Payoff Charts for Options
Payoff charts graphically display the profit or loss of option positions at expiry. They are essential for visualising risk‑reward and for answering many NISM exam questions that test understanding of option outcomes. This sub‑topic explains how to read and construct payoff charts for long and short calls and puts, breakeven calculations, and their practical use in strategy selection.
Learning Objectives
- 1Identify the axes and key components of a payoff chart
- 2Derive payoff formulas for long and short call and put options
- 3Calculate breakeven points and interpret profit zones
- 4Apply payoff charts to choose appropriate option strategies
Understanding a Payoff Chart
A payoff chart plots the option holder's profit or loss (vertical axis) against the underlying asset's spot price at expiry (horizontal axis). The vertical axis is measured in rupees and may be shown as net profit after accounting for the premium paid or received.
The chart typically has three regions: a flat region where the option expires worthless, a sloping region where the option is in‑the‑money, and the breakeven point where profit switches from negative to positive. Recognising these regions helps you quickly answer questions about maximum loss, maximum gain, and the price range where the option is profitable.
In the NISM exam, candidates are often given a diagram and asked to identify the option type (long call, short put, etc.) or to compute the breakeven price. Knowing the shape of each payoff chart eliminates guesswork and saves valuable time.
- Horizontal axis – Spot price of the underlying at expiry (₹).
- Vertical axis – Net payoff (₹) after premium.
Students often confuse the raw payoff (max(S‑K,0) or max(K‑S,0)) with actual profit. Remember to subtract the premium paid (for long positions) or add the premium received (for short positions) to obtain the net profit shown on the chart.
Payoff of a Long Call Option
A long call gives the holder the right, but not the obligation, to buy the underlying at the strike price (K) on expiry. The intrinsic payoff is the difference between the spot price (S) and the strike, but only when S exceeds K.
The payoff function is therefore a "hockey‑stick" shape: zero payoff when S ≤ K and a line with slope +1 when S > K. The net profit is the payoff minus the premium (C) paid at initiation.
Exam questions may present the premium and ask for the breakeven price, or they may give a spot price and ask for the net profit. Use the payoff formula first, then adjust for the premium.
Where:
S= Spot price of the underlying at expiry (₹)K= Strike price of the call option (₹)Worked Example
Given S = 120, K = 100: Step 1: Compute S - K = 120 - 100 = 20 Step 2: Payoff = max(20, 0) = 20 Verification: max(120 - 100, 0) = 20.
Payoff of a Long Put Option
A long put grants the right to sell the underlying at the strike price (K). The payoff becomes positive when the spot price falls below the strike.
The payoff function mirrors the long call: zero when S ≥ K and a line with slope -1 when S < K. Net profit equals payoff minus the put premium (P) paid.
Typical exam items ask you to compute the profit for a given S, or to determine the spot price at which the put starts making a profit (breakeven). Apply the payoff formula first, then subtract the premium.
Where:
S= Spot price of the underlying at expiry (₹)K= Strike price of the put option (₹)Worked Example
Given S = 80, K = 100: Step 1: Compute K - S = 100 - 80 = 20 Step 2: Payoff = max(20, 0) = 20 Verification: max(100 - 80, 0) = 20.
Payoff of Short Positions
When you sell (write) an option, you receive the premium upfront. The payoff to the writer is the negative of the holder's payoff because the writer must deliver the opposite cash flow.
For a short call, the payoff is 0 when S ≤ K and –(S‑K) when S > K, resulting in unlimited loss potential. For a short put, the payoff is 0 when S ≥ K and –(K‑S) when S < K, with loss limited to the strike price minus zero.
In the exam, remember that the maximum profit for any short option equals the premium received, while the loss profile mirrors the corresponding long position but with opposite sign.
Comparison of Long and Short Option Payoff Characteristics
| Position | Payoff Shape | Maximum Loss | Maximum Gain |
|---|---|---|---|
| Long Call | Flat at 0, then upward slope | Premium paid (C) | Unlimited |
| Long Put | Flat at 0, then downward slope | Premium paid (P) | Unlimited |
| Short Call | Flat at 0, then downward slope | Unlimited | Premium received (C) |
| Short Put | Flat at 0, then upward slope | Strike – 0 (minus premium) | Premium received (P) |
Breakeven Points and Profit Zones
The breakeven point is the underlying price at which net profit equals zero. For a long call, you add the premium (C) to the strike; for a long put, you subtract the premium (P) from the strike.
These points split the payoff chart into loss and profit zones. Knowing the breakeven helps you answer "at what price will the option start making money?" which is a frequent NISM question.
Remember that the breakeven calculation does not consider transaction costs or taxes, which are outside the syllabus scope.
Where:
K= Strike price of the call (₹)C= Premium paid for the call (₹)Worked Example
Given K = 100, C = 5: Step 1: Breakeven = 100 + 5 = 105 Verification: 100 + 5 = 105.
Where:
K= Strike price of the put (₹)P= Premium paid for the put (₹)Worked Example
Given K = 100, P = 4: Step 1: Breakeven = 100 - 4 = 96 Verification: 100 - 4 = 96.
Net Profit of a Long Call (K=100, Premium=5)
Scenario
Rohit buys a European call option on Reliance Industries with a strike price of ₹1,500 and pays a premium of ₹50. At expiry, the share price is ₹1,560. Calculate Rohit's net profit.
Solution
Step 1: Compute the intrinsic payoff: max(1,560 – 1,500, 0) = 60. Step 2: Subtract the premium paid: Net profit = 60 – 50 = ₹10. Since the profit is positive, Rohit is in the profit zone of his payoff chart. If the share price had been ≤ ₹1,500, the payoff would be zero and the net loss would equal the premium of ₹50.
Conclusion
The example illustrates how to move from the payoff formula to the net profit used in exam questions.
When a payoff chart is given without a premium, assume the vertical axis already reflects net profit. If the premium is shown separately, always adjust the chart by adding (short) or subtracting (long) the premium.
Using Payoff Charts for Strategy Selection
Payoff charts are not limited to single‑leg options; they also help visualise multi‑leg strategies such as bull spreads, bear spreads, straddles, and strangles. Each strategy produces a distinct composite shape that indicates risk‑reward trade‑offs.
For instance, a bull call spread combines a long call (lower strike) and a short call (higher strike). The resulting chart shows limited loss (net premium) and limited gain (difference between strikes minus net premium). Recognising these shapes speeds up answer selection for strategy‑based questions.
In the NISM exam, you may be asked to match a described payoff pattern with the correct strategy. Practice drawing the four basic single‑leg charts first; then combine them mentally to form the composite shapes.
Common Two‑Leg Option Strategies and Their Payoff Shapes
| Strategy | Description | Typical Payoff Shape |
|---|---|---|
| Bull Call Spread | Buy lower‑strike call, sell higher‑strike call | Limited loss, capped gain – flat then upward, then flat |
| Bear Put Spread | Buy higher‑strike put, sell lower‑strike put | Limited loss, capped gain – flat then downward, then flat |
| Straddle | Buy ATM call and put | V‑shaped – large loss near strike, large gain on either side |
| Strangle | Buy OTM call and put | Wider V‑shaped – loss between strikes, gain beyond each strike |
⭐Exam Takeaways
- Payoff charts plot net profit (₹) vs. spot price (₹) at expiry and consist of flat, sloping, and breakeven regions.
- Long Call payoff = max(S‑K,0); Long Put payoff = max(K‑S,0). Subtract the premium to obtain net profit.
- Short option payoff is the negative of the corresponding long payoff; maximum profit equals the premium received.
- Breakeven for a long call is K + premium; for a long put it is K – premium. Use these formulas to locate profit zones quickly.
- Remember to adjust the vertical axis for premiums when the chart does not already show net profit.
- Comparative tables of long vs. short positions help recall maximum loss/gain characteristics.
- Composite strategies produce characteristic shapes (e.g., bull spread, straddle); matching shape to strategy is a common NISM question.
- Always verify calculations with the worked examples provided to avoid sign errors.
Practice Questions
8 questions on Payoff Charts for Options
In a payoff chart for options, what is plotted on the horizontal axis?
What is the payoff formula for a long call option?
A trader buys a call with strike ₹200 and pays a premium of ₹12. What is the breakeven price at expiry?
Which statement correctly describes the maximum loss for a long put and a short call?
An investor purchases a European call with strike ₹1,500, paying a premium of ₹50. At expiry the spot price is ₹1,560. What is the net profit?
Which two‑leg option strategy is described by a payoff shape that is flat, then rises, then flattens again, indicating limited loss and capped gain?
When a payoff chart is given without a premium, what should a candidate assume about the vertical axis?
A payoff chart for a long call (K=100, premium=5) shows net profit values of -5 at spot 80, -5 at 90, -5 at 100, 5 at 110, and 15 at 120. Based on this chart, what is the premium paid for the option?