Calls and Puts: Payoffs, Break-Even Points, and Common Misunderstandings

Calls and Puts in One Sentence Each

Call option: a contract where the buyer pays a premium for the right (not obligation) to buy 100 shares at a fixed price (the strike) by expiration; the seller receives the premium and takes the obligation to sell shares at the strike if assigned.

Put option: a contract where the buyer pays a premium for the right to sell 100 shares at the strike by expiration; the seller receives the premium and takes the obligation to buy shares at the strike if assigned.

Comprehension check

• Which side has a right and which side has an obligation?
• For a call, who benefits when the stock rises?

Payoff Diagrams: The Shape Matters More Than the Story

Payoff diagrams show profit/loss at expiration as a function of the stock price. They help you see: (1) maximum gain, (2) maximum loss, and (3) break-even point.

Key notation used below

• S = stock price at expiration
• K = strike price
• Premium = option price paid/received (per share)
• Contract multiplier is typically 100 shares per contract

Calls: Upside Exposure vs Premium Collection

Long Call (Buy a Call): why buyers want upside exposure

A long call is a bullish position: you want the stock to rise above the strike enough to overcome the premium you paid. Your risk is limited to the premium; your upside can be large.

Long call payoff at expiration

Profit = max(S - K, 0) - Premium

Max loss: Premium (if the call expires worthless).
Max gain: theoretically unlimited as S rises.
Break-even: K + Premium.

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ASCII payoff diagram (long call)

Profit/Loss at Expiration (Long Call, per share)   ^ Profit   |                 /   |                /   |               /   |______________/____________> S (stock price)                K      K+Premium   |   -Premium (max loss)

Step-by-step break-even example (long call)

• Stock is at $50 today.
• You buy a $55 strike call for a premium of $2.00.
• Break-even at expiration = 55 + 2 = $57.
• If S = $60 at expiration: intrinsic value = 60 - 55 = $5; profit per share = 5 - 2 = $3.
• Profit per contract (multiplier 100) = $3 × 100 = $300.

Practical scenario: “I want upside without buying 100 shares”

You believe a stock could jump on earnings. Buying a call can give upside participation with defined risk (the premium). The trade-off is that the stock must move enough (and by expiration) to exceed the break-even.

Comprehension check

• If you pay a $1.50 premium for a $40 call, what is the break-even?
• At expiration, if the stock is below the strike, what is the long call’s profit/loss?

Short Call (Sell a Call): why sellers collect premium but face capped profit/uncapped risk

A short call is generally bearish-to-neutral: you want the stock to stay at or below the strike so you keep the premium. Your profit is capped at the premium received. If the stock rises sharply, losses can grow very large because you may have to sell shares at the strike while the market price is much higher.

Important nuance: If the short call is covered (you already own 100 shares), the risk is not unlimited in the same way; the shares you own can be delivered if assigned. The trade-off becomes “capped upside” on the stock position.

Short call payoff at expiration

Profit = Premium - max(S - K, 0)

Max gain: Premium (if option expires worthless).
Max loss: theoretically unlimited (if uncovered).
Break-even: K + Premium (above this, losses begin).

ASCII payoff diagram (short call)

Profit/Loss at Expiration (Short Call, per share)   ^ Profit   | Premium ________   |               \   |                \   |                 \   |__________________\___________> S                K      K+Premium

Step-by-step break-even example (short call)

• You sell a $55 strike call and receive $2.00 premium.
• Break-even at expiration = 55 + 2 = $57.
• If S = $56: option intrinsic value = 1; profit per share = 2 - 1 = $1.
• If S = $65: intrinsic value = 10; profit per share = 2 - 10 = -$8 (loss).
• Loss per contract = $8 × 100 = $800.

Comprehension check

• What is the maximum profit of a short call?
• Why can an uncovered short call have very large losses?

Puts: Downside Protection and Bearish Speculation

Long Put (Buy a Put): downside protection/speculation

A long put is bearish or protective. You want the stock to fall below the strike enough to overcome the premium. Risk is limited to the premium; profit potential increases as the stock drops (down to zero).

Long put payoff at expiration

Profit = max(K - S, 0) - Premium

Max loss: Premium.
Max gain: approximately K - Premium (if the stock goes to 0).
Break-even: K - Premium.

ASCII payoff diagram (long put)

Profit/Loss at Expiration (Long Put, per share)   ^ Profit   |\   | \   |  \   |   \___________   |_______________\___________> S            K-Premium   K   |            -Premium (max loss)

Step-by-step break-even example (long put)

• Stock is at $50 today.
• You buy a $45 strike put for $1.50 premium.
• Break-even at expiration = 45 - 1.50 = $43.50.
• If S = $40: intrinsic value = 45 - 40 = $5; profit per share = 5 - 1.5 = $3.5.
• Profit per contract = $3.50 × 100 = $350.

Practical scenario: “I want protection if my stock drops”

If you own shares and worry about a near-term drop, a put can act like insurance: you pay a premium to set a worst-case sale price (approximately the strike, offset by premium). The cost is the premium, which reduces your net outcome if the stock does not fall.

Comprehension check

• If you buy a $30 put for $1.00, what is the break-even?
• What happens to a long put if the stock finishes above the strike at expiration?

Short Put (Sell a Put): the obligation a put seller takes on

A short put is typically bullish-to-neutral. You receive premium, and you are obligated to buy 100 shares at the strike if assigned. You want the stock to stay above the strike so the put expires worthless. If the stock falls, you may be forced to buy at the strike even though the market price is lower.

Short put payoff at expiration

Profit = Premium - max(K - S, 0)

Max gain: Premium.
Max loss: large but not unlimited (worst case is stock goes to 0): loss per share ≈ K - Premium.
Break-even: K - Premium (below this, losses begin).

ASCII payoff diagram (short put)

Profit/Loss at Expiration (Short Put, per share)   ^ Profit   | Premium ________   |              /   |             /   |            /   |___________/________________> S        K-Premium        K

Step-by-step break-even example (short put)

• You sell a $45 strike put and receive $1.50 premium.
• Break-even at expiration = 45 - 1.50 = $43.50.
• If S = $44: intrinsic value = 45 - 44 = $1; profit per share = 1.5 - 1 = $0.5.
• If S = $40: intrinsic value = 5; profit per share = 1.5 - 5 = -$3.5 (loss).
• Loss per contract = $3.50 × 100 = $350.

Comprehension check

• What are you obligated to do if you are assigned on a short put?
• Is the maximum loss on a short put unlimited? Why or why not?

Break-Even Summary Table (At Expiration)

Common Beginner Errors (and How to Catch Them)

1) Confusing direction: “Calls are always safer” / “Puts are always bearish”

Fix: Separate the option type from the position direction. A call can be bullish (long call) or bearish/neutral (short call). A put can be bearish (long put) or bullish/neutral (short put).

• Quick test: Ask “Do I benefit if the stock goes up?” If yes, you’re net bullish; if no, you’re net bearish/neutral.

Comprehension check

• Is selling a put bullish or bearish (in typical intent)?
• Is selling a call bullish or bearish/neutral (in typical intent)?

2) Mixing up strike price vs stock price

Fix: The strike (K) is fixed in the contract; the stock price (S) moves. Intrinsic value at expiration depends on the difference between S and K:

• Call intrinsic value: max(S - K, 0)
• Put intrinsic value: max(K - S, 0)

Quick test: If you see max(…) and get a negative number inside, intrinsic value becomes 0—not negative.

Comprehension check

• If S = 48 and K = 50, what is call intrinsic value at expiration?
• If S = 48 and K = 50, what is put intrinsic value at expiration?

3) Ignoring the contract multiplier (100 shares)

Fix: Options are usually quoted per share, but your real dollar P/L is typically per-share P/L × 100 × number of contracts.

Example: You make $0.40 per share on one contract. That is $0.40 × 100 = $40, not $0.40.

Comprehension check

• If you lose $2.25 per share on 2 contracts, what is the total loss?

4) Assuming premium is “free money” when selling options

Fix: Premium is payment for taking risk. When you sell a call or put, you are paid upfront because you accept an obligation that can become costly.

• Short call: obligation to sell shares at K if assigned (risk grows as stock rises).
• Short put: obligation to buy shares at K if assigned (risk grows as stock falls).

Practical step-by-step risk check before selling:

• Step 1: Write down the obligation in plain language (sell shares at K / buy shares at K).
• Step 2: Compute break-even (K + Premium for short call, K - Premium for short put).
• Step 3: Compute worst-case thought experiment: “What if the stock doubles?” (short call) or “What if it goes to 0?” (short put).
• Step 4: Convert to dollars using × 100.

Comprehension check

• Why does a short call seller get paid premium upfront?
• For a short put, what stock move creates the biggest losses?

Mini Practice Set: Identify Payoff and Break-Even

• A: Buy 1 call, K=100, premium =3. What is break-even? What is max loss?
• B: Sell 1 put, K=50, premium =1.20. What is break-even? What happens if S=45 at expiration?
• C: Sell 1 call, K=30, premium =0.80. What is max gain? At what price do losses begin?