1. Selling naked options: picking up coins in front of the steamroller
Derivatives 6: When it goes wrong
So far the course has treated derivatives from the comfortable side: a future to lock in a price, a put to put a floor under things, a spread to cap what a hedge costs. This level switches sides. Now you are the one taking on the risk, you are paid up front for taking it, and the market decides when it comes to collect. We start with the trade that has emptied more retail accounts than any other: selling options without holding the position that backs them.
The shape of the payoff outranks the probability
Buying an option is a bet with a capped loss: the worst that can happen is that the premium evaporates entirely. Selling is the mirror image. You take in a known amount on day one and sign up to an obligation whose size is not yet determined and which the market will decide. Level 2 told it as accounting; what matters here is the practical consequence.
That asymmetry produces a very particular distribution of outcomes: nearly every trade ends in a small, similar-looking profit, and every so often a loss appears that looks nothing like the others. Nassim Taleb has spent decades repeating the same warning in different words, and it is worth translating it without decoration: how often you are right and how much you make on average are two different things, and they can point in opposite directions.
The sum worth doing before you sell your first option
A case with round numbers. Every month you sell puts on an index with a strike 5% below the current level, and you take in 1% of notional for doing so. Twelve quiet months in a row leave 12% gross on the notional committed, a result that catches the eye and therefore sells well.
Now comes a month in which the index falls 20%. Your strike was only 5% below, so the option expires with an intrinsic value of 15% of notional. Subtract the 1% you had collected and the result is a loss of 14%. In other words: that single month wipes out fourteen good ones. With twelve months of income banked, one episode leaves you below where you started, and that is before commissions, spreads and taxes, which in the good months you have duly been paying.
There is a second blow that almost nobody counts. After the fall, implied volatility spikes and premiums become the most generous you will see in years: the moment when selling options looks best arrives exactly when you have no margin left to do it with.
The 95% hit rate that hides a negative expectancy
The arithmetic at its barest. Imagine a trade that in nineteen months out of twenty makes 1 unit and in the remaining month loses 25. The hit rate is 95%, a figure that looks spectacular in any presentation. Add up the twenty months: the wins give 19 and the miss takes away 25. The total is a loss of 6 units, three tenths a month on average.
Nobody designs this on purpose; you get there by accretion. You sell further out of the money so that "it never gets there", which raises the hit rate and worsens the relationship between what you take in and what you risk. And you increase size because the recent record says the previous position was excessively prudent. Both decisions look like improvements and both push expectancy down.
Why a long run of wins is evidence of nothing
Suppose the trade genuinely does have 95% good months. The probability of stringing together twelve clean months is 0.95 to the power of twelve, a little over 54%. In other words: more than half of those who take this up will have a spotless first year even if expectancy is negative. At two years, close to 29% will still not have seen a single serious loss. That seller has twenty-four months of impeccable record, an equity curve that rises in an almost straight line and, if he publishes, followers.
It is not that the seller is lying: his sample has not had time to include the only thing that matters. And since those who did live through it disappeared, what you see published is filtered by survivorship. It is the same problem level 3 raised with the volatility risk premium: it exists and it is collected persistently, but it is the payment for enduring the episode you have not yet seen.
Selling a put and selling a naked call are not the same animal
The two trades are worth separating because they tend to be lumped together and they do not share a ceiling on losses.
- Short put. If you sell a put with a strike of 40 and take in 2, your worst case is that the underlying goes to zero: you lose 40 and keep the 2, so the maximum damage is 38 per share. It is an enormous figure, but it is a figure, and you can work it out before trading.
- Naked call. If you sell a call with a strike of 55 on a share you do not own and also take in 2, no equivalent number exists. The price has no ceiling. In October 2008, during the short squeeze on Volkswagen, the share went in two sessions from trading at a few hundred euros to above 1,000 euros intraday, briefly making the company the most valuable in the world. Anyone short lost multiples of everything they had ever taken in selling premium.
That difference alone should be enough not to size the two trades by the same yardstick.
What separates the option seller who is still standing
- Sizes by the worst-case loss, not by the premium collected nor by the hit rate.
- Knows that a short position grows on its own: level 4 called it negative gamma, and it means your exposure grows against you without your touching anything.
- Accepts making less in exchange for there being a number, written down in advance, that describes the most that can be lost.