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id: payoff-basics title: Payoff Basics summary: Master payoff diagrams, compute breakevens precisely, and understand max profit/loss for every position. outlook: neutral tags:

• foundations
• payoff
• beginner

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Learning goals

By the end of this lesson you should be able to:

• Read any payoff diagram and map it to a real position.
• Compute breakeven, max profit, and max loss for calls and puts.
• Distinguish between payoff (at expiration) and profit (after premium).
• Explain why options have nonlinear payoffs and what that means.
• Draw payoff diagrams for long and short positions.

The picture that governs everything

A payoff diagram shows profit or loss at every possible stock price at expiration.

• X-axis: stock price at expiration ($S_T$)
• Y-axis: profit or loss (in dollars)

If you can read this diagram, you understand the trade.

Linear vs nonlinear payoffs

Stock (linear)

A stock payoff is a straight 45° line: $\text{Profit}_{\text{stock}} = S_T - S_0$

For every $1 the stock rises, you make$1. Simple.

Options (nonlinear)

Options have kinked payoffs—flat in one region, sloped in another: $\text{Call payoff} = \max(S_T - K, 0)$ $\text{Put payoff} = \max(K - S_T, 0)$

This creates asymmetry: defined risk on one side, unlimited potential on the other.

The three numbers every trade needs

Before entering any position, compute:

1. Max profit — best case scenario
2. Max loss — worst case scenario
3. Breakeven(s) — where you go from loss to profit

If you cannot write these down, do not take the trade.

Long call: the bullish bet

Setup: Buy a call with strike $K$ for premium $C_0$.

Payoff at expiration

$\text{Payoff} = \max(S_T - K, 0)$

Profit at expiration

$\text{Profit} = \max(S_T - K, 0) - C_0$

The three numbers

• Max loss: $C_0$ (premium paid) — occurs when $S_T \leq K$
• Max profit: unlimited — grows as stock rises
• Breakeven: $K + C_0$

Example

• $K = 100$, $C_0 = 4$
• Max loss: $4 per share ($400 per contract)
• Breakeven: $104
• If $S_T = 115$: Profit = $(115 - 100) - 4 = 11$ per share

Long put: the bearish bet

Setup: Buy a put with strike $K$ for premium $P_0$.

Payoff at expiration

$\text{Payoff} = \max(K - S_T, 0)$

Profit at expiration

$\text{Profit} = \max(K - S_T, 0) - P_0$

The three numbers

• Max loss: $P_0$ (premium paid) — occurs when $S_T \geq K$
• Max profit: $K - P_0$ (if stock goes to $0)
• Breakeven: $K - P_0$

Example

• $K = 100$, $P_0 = 3$
• Max loss: $3 per share
• Breakeven: $97
• Max profit: $97 (if stock goes to$0)
• If $S_T = 85$: Profit = $(100 - 85) - 3 = 12$ per share

Short call: the obligation to sell

Setup: Sell a call with strike $K$, receive premium $C_0$.

Profit at expiration

$\text{Profit} = C_0 - \max(S_T - K, 0)$

The three numbers

• Max profit: $C_0$ (keep the premium) — occurs when $S_T \leq K$
• Max loss: unlimited — grows as stock rises
• Breakeven: $K + C_0$

Short put: the obligation to buy

Setup: Sell a put with strike $K$, receive premium $P_0$.

Profit at expiration

$\text{Profit} = P_0 - \max(K - S_T, 0)$

The three numbers

• Max profit: $P_0$ (keep the premium) — occurs when $S_T \geq K$
• Max loss: $K - P_0$ (if stock goes to $0)
• Breakeven: $K - P_0$

Summary table: all four basic positions

Payoff vs profit: the critical distinction

Payoff = what the option is worth at expiration (ignores what you paid) Profit = payoff minus premium paid (or plus premium received)

$\text{Profit} = \text{Payoff} - \text{Premium paid}$

For sellers: $\text{Profit} = \text{Premium received} - \text{Payoff to buyer}$

Contract size: don't forget the multiplier

Everything above is per share. Options control 100 shares.

$\text{Total profit/loss} = \text{Per-share profit/loss} \times 100$

Example: Long call profit of $5/share =$500 per contract.

The visual language

Long call shape

Profit
  │           ╱
  │         ╱
  │_______╱_______ S_T
  │    K
 -C₀

Long put shape

Profit
  │
  │╲
  │ ╲_______
  │      K    S_T
 -P₀

Short positions

Short positions are mirror images of long positions (flip vertically).

Payoff formulas referenceRead more

Long call payoff: $\text{Payoff} = \max(S_T - K, 0)$

Long call profit: $\text{Profit} = \max(S_T - K, 0) - C_0$

Long put payoff: $\text{Payoff} = \max(K - S_T, 0)$

Long put profit: $\text{Profit} = \max(K - S_T, 0) - P_0$

Breakeven formulas: $\text{Long call BE} = K + C_0$ $\text{Long put BE} = K - P_0$

Piecewise notation (call): $\text{Payoff}(S_T) = \begin{cases} 0 & S_T \leq K \\ S_T - K & S_T > K \end{cases}$