Where you are. You have four basic payoffs and a way to price and measure them. This lesson is the short, satisfying one: those four compose, and every option strategy with an intimidating name is a sum of them.
A wall of names hiding four ingredients
Covered call. Protective put. Straddle. Strangle. Butterfly. Iron condor. Risk reversal. Calendar spread.
Options writing is full of vocabulary that sounds like it requires an initiation, and every one of those is a sum of long calls, short calls, long puts and short puts at chosen strikes. Nothing else. Once you can add payoff functions, the vocabulary stops being a barrier and becomes what it actually is: names for shapes.
The idea in one paragraph
A strategy is a portfolio of options whose combined payoff has a shape somebody wants, and because payoffs add, building one is composing functions. Want income while you hold a share? Sell a call against it, and your upside is capped in exchange for the premium. Want protection? Buy a put, and you have insurance with a deductible. Want to bet on movement without picking a direction? Buy a call and a put at the same strike, and you profit from a large move either way. Want income with both tails capped? Sell a near pair and buy a far pair, and you have the iron condor the exercise builds. The design question is always the same: which region of outcomes do you want to be paid in, and what are you willing to give up everywhere else.
The one worth building
The iron condor is the best teaching example because it is four legs and its shape is genuinely engineered.
Sell a put below the current price and a call above it: that is the income, and it is what you keep if the price stays in the middle. On its own it is dangerous, because both of those short legs have the unbounded tail from lesson 5.
So buy a further-out put and a further-out call. Those cost premium and cap both tails, converting an unbounded risk into a known maximum loss.
Where the worst case actually is
The exercise checks something worth checking: that the worst case is bounded, and that the best case is the quiet middle.
That verification matters more than it looks, because the commonest way to lose badly with options is to build a strategy whose tail you have not evaluated. A short strangle - the near pair alone, without the wings - looks superb across every price anyone expects, and its worst case is unbounded. The difference between it and the condor is two cheap legs, and it is entirely invisible unless you evaluate the payoff across the full range rather than the plausible one.
Two you will meet constantly
The covered call is a share you own plus a call sold against it. The premium is income; the cost is that your upside above the strike is gone. It is popular because it feels free and is not: you have sold the good outcome.
The protective put is a share you own plus a put bought below it. It is insurance, priced like insurance, with the strike as the deductible. It costs money every period and pays in the period you were most afraid of.
Both are the same move as the hedger in lesson 2: trading away part of the distribution for certainty about the rest.
Check yourself
1. Why is building a strategy the same operation as adding functions?
Because each leg’s payoff is a function of the settlement price, and holding several legs means holding the sum of their payoffs. The strategy’s shape is entirely determined by which legs are included and where their strikes sit, so composing them is arithmetic rather than a separate concept.
2. A short strangle and an iron condor look identical across every price anyone expects. What is the difference and why does it not show up?
The condor buys two further-out legs that cap both tails; the strangle does not. In the expected range both behave the same and the strangle earns more, because it did not pay for the wings. The difference appears only in the tails, which is exactly where nobody was looking.
3. A covered call is often described as free income. What has actually been sold?
The upside above the strike. The premium is real, and so is the fact that if the share rises well beyond the strike, that gain now belongs to the option’s buyer. It is a trade of the good tail for certain income, not income from nowhere.
4. Why can a strategy’s track record fail to tell you whether it was well priced?
Because strategies that take the unbounded side win in almost every period, so a correctly priced one and a badly underpriced one produce the same statements until the rare outcome arrives. The information is in the shape of the payoff and the premium received, not in the sequence of wins.
Do this
Compose four legs and verify where the worst case is.
python3 code/strategies.pyThe starter leaves you iron_condor: sum the payoffs of a short put and short call near the money with a long put and long call further out, all at the same premium for clean arithmetic. The assertions check that the worst case is bounded, that the best case is the quiet middle, and that the wings are symmetric. Success prints the payoff across the grid and the line:
best +8.00 in the middle, worst -12.00 in the tails: bounded on both sides because the wings were bought, not borrowedThe completed version is in solutions/strategies.py.
What you can now do. You can compose payoffs into a chosen shape and prove where the worst case is rather than assuming it. That closes the options half of the amplifier. The next three lessons take the same amplification into lending, starting with the most familiar levered position most people will ever hold.