for the holder of the contract.

Because a futures contract is a linear derivative, the chart is a straight line. For a long (buyer) position the line slopes upward, indicating profit when the spot price exceeds the futures price. For a short (seller) position the line slopes downward, reflecting profit when the spot price falls below the futures price.

The slope of the line is determined by the contract size – the number of foreign‑currency units covered by one futures contract. In Indian currency futures, a standard contract size is often 10,000 USD or 100,000 EUR, but the exact size is specified in the exchange’s contract specifications.

Break‑even point – the spot price where payoff equals zero; it coincides with the futures price at entry.
Maximum gain/loss – theoretically unlimited for both long and short positions because the spot price can move indefinitely.

ℹ️Exam Trap – Mixing Up Axes

Students often reverse the axes and plot payoff on the X‑axis and spot price on the Y‑axis. Remember: spot price is always the horizontal axis; payoff is always vertical.

Long Position Pay‑off

A trader who buys (goes long) a currency futures contract expects the spot price to rise above the agreed futures price (also called the contract price). The profit or loss at expiry is simply the difference between the spot price at expiry (S_T) and the futures price at entry (F_0), multiplied by the contract size (Q).

If the spot price is higher than F_0, the trader gains; if it is lower, the trader incurs a loss. Because the relationship is linear, the payoff line for a long position passes through the origin of the chart when the spot price equals the futures price.

In exam questions, you may be given the futures price, contract size and a set of possible spot prices. You will need to calculate the payoff for each spot price and then select the correct chart or draw the line yourself.

∑Formula: Long Futures Pay‑off

(S_{T} - F_{0}) \times Q

Where:

S_{T}= Spot price of the underlying currency at contract expiry (INR per unit)

F_{0}= Futures price at which the contract was entered (INR per unit)

Q= Contract size – number of foreign‑currency units covered by one futures contract

Worked Example

Given F_{0}=75 INR/USD, Q=10,000 USD, and S_{T}=80 INR/USD: Step 1: Payoff = (80 - 75) × 10,000 Step 2: Payoff = 5 × 10,000 = 50,000 INR Verification: (80 - 75) × 10,000 = 50,000 INR.

Short Position Pay‑off

A trader who sells (goes short) a currency futures contract anticipates a fall in the spot price. The payoff for a short position is the opposite of the long payoff: the difference between the futures price at entry and the spot price at expiry, multiplied by the contract size.

When the spot price is below the futures price, the short seller earns a profit; when the spot price exceeds the futures price, the short incurs a loss. The payoff line therefore slopes downward, intersecting the X‑axis at the break‑even spot price (which equals F_0).

Examination questions may present a short position and ask you to mark the correct payoff line, or to compute the payoff for a given spot price. Apply the same linear logic, just with the sign reversed.

∑Formula: Short Futures Pay‑off

(F_{0} - S_{T}) \times Q

Where:

F_{0}= Futures price at entry (INR per unit)

S_{T}= Spot price at expiry (INR per unit)

Q= Contract size – number of foreign‑currency units per contract

Worked Example

Given F_{0}=75 INR/USD, Q=10,000 USD, and S_{T}=70 INR/USD: Step 1: Payoff = (75 - 70) × 10,000 Step 2: Payoff = 5 × 10,000 = 50,000 INR Verification: (75 - 70) × 10,000 = 50,000 INR.

Key Components of a Pay‑off Chart

The three elements that define any payoff chart are:

1. Futures (strike) price (F_0) – the price at which the contract was entered. It marks the break‑even point on the X‑axis where payoff is zero.

2. Contract size (Q) – determines the steepness of the line. Larger Q results in a steeper slope, meaning each rupee move in the spot price translates into a larger rupee payoff.

3. Position type (long or short) – decides the direction of the slope. Long positions have a positive slope; short positions have a negative slope.

Exam‑writers often embed these components in a single question. Spot the contract size and position type first, then use the appropriate formula to compute payoffs for the given spot prices.

Long vs Short Futures Pay‑off Characteristics

Aspect	Long Position	Short Position
Pay‑off Formula	(S_T - F_0) × Q	(F_0 - S_T) × Q
Slope of Chart	Positive (upward)	Negative (downward)
Profit When	Spot > Futures price	Spot < Futures price
Break‑even Point	Spot = Futures price	Spot = Futures price

Constructing a Pay‑off Chart – Stepwise

Step 1: Identify the futures price (F_0) and contract size (Q) from the contract specifications. In Indian currency futures, Q is usually 10,000 USD for USD/INR contracts.

Step 2: Choose a range of plausible spot prices (S_T) around F_0. Typical exam ranges are ±10% of the futures price.

Step 3: Apply the appropriate payoff formula – long or short – to each spot price to calculate the monetary payoff.

Step 4: Plot the spot prices on the X‑axis and the corresponding payoffs on the Y‑axis. Connect the points with a straight line; the line will pass through (F_0, 0).

Step 5: Label the axes clearly, indicate the break‑even point, and note whether the line represents a long or short position. A correctly labelled chart earns full marks in the exam.

Long USD/INR Futures Pay‑off (Contract Size = 10,000 USD, Futures Price = 75 INR)

Numerical Example – Indian Currency Futures

Example: Investor A goes long on USD/INR futures

Scenario

Investor A buys one USD/INR futures contract at a futures price of 75 INR per USD. The contract size is 10,000 USD. At expiry, the spot price is observed at 82 INR per USD. Calculate Investor A's payoff and indicate where this point lies on the payoff chart.

Solution

Step 1: Use the long payoff formula: Payoff = (S_T - F_0) × Q. Step 2: Substitute the values: (82 - 75) × 10,000 = 7 × 10,000 = 70,000 INR. Step 3: Because the payoff is positive, the point lies above the X‑axis, to the right of the break‑even at 75 INR. On the chart, it would be plotted at (82, 70,000).

Conclusion

The investor earns a profit of 70,000 INR. The example illustrates how a single spot price determines the exact location on the payoff line, a skill frequently tested in NISM exams.

⚠️Common Mistake – Ignoring Contract Size

Students sometimes calculate payoff as (Spot - Futures) without multiplying by Q, leading to a 10‑fold error for a 10,000‑unit contract. Always remember to scale the price difference by the contract size.

Exam Relevance and Quick Memory Aid

In the NISM exam, payoff charts appear in multiple‑choice questions (identifying the correct chart) and in case‑study questions (drawing the chart). The quickest way to avoid errors is the acronym "L‑S‑Q": Long/Short, Spot‑Futures difference, multiply by Quantity (contract size).

Remember that the break‑even spot price is always the futures price, regardless of position. If the chart does not cross the X‑axis at the futures price, it is wrong.

When a question provides only the payoff values, you can reverse‑engineer the futures price by locating the zero‑payoff point on the X‑axis. This technique often saves time compared to calculating each payoff from scratch.

⭐Exam Takeaways

A payoff chart plots spot price (X‑axis) against monetary payoff (Y‑axis) for a futures contract.
Long payoff formula: (Spot – Futures) × Contract Size; short payoff formula: (Futures – Spot) × Contract Size.
The break‑even point is always at the futures price; the line passes through (F_0, 0).
Slope direction indicates position type: upward for long, downward for short.
Always multiply the price difference by the contract size (Q) to obtain the correct rupee payoff.

Practice Questions

8 questions on Pay off Charts of Futures Contract

In a payoff chart for a currency futures contract, what is plotted on the horizontal (X‑axis)?

Which formula correctly represents the payoff for a long currency futures position?

A trader goes long on a USD/INR futures contract with futures price 78 INR/USD and contract size 10,000 USD. If the spot price at expiry is 83 INR/USD, what is the monetary payoff?

For a short currency futures position, how does the slope of the payoff chart appear?

A payoff chart for a futures contract shows the points (70, -100,000), (75, 0), (80, 100,000). Assuming the contract is a long position, what is the contract size?

A student calculates the payoff of a long USD/INR futures contract as (Spot – Futures) = 5 INR and reports a payoff of 5 INR. Which mistake is reflected in this calculation?

On a payoff chart, the point where the line crosses the X‑axis corresponds to which of the following?

Which of the following is a common exam trap when drawing a payoff chart?

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