Payoff, breakeven and max profit/loss

Payoff versus profit and loss

The payoff is what the legs pay at expiry for a given settlement price, before counting what you paid or received to open them. Profit at expiry is payoff minus the net cost of entry. Before expiry, a position's P&L also depends on the time value still left in each leg, so it is not on the payoff line yet; it converges to it as expiry nears (see P&L attribution). BOSS's payoff chart and scenario table show profit at expiration.

The numbers that describe a payoff

• Breakevens are the settlement prices where profit at expiry is exactly zero. A vertical spread has one; a straddle or condor has two.
• Max profit and max loss are the highest and lowest points of the profit line.
• Either can be capped or uncapped. A long call's profit is uncapped; a short call's loss is uncapped. A short put's loss stops at the underlying reaching zero: BOSS's classification counts it as uncapped risk, while the live result summary shows its actual bounded max loss, strike minus premium.
• A naked position is a short option with no long option or underlying covering it: a short call on its own, or the extra short calls of a call ratio spread. Naked short calls are where uncapped losses come from, and BOSS shows an unlimited-loss warning whenever a structure's loss has no cap.
• Reward-to-risk is max profit ÷ max loss: the best case per dollar at risk. It is only defined when both are capped, and it is not an expected return. Read it next to the probability of profit: a high ratio usually comes with a low probability, and the reverse.

A worked example: a bull call spread

With a 30-day forward of $100,000 and 50% implied volatility, buy the $100,000 call at a mid of $5,710 and sell the $110,000 call at a mid of $2,280. At mid:

• Net debit: $5,710 − $2,280 = $3,430. That is the max loss, below $100,000.
• Breakeven: long strike + net debit = $100,000 + $3,430 = $103,430.
• Max profit: width − debit = $10,000 − $3,430 = $6,570, at $110,000 or above.
• Reward-to-risk: $6,570 ÷ $3,430 = 1.92.

Now after costs. Buying pays the ask, say $5,760, and selling receives the bid, say $2,230, plus an estimated $30 fee per leg (0.03% of $100,000):

• Net debit: $5,760 − $2,230 + $60 = $3,590, the max loss.
• Breakeven: $103,590. Max profit: $10,000 − $3,590 = $6,410. Reward-to-risk: 1.79.

Crossing the spread and paying fees cost $160, which moved the breakeven up by $160 and cut the max profit by the same amount. With BTC settling lognormally around the forward at 50% volatility, the chance of finishing above $103,590 is about 38%. That is why BOSS draws two curves on the payoff chart, after costs and at mid price, and computes the net cost, breakevens, max profit and loss and the scenario table after costs, the same way the Scanner ranks structures.

Lopsided structures

A structure is lopsided when its loss is capped but more than 5 times what it can realistically make. For a capped profit, that means a reward-to-risk below 0.20; for an uncapped profit, BOSS uses the best profit within two standard deviations of the forward instead of an infinite one. A lopsided trade often shows a high probability of profit, because it wins small and often and loses big and rarely. BOSS shows a warning on the strategy page and the Scanner ranks such structures below better-balanced ones. A wide butterfly sits at the other extreme: a cheap, capped loss against a larger, less likely peak. A short strangle has an uncapped loss, so no ratio is shown at all.

Calendars and diagonals have legs at two expiries, so a single payoff at one settlement price would misstate them; BOSS doesn't show their max profit, max loss or probability.