Every options position, however many legs it has, comes down to one picture: what it is worth at expiration for each possible stock price. Learn to draw that picture for a single call and a single put and you can draw it for anything.
Value at expiration
At expiration only intrinsic value is left, so valuing an option is arithmetic.
- A call is worth the stock price minus the strike, or zero if the stock finishes below the strike.
- A put is worth the strike minus the stock price, or zero if the stock finishes above the strike.
Your profit is that value minus what you paid. Nothing else enters.
Breakeven
A call buyer needs the stock to finish above the strike by at least the premium paid to get their money back. So the breakeven for a long call is the strike plus the premium. For a long put it is the strike minus the premium, because a put earns as the stock falls.
Take a $100 strike call bought for $3. Below $100 it expires worthless and you lose the full $3, which is $300 on one contract. At $100 it is still worth nothing. At $103 it is worth $3, which is what you paid, so you break even. At $110 it is worth $10 and you made $7 a share, $700 a contract. Every dollar above $103 is a dollar of profit, with no ceiling.
The shape
Plot profit on the vertical axis against the stock price at expiration on the horizontal and a long call is a hockey stick: a flat line at minus the premium below the strike, then a line rising one for one above it, crossing zero at the breakeven. A long put is the same shape facing the other way. The chart draws both for a $100 strike on a $100 stock with 30 days left, priced by the same model the later modules use.
Profit or loss per contract for buying the $100 strike on a $100 stock with 30 days left, at expiration (black) and before it (green). The breakeven is marked. Switch to Put to see the shape face the other way, then drag days toward 1.
The black line is the result if you hold to expiration. The green line is what the position is worth before then, at the days and volatility on the sliders. It sits above the black line because the option still has time value. You do not have to hold to the end: sell the call back on any day and your result is the green line at that day's stock price. As the days run out, the green line sinks onto the black one.
A short call or short put is the buyer's line flipped upside down, the seller's side you saw in the first lesson. Spreads, straddles, condors and every other strategy in this course are these four lines added together, and you will build them by hand in Modules 8 and 9 before letting the Terminal draw them.
Maximum loss
The most a buyer can lose is the premium, and it is lost in full only if the option finishes out of the money. That is the trade the buyer makes: a known, capped loss in exchange for an open-ended gain. The seller takes the opposite deal, a capped gain of the premium against a loss that grows with every dollar the stock moves through the strike. In dollars per contract, the buyer's maximum loss is the premium times 100.
How far is the stock likely to go
A breakeven only means something next to a sense of how far the stock tends to travel. The option prices themselves carry that sense. Traders turn them into one number, called implied volatility, and from it draw a range of likely prices at expiration. The chart below is that range for a $100 stock at 30% volatility with 30 days left. The darker band holds about two outcomes in three, the lighter one about nineteen in twenty.
Likely stock prices at expiration for a $100 stock at 30% volatility with 30 days left. Drag volatility up and the range widens; drag days down and it narrows. The note under the chart prints the band edges.
Set the long call from the chart above against it. Its breakeven, near $103.60, sits well inside the darker band, which runs from about $92 to $109. The stock does not need a freak move to pay off; it needs an ordinary one in the right direction. Drag days down and the band narrows: with less time the stock has less room to travel, which is why short-dated options are cheaper. Implied volatility gets its own modules later. For now, read it as the market's estimate of the range.
Why the chain beats a guess
The breakeven depends on the premium, and the premium is whatever the market is charging right now, not what a rule of thumb says. On a live chain the Mid for each strike sits next to the strike, so the breakeven for any call is one addition, and you can compare it across strikes: the $155 call may break even at $158 while the $160 call breaks even at $161.50. On a $150 stock that is the difference between a trade that needs a 5.3% move and one that needs a 7.7% move, and it is visible in one row of the chain.
The maths: breakevens, maximum loss and the move you need
For a call with strike K bought at premium C, and a put with strike K bought at premium P:
- Call breakeven:
K + C - Put breakeven:
K - P - Maximum loss per contract:
100 × Cfor the call,100 × Pfor the put - Maximum gain per contract: unlimited for the call,
100 × (K - P)for the put, because a stock cannot fall below zero - Move needed to break even on a call, in percent:
(K + C - S) / S × 100
Worked example: a stock at $150 and the $155 call at $2.40. The breakeven is 155 + 2.40 = $157.40. The move needed is (157.40 - 150) / 150 × 100, about 4.9%. The most you can lose is 100 × 2.40 = $240.
For the range, a one standard deviation move over T years is roughly S × v × √T. At 30% volatility with 30 days left that is 150 × 0.30 × 0.287, about $12.90, so the $7.40 the breakeven needs is a bit over half of one standard deviation. The seller's numbers are the buyer's with the signs flipped: the call seller's maximum gain is 100 × C and their breakeven is the same K + C.
Your turn
Open the AAPL chain on the expiration in the question and find the at-the-money call. Add its Mid to the strike for the breakeven, and multiply the Mid by 100 for the most you could lose on one contract. Then work out the breakeven of the at-the-money put on the same row.