The assumption underneath every gamma chart

Exchanges publish how many contracts exist at each strike. They do not publish who is long and who is short. Every gamma exposure figure, every wall, every flip level is built on a guess about that missing half, and the guess is load-bearing.

This is not a minor caveat to append at the end. It is the single fact that determines whether any of these numbers mean anything, and it is almost never stated by the people publishing them. So it gets its own page.

What the exchange actually gives you

For each strike and expiry, the exchange publishes open interest: the number of contracts outstanding. It also publishes volume, and the prints that make it up. That is the complete public record.

What it does not contain is direction of ownership. An open interest figure of 40,000 contracts at a strike tells you 40,000 contracts exist. It does not tell you whether customers bought them from dealers or sold them to dealers. Those two situations produce hedging flows in opposite directions, and the published data is identical in both cases.

Every step that follows is an attempt to fill that gap by assumption.

The standard convention

The most common model assumes that customers buy calls and sell puts, and that market makers take the opposite side of both. The reasoning is behavioural rather than mathematical: retail and many institutional participants are structurally long upside and structurally hedged on the downside, so calls tend to be bought and puts tend to be sold to fund or express that.

Under that model, dealers are short calls and long puts. Both positions leave them short gamma above and long gamma below in ways that produce the familiar exposure profile, with a crossover point somewhere near the money.

The convention is not stupid. It captures something real about how retail flow is shaped, and profiles built on it have often looked broadly sensible when compared against subsequent behaviour. But "broadly sensible" is doing a great deal of work in that sentence, and it is not the same as verified.

Where it breaks

The assumption fails in specific, identifiable situations, and it fails hardest in the markets people most want to analyse.

Systematic call selling. Covered-call and buy-write funds sell calls in size, on a schedule, at predictable strikes. Under the standard convention those contracts get attributed to customers buying, which flips the assumed dealer side. The strategy has grown substantially, and it is concentrated in exactly the index products where gamma analysis is most popular.
Put buying as insurance. A pension fund buying downside protection is a customer buying puts, not selling them. The convention assumes the opposite.
Spreads. A large fraction of options volume is multi-leg. One leg looked at in isolation implies a position the trader does not hold, and open interest records legs, not structures.
Dealer-to-dealer trades. Not every counterparty is a customer. Market makers trade with each other constantly, and those contracts sit in open interest looking exactly like customer flow.
Single stocks versus indices. Flow composition differs sharply. A model calibrated on index behaviour applied to a single name is being asked to describe a different population.
Zero-day expiries. A large and growing share of index option volume now expires the same day, much of it never becoming open interest at all. Any figure computed from end-of-day open interest is blind to it.

Why the sign matters more than the size

If the assumption is somewhat wrong, the magnitude is off, which is survivable. If it is wrong about who holds which side at a strike carrying meaningful size, the sign of the exposure flips.

That is not a smaller version of the same conclusion. It is the opposite conclusion. A market described as long gamma, where hedging is said to dampen moves, becomes a market described as short gamma, where hedging is said to amplify them. Someone reading the chart would take away precisely the reverse of what the chart intended to convey, with no visible indication that anything had gone wrong.

This is the characteristic failure mode of derived data. A noisy measurement tells you it is noisy. A confidently signed estimate built on a wrong premise does not.

Attempts to do better

Practitioners are aware of the problem and there are several standard refinements. None of them close the gap; they narrow it.

Trade-side inference. Rather than assuming, classify each print by whether it traded nearer the bid or the offer, and build up positioning from the flow. Better in principle. It inherits every weakness described in the data integrity essay, because the same classification problem applies, and it accumulates those errors over time.

Open interest change. Comparing volume against the change in open interest distinguishes new positions from closed ones. Genuinely useful, and it is real reported data rather than inference. It still does not say which side opened.

Exchange-published participant data. Some venues publish aggregate positioning by participant category, at low frequency and high aggregation. Real data, too coarse and too slow for the levels people want to draw on an intraday chart.

The honest summary is that the refinements improve the estimate without ever making it a measurement.

What you can and cannot say

The mechanism is not in doubt. A dealer who takes the other side of an options trade does hedge in the underlying, does adjust that hedge as price, volatility and time move, and those adjustments are large in aggregate. None of that depends on any assumption. It follows from how market making works.

What is in doubt is the direction and size of the aggregate at any given moment. So:

Defensible: options hedging generates real flow in the underlying, and it concentrates where open interest is large and where gamma is highest.
Defensible: open interest by strike is reported data, and the concentrations it shows are real.
An estimate: the sign and magnitude of aggregate dealer gamma.
An estimate built on an estimate: the gamma flip level, which depends on the sign being right across the whole profile.
Not supported: any statement of the form "dealers are positioned such that this level will hold", said with confidence and no error bar.

How to read a gamma chart honestly

Ask what convention produced it. Providers differ, and a chart that will not tell you its assumption is not showing you a measurement.
Treat the levels as approximate. They are recomputed from data that updates daily, on a model that cannot be checked. A level quoted to the point is false precision.
Weight open interest above derived exposure. Where contracts sit is reported. What that implies about hedging is not.
Distrust anything that flips on a small parameter change. If a conclusion depends on which convention was used, you have found a property of the model.
Watch for the situations above. Heavy systematic call selling, expiry weeks, and single names with unusual flow are the conditions where the assumption is most likely to be wrong.

Nothing here is an argument for ignoring options flow. The hedging obligation is one of the more genuinely mechanical forces in markets, and understanding it explains behaviour that price alone does not. It is an argument for holding the numbers at the confidence they actually deserve, which is lower than the way they are usually presented.