Maximum gain and loss

A buyer can lose only the premium

You buy an option. What's the most you could lose? As the buyer, you pay the premium up front. The premium is the price of the option.

Think back to Maria and her $200 car deal. If things go badly, she walks away. She can't lose more than the $200. Option buyers are the same. A buyer never has to use the right. So the worst case is letting it expire, and losing the premium.

Buy a 50 call for 3, and the most you can lose is 3 times 100, or $300. That's the floor on the chart. Now flip to the writer. The writer collects the premium. The best the writer can do is keep all of it when the option expires.

One side's loss is the other side's gain. So the buyer's maximum loss and the writer's maximum gain are the same number, the premium. The slip is answering for the wrong side. Before you answer, check whether the question is about the buyer or the writer.

A buyer can lose only the premium. A writer can gain only the premium.

Calls have no ceiling

How high can a stock price go? There's no limit. A call is the right to buy at the strike price. The higher the stock goes, the more that right is worth.

So a call buyer's maximum gain is unlimited. Long means you bought the option. Now the writer. An uncovered call writer sold a call without owning the stock. Uncovered is also called naked.

If assigned, that writer must sell at the strike. To deliver, they first have to buy the shares at the market price, however high it is. So an uncovered call writer's maximum loss is unlimited. Short means you sold the option. The best case is keeping the premium.

The slip is putting a number on it, like the strike plus the premium. A stock has no ceiling, so neither does this. A stock has no ceiling. So a long call's gain and an uncovered short call's loss are unlimited.

A stock stops at zero, so a put has a ceiling

How low can a stock price go? Zero, and no lower. A put is the right to sell at the strike price. The best thing for a put buyer is the stock falling to zero.

Say you buy a 35 put for 2, and the company fails. The stock goes to zero. You can sell at 35 something worth nothing, so the put is worth 35. Take off the 2 you paid, and you're up 33.

Times 100 shares, that's $3,300. It can't get better, because the stock can't fall below zero. So a put buyer's maximum gain is the strike minus the premium, times 100.

The put writer is the mirror. At zero, they must buy at 35 something worth nothing. They keep the 2, so they lose 33 a share. The slip is calling a put's payoff unlimited. Unlimited belongs to calls, because only a rise has no ceiling.

A stock stops at zero. So a put's best and worst case is the strike minus the premium, times 100.

Worked example: Long put: best and worst case

1. You buy one June 45 put for 3. What's the most you can make, and the most you can lose?
2. Start with the worst case. The stock finishes above 45, so the put expires worthless. You lose the premium, 3 times 100, or $300.
3. Now the best case. The stock goes to zero, so the put is worth 45. Take off the 3 you paid, and times 100, that's $4,200.
4. Don't call it unlimited. A stock can't fall below zero, so the put's gain has a ceiling.

Common mistakes

A stock stops at zero

Said a put's payoff was unlimited? Look at the floor. A stock can't fall below zero. So a put buyer's best case, and a put writer's worst case, is the strike minus the premium, times 100. Unlimited belongs to calls.