2. The four basic positions and their payoff profiles

Derivatives 2: Options, the mechanics

With two types of contract, call and put, and two possible sides, buyer and seller, you get four elementary positions. There is no fifth. Any option structure you ever see, however complicated its label may look, is a combination of these four pieces. It is worth knowing them, therefore, with concrete numbers rather than vague impressions.

We continue with the example from the previous module. The share trades at 100. We are working with two contracts expiring in three months: the 105 call with a premium of 3 and a 95 put with a premium of 2. For each position four things matter: maximum gain, maximum loss, break-even point and the scenario in which it makes sense.

Buying a call

You pay 3 and acquire the right to buy at 105.

• Maximum loss: 3, the premium. It is reached at any close at or below 105.
• Maximum gain: no defined ceiling. It grows by one euro for every euro the share rises above 108.
• Break-even point: 108, that is, strike plus premium.
• Concrete outcomes: at 90, you lose 3. At 105, you lose 3. At 108, zero. At 115, you gain 7. At 130, you gain 22.

It makes sense when you expect an appreciable rise and within a defined period. Watch that word *appreciable*: buying this call and being right that the share goes from 100 to 107 is still a loss of 1. Getting the direction right is not enough; you have to clear the break-even point within the time available.

Selling a call

You collect 3 and accept that you will deliver at 105 if called upon.

• Maximum gain: 3, the premium. It is reached at any close at or below 105.
• Maximum loss: no defined limit, growing by one euro for every euro above 108.
• Break-even point: 108, the same as the buyer's, because it is the same contract seen from both sides.
• Concrete outcomes: at 90, you gain 3. At 108, zero. At 115, you lose 7. At 130, you lose 22.

This is the position of somebody paid to put a ceiling on his share of the upside. If he also owns the 100 shares, delivering at 105 does not mean going out to buy them in the market; if he does not own them, he will have to get hold of them at whatever price is going. The implications of that "whatever price is going" are dealt with in the level devoted to selling options.

Buying a put

You pay 2 and acquire the right to sell at 95.

• Maximum loss: 2, the premium. It is reached at any close at or above 95.
• Maximum gain: 93, which would occur in the extreme case of the share reaching zero: you sell at 95 something worth nothing, less the 2 of premium.
• Break-even point: 93, that is, strike minus premium.
• Concrete outcomes: at 110, you lose 2. At 95, you lose 2. At 93, zero. At 85, you gain 8. At 70, you gain 23.

This is the insurance position. Somebody holding the shares bought at 100 who adds this put knows that, whatever happens, he will be able to get rid of them at 95. It has cost him 2 and he has bought peace of mind until expiry. It is exactly the logic of an insurance excess: you absorb the first 5 euros of the fall and pass on the rest.

Selling a put

You collect 2 and commit to buying at 95 if it is imposed on you.

• Maximum gain: 2, the premium.
• Maximum loss: 93, in the extreme scenario of the share reaching zero.
• Break-even point: 93.
• Concrete outcomes: at 110, you gain 2. At 95, you gain 2. At 93, zero. At 85, you lose 8. At 70, you lose 23.

This is the position of somebody who accepts buying the asset cheaper than it trades today and is paid for committing to it. If the share does not fall, he keeps the premium and buys nothing. If it falls a long way, he ends up buying at 95 something worth considerably less.

How to read the four profiles without memorizing them

There are three regularities that spare you learning a table:

• The buyer always has his loss limited to the premium and the seller always has his profit limited to the premium. Call or put, without exception.
• The break-even point is worked out by adding the premium to the strike in calls and subtracting it in puts. In both cases, the price has to move in your favor by enough to pay for the ticket.
• Buyer and seller of the same contract have the same break-even point and opposite results. There are not two different profiles, there is one and its mirror image.

And one more regularity, which comes as a surprise: calls and puts are not the bullish and bearish bets respectively. Buying a put and selling a call are the two bearish positions; buying a call and selling a put, the two bullish ones. What separates each pair is not the direction, but the shape of the risk.

Worked example: two investors, the same forecast

Ana and Bruno believe the same thing: that the share, at 100 today, is not going to rise over the next three months. Ana sells the 105 call and collects 3. Bruno buys the 95 put and pays 2.

• If the share closes at 100, exactly where it was: Ana gains 3, Bruno loses 2. They were right, and only one of them is paid for it.
• If it closes at 88: Ana gains 3 and Bruno gains 5. The sharp fall rewards Bruno.
• If it closes at 125: Ana loses 17 and Bruno loses 2. The scenario neither of them expected ruins one and barely grazes the other.

The lesson is not which of the two positions is better, because it depends on the scenario. The lesson is that the same forecast can be expressed with radically different risk profiles, and that the choice between them matters more than the forecast itself. Ana is paid for being right in the central scenario and pays dearly for the extreme; Bruno pays to be right and his disaster is capped at 2.

None of this is a recommendation: it is a description of how four contracts work.