Complex Strategy Payoff Mapping: Spreads, Calls and Puts
Map a complex strategy by pricing each leg at the same terminal underlying value, adding the signed payoffs and then including the initial net premium. Show the breakpoints so that maximum gain, maximum loss and breakeven are visible.
Put-spread payoff grid
Sell the $100 put for $6 and buy the $90 put for $2, with the same expiration. Net credit is $4 per unit. Ignore fees, interest and early assignment.
Swipe the table to compare every option leg.
| Terminal price | Short $100 put | Long $90 put | Net credit | Profit |
|---|---|---|---|---|
| $80 | -$20 | +$10 | +$4 | -$6 |
| $90 | -$10 | $0 | +$4 | -$6 |
| $95 | -$5 | $0 | +$4 | -$1 |
| $96 | -$4 | $0 | +$4 | $0 |
| $100 | $0 | $0 | +$4 | +$4 |
| $110 | $0 | $0 | +$4 | +$4 |
Maximum gain $4; maximum loss $6; breakeven $96. Original numbers applying the OIC bull-put-spread mechanics.
Original worked case
A defined-risk put spread
Given: Sell a $100-strike put for $6 and buy a $90-strike put for $2. Both expire together. Net credit is $4 per unit. Ignore interest, fees and early assignment.
01 At $110
Both puts expire worthless; profit = $4.
02 At $95
Short put = -$5; long put = $0; profit = -$1.
03 At $80
Short put = -$20; long put = $10; profit = -$6.
Answer and interpretation
Maximum gain is $4; maximum loss is $6; breakeven is $96. The lower-strike put caps the loss below $90.
$ per unit · scale -6 to 4
| Scenario | Value |
|---|---|
| S = $80 | -6 |
| S = $90 | -6 |
| S = $95 | -1 |
| S = $96 | 0 |
| S = $100 | 4 |
| S = $110 | 4 |
Illustrative put-spread payoff including $4 net credit. These are price scenarios, not historical observations.
Change one assumption
For a contract multiplier of 100, multiply every dollar result by 100. This does not change the $96 underlying breakeven.
Independent teaching example with the stated assumptions. Not an official exam question, marking key or observed market trend.
The key decisions, at a glance
| Concept | What to do | Watch for |
|---|---|---|
| Long put | Payoff = max(K - S, 0). | The holder has a right, not the writer’s obligation. |
| Short put | Payoff = -max(K - S, 0). | Premium income is separate from the terminal payoff. |
| Net profit | Add leg payoffs and net premium received. | Use matching units and contract multipliers. |
| Breakpoints | Evaluate below, between and above strikes. | One terminal price cannot reveal the whole shape. |
1. Long put
Payoff = max(K - S, 0).
Watch for: The holder has a right, not the writer’s obligation.
2. Short put
Payoff = -max(K - S, 0).
Watch for: Premium income is separate from the terminal payoff.
3. Net profit
Add leg payoffs and net premium received.
Watch for: Use matching units and contract multipliers.
4. Breakpoints
Evaluate below, between and above strikes.
Watch for: One terminal price cannot reveal the whole shape.
Understand the method
Part 1
Write the long-leg payoff before applying position signs
At expiry, a long call has payoff max(S - K, 0), while a long put has payoff max(K - S, 0). A short position takes the negative of the corresponding long payoff. Add the initial premium with the correct sign: premium paid is a cost, and premium received is a benefit. These equations describe expiry profit only after premiums are included.
State the unit. Per-share option profit must be multiplied by contract size and contract count to obtain position profit. Different contracts can have different multipliers and settlement conventions. The exercises here use one underlying unit, the same expiry within each structure and no costs, financing, dividends or early exercise unless stated.
Part 2
Use strikes as breakpoints and test every region
An option payoff is piecewise linear at expiry. Its slope changes at a strike, so a robust table includes prices below the lowest strike, at each strike, between strikes and above the highest strike. Calculate each leg first and then sum. This method catches sign errors that a memorized strategy label can conceal.
For the bull put spread above, selling the higher-strike put and buying the lower-strike put creates a capped credit strategy. Between the strikes, the short put’s loss changes with the underlying while the lower-strike put remains out of the money. Below both strikes, the long put offsets further deterioration and caps the expiry loss under the stated assumptions.
Part 3
Include the stock leg in covered calls and protective puts
A covered call combines a long underlying position with a short call. The premium provides a limited buffer while the call caps upside above its strike. It does not protect against most of a large stock decline. A protective put combines the underlying with a long put, creating a floor at expiry at the cost of the premium.
For a stock bought at $100, a $95 protective put costing $3 produces profit S - 100 + max(95 - S, 0) - 3. Below $95, the position’s loss is capped at $8 per share. Above $95, the stock participates in gains but must recover the $3 premium before the combined position breaks even at $103.
Part 4
Do not use an expiry diagram as a complete risk report
Before expiry, option values depend on remaining time, volatility, rates and other inputs. A position can incur mark-to-market losses or margin calls even when its expiry loss is limited. American-style exercise and assignment can alter interim holdings and cash flows. Settlement and execution risk also matter when legs are closed separately.
After constructing the expiry table, identify the maximum gain, maximum loss and breakevens under the assumptions. Then separately discuss path and implementation risks. This separation keeps the arithmetic clear without implying that a bounded diagram guarantees easy financing or frictionless execution throughout the holding period.
Protective put: stock bought at $100, $95 put costs $3
$80
- Stock profit
- -$20
- Put payoff
- $15
- Premium
- -$3
- Total profit
- -$8
$95
- Stock profit
- -$5
- Put payoff
- $0
- Premium
- -$3
- Total profit
- -$8
$100
- Stock profit
- $0
- Put payoff
- $0
- Premium
- -$3
- Total profit
- -$3
$110
- Stock profit
- $10
- Put payoff
- $0
- Premium
- -$3
- Total profit
- $7
Per share at expiry. Financing, dividends, trading costs and early exercise are omitted.
More worked practice
Original teaching cases. Use the stated assumptions; these are not official exam questions or marking keys.
A covered call caps the gain but leaves substantial downside
Given: Buy stock at $100 and sell a call with strike $110 for $4. Use one share-equivalent, hold to expiry and ignore costs and dividends.
- 1At S = $80: stock profit is -$20, short-call payoff is $0, and net profit is -$16.
- 2At S = $110: stock profit is $10 and net profit including premium is $14.
- 3At S = $130: stock profit is $30, short-call payoff is -$20, and net profit remains $14.
Interpretation: Maximum expiry gain is $14 per share and breakeven is $96. If the stock falls to zero, the position loses $96; the premium is a limited buffer, not comprehensive downside protection.
Check your understanding
Answer first, then open the explanation. These checks are original practice and do not generate an exam score.
1. A $100-strike long straddle costs $12 total. What are its expiry breakevens?
$88 and $112, because the combined intrinsic payoff must equal the $12 premium.
2. Why calculate each leg separately?
It preserves long/short signs, premiums and units, making errors easier to detect before summing the position.
3. Does a capped expiry loss eliminate interim margin needs?
No. Contract, broker and settlement rules can create interim cash demands or assignment effects.
Common questions
Why is breakeven $96?
Between the strikes, the short put loses $100 - S and the long put is worthless. The $4 credit offsets that loss when S = $96.
Can the spread lose more than $6 in the simplified model?
No. Below $90, additional short-put losses are offset by the long put. Real implementation can add fees, financing and assignment complications.
Sources and scope
The sources below establish their stated framework or subject context. Calculations and cases are our own teaching material; these sources do not endorse them or establish complete exam coverage.
- Options Industry Council: Bull put spread
The exact two-leg structure, maximum profit, maximum loss and breakeven used in the payoff lesson. Case numbers are our own.
- CAIA curriculum and study tools
Official curriculum, companions and required readings for the exam year. The current page now links to 2027 materials.
- CFA Institute: Options Strategies (2026)
Payoff construction and risk characteristics of covered calls, protective puts, spreads and straddles. Cases assume expiry and omit costs unless stated.
- Options Industry Council: Long straddle
Two-option structure, premium cost and expiry breakevens. Our figures are independent examples.
- CAIA 2027 curriculum overview
Published topic categories and Emerging Topics reading titles for 2027. The overview is not the complete learning-objective list.
By MiloPrep editorial team. Updated 10 October 2026. Independent study notes, not affiliated with or endorsed by CAIA Association. How we prepare our content.
Notes
- * Study scope: Selected study concepts, not complete curriculum coverage. Match your sitting to the official exam-year materials; CAIA’s current resource page now links to 2027. ↩ Return to content