The trading models used to allocate capital were built on decades of academic research, tested against historical data and supervised by world-class risk managers. Those models said that what happened in the autumn of 1998 was, statistically speaking, impossible. Several times over.

The models were wrong. Not in the sense of a bad spreadsheet entry. Wrong in a deeper way: they were the wrong kind of model for the system they were attempting to describe. Foundational assumptions failed at critical points — the assumption of continuous liquidity, for example.

This is not a story about a failure of intelligence. It is a story about a category error. One that is still being made today, with the same conviction, inside most financial institutions. And when the assumptions the models are built on are tested under stress conditions, they will fail again.

Markets are not just complicated — they are complex. That distinction sounds semantic. It is not. It describes the difference between a system that rewards more analysis and a system that will always slip through the tightening net of formulas. It is the difference between getting a better answer and asking the right question. And it is the difference between using models as tools and mistaking them for certainty.

Complexity theory originated at the Santa Fe Institute, founded in 1984 by a group that included the physicist Murray Gell-Mann and the economist Brian Arthur. The idea emerged from an interdisciplinary research programme drawing on physics, biology, economics, computer science and ecology to study a particular kind of system that was seemingly impossible to model — the same kind of system that markets are. The economic theory that came from this work presents a rigorous alternative to the equilibrium-based models that still dominate financial textbooks. Eric Beinhocker’s The Origin of Wealth is the popular synthesis.

A direct cause-and-effect model — equilibrium economics — says markets can in principle be reduced to a sufficiently complete set of equations. A complexity model says they cannot. That is not a disagreement about mathematics. It is a disagreement about what you think you are looking at.

Man is good at understanding complicated systems. We build them. A jet engine is complicated. Nature builds complexity. A rainforest is complex. But this is not a question of scale.

A jet engine has many parts and many interactions. Each part has a specified function. The interactions are governed by rules that are themselves specified. If you have perfect knowledge and data on these, you can predict the engine’s behaviour under any set of conditions. You can understand any cause of any failure and design it better in each iteration. Any complicated thing is, in the strict sense, entirely knowable.

A rainforest is also a system of many parts and many interactions. But the interactions are not governed by rules. They evolve. Species adapt to one another and new species emerge. Unpredictable patterns dominate at the macro level. They emerge from the aggregate behaviour of every living entity following their own local rules and adapting to changing environmental conditions.

An emergent system is not random. Its outcomes fall within bounds — there are patterns, recurring shapes, a probability structure — but the precise outcome cannot be predicted. A rainforest model is a useful approximation that leaves out features which may, under conditions not yet observed, turn out to matter. Much like market models.

Macro-level behaviour in a complex system arises from the interactions of individual agents following relatively simple rules — and that emergent behaviour is qualitatively different from anything any individual agent intends, contains, or could produce alone. The whole is not the sum of the parts. It is something the parts collectively generate but none of them, examined in isolation, would predict.

In an ant colony, each ant follows a small set of behavioural rules. Follow this pheromone gradient, attack this kind of intruder, return food along this path. No ant knows where the colony is going. No ant has a map of the colony’s foraging strategy. There is no central planning function, no ant in charge. And yet ant colonies produce coordinated foraging patterns, build complex nest architectures, optimise food sources across acres of terrain, and adapt as a unit to changes in their environment. The colony has properties — collective intelligence, problem-solving capability, adaptive behaviour — that no individual ant possesses or could be designed to possess.

The colony is the emergent property. It exists at a level above the ants, produced by them but not contained in any of them.

Emergence is everywhere once you start looking for it. Consciousness emerging from neurons. Language evolving across millions of speakers with no committee in charge of grammar. The emergent property is the point. It is the thing the system actually is, at the level that matters.

In a complicated system, large effects generally have large causes; small inputs produce small outputs; the relationship between cause and effect is broadly proportionate and predictable. In a complex system, this relationship breaks down. Small inputs can produce disproportionately large outputs. The same conditions can produce entirely different outcomes depending on the state of the system. And systems can absorb repeated shocks without apparent effect — until suddenly they cannot.

The consequence of non-linearity is that the distribution of outcomes in a complex system has fat tails. Extreme events are not statistical outliers occurring at the predicted infrequency. They are a structural feature of how the system generates outcomes. Earthquake magnitudes follow a power law — the very large earthquakes are far more frequent than a normal distribution would predict, because the geological system that produces them is complex, not random.

Benoit Mandelbrot, who built the mathematical apparatus for fat-tailed distributions, made the case for forty years that financial returns are not normally distributed and that the assumption they are is the root cause of a long sequence of financial disasters. He was largely ignored by mainstream finance during his career and largely vindicated since.

The output of the system feeds back into its input and changes it. Critically, those loops can be amplifying — adding to the signal that produced them — rather than stabilising.

Take the spread of a contagious disease. One infected person, on average, infects more than one other and each of those infects more than one. The cases are not added linearly; they multiply. The output of the system (more infected people) becomes the input (more people transmitting), which produces more output, which becomes more input. The visceral impact of this was felt by all in 2020.

What matters is that feedback loops do not require any change in the underlying behaviour to produce dramatic shifts in outcome. Individual investors acting in their supposedly rational manner can produce a radical impact under certain feedback loop conditions: markets crash, or have manias. And they do it much more often than any equilibrium model allows. The same agents, doing the same things, in a different feedback state, produce a completely different macro pattern. Markets are discontinuous, and assuming continuous liquidity under all conditions is potentially a very expensive error.

Most complex systems contain a mix of amplifying and dampening loops. But when amplifying loops dominate, complex systems produce their most dramatic moves: epidemics, viral content, ecological collapse, financial booms and busts.

Complex systems do not change state smoothly. They can absorb pressure, maintain their apparent state, and then transition rapidly and discontinuously to a new one. The change looks sudden from the outside. From inside the system, the conditions had been building for some time.

The Danish physicist Per Bak made a substantial contribution with the sandpile model. Imagine grains of sand dropped one at a time onto a flat surface. For a long time, the pile simply gets larger. Then it begins to slope. As more grains are added, the slope steepens, and the pile reaches what Bak called self-organised criticality — a state where adding a single additional grain might do nothing, or might trigger an avalanche that takes most of the pile down. The critical state is not externally imposed. The system organises itself toward it. And the size distribution of the avalanches follows a power law.

This matters because it describes how complex systems most often produce their largest moves. The conditions accumulate quietly. Stability appears to persist. Then a triggering event — often trivial in itself — produces a cascading reorganisation that observers experience as a sudden break with the previous regime.

Adaptation. Complex systems are populated by agents that change their behaviour based on the outcomes they observe. Adaptation means the system is never stationary. The rules the agents are following at any moment are themselves the product of feedback from previous outcomes, and will change again as new outcomes arrive.

Path dependence. Where the system can go next depends on where it has been. Small contingent events in a complex system’s history have outsized consequences for its eventual structure. Once a complex system has gone down a path, the path constrains its future options. History matters in ways equilibrium models systematically ignore.

The observer effect. In a complicated system, the analyst studies the subject without affecting it. In a complex system populated by adaptive agents, the participants are the system, and their participation changes it. The observer is not outside the system. Once that is accepted, much of what looks like noise in markets begins to look like signal.

One more concept needs to be in place before we apply this framework to markets. It is the distinction between risk and uncertainty, made by the economist Frank Knight in 1921 and largely forgotten by modern finance.

Risk, in Knight’s strict usage, is a situation in which the distribution of possible outcomes is known and meaningful probabilities can be assigned to them. The roulette wheel offers risk — you don’t know which number will come up, but you know exactly what the possible numbers are and exactly how likely each is. Probability theory was built to handle exactly this kind of situation.

Uncertainty is different. Uncertainty is a situation in which the distribution of outcomes is itself unknown. You don’t know the shape of the space you are operating in. Probability theory applied to a Knightian uncertainty environment doesn’t produce useful answers — it produces the appearance of useful answers, which is worse.

The features of complex systems — emergence, non-linearity, feedback, phase transitions, adaptation, path dependence, the observer effect — generate genuine uncertainty in Knight’s sense, not calculable risk. Most quantitative risk frameworks treat uncertainty as if it were risk. This is not a small modelling shortcut. It is a category error of the most fundamental kind.

Markets are social structures. Large numbers of individuals, each acting on their own information, their own incentives, their own time horizon, and their own emotional response to the same events. They interact — buying from and selling to each other — and the prices that result are the visible output of all those interactions.

That is the definition of a complex adaptive system. Each feature of complex systems explains a category of market behaviour that the standard models treat as anomalous, irrational, or simply unexplained.

No one designs a bubble. There is no committee, no plan, no individual participant who decides that tulip bulbs in 1637, or internet stocks in 1999, should reach the price they reach. Every participant is making a decision that, within their own frame of reference, looks reasonable. The buyer in 1999 was not stupid. He had watched the price rise for three years, watched colleagues make money, and read the analysts explaining why this time the old valuation rules did not apply. Buying was the rational move, given what he could see from where he stood.

The mania is the emergent property. It is produced by the aggregate of all those individually reasonable decisions, and it is not contained in any of them.

This tells you where to look. If you want to understand a mania, studying the individual investor will not get you there. The thing to study is the system: the feedback between rising prices and rising participation, the point at which a sceptic starts to pay a social cost for scepticism, the structure that turns reasonable individual decisions into a collective result none of them intended.

On 19 October 1987, the Dow Jones Industrial Average fell 22.6% in a single day. Nothing about the news that morning explained it. There was no war, no assassination, no bankruptcy of consequence. The largest one-day fall in the history of the US market arrived on a day that, by the standards of news flow, was unremarkable.

Under the statistical assumptions built into the standard finance models — returns distributed normally, along the familiar bell curve — a one-day move of that size was effectively impossible. Not unlikely. Impossible.

This is the point Mandelbrot spent forty years making. Markets are not normally distributed. They have fat tails — extreme events occur far more often than the bell curve predicts, because the system producing them is complex, driven by feedback and crowd behaviour, not a random scatter of independent events. Mainstream quantitative finance heard him, found his conclusions inconvenient, and largely carried on as before.

In 1987, a widely used strategy called portfolio insurance was designed to protect institutional portfolios from losses. The mechanism was simple: as the market fell, the strategy automatically sold index futures, reducing exposure and limiting the downside. Sensible enough for a single fund acting alone.

But portfolio insurance was not used by a single fund acting alone. It was used by many, all running the same logic at the same time. So when the market began to fall on 19 October, the strategies began to sell. The selling drove prices lower. Lower prices triggered the strategies to sell more. A mechanism designed to dampen risk had, at the scale of the whole market, become a mechanism that amplified it. The thing built to be the brake turned out, when everyone installed the same brake, to be an accelerator.

The US housing market in the mid-2000s ran a slower version: rising house prices made the collateral behind mortgages worth more, which supported more lending, which funded more buying, which pushed prices higher still. The loop ran in reverse just as efficiently from 2007.

Return to Long-Term Capital Management. The conventional account is that LTCM was undone by the Russian government’s default on its debt in August 1998. That is true as far as it goes, but it mistakes the trigger for the cause.

LTCM had built a very large set of positions, many of them bets that two related prices which had diverged would converge again. Each position was reasonable and the historical evidence supported it. But the positions were highly leveraged, and many other sophisticated funds had noticed the same opportunities and put on similar trades. The market had quietly arrived at a critical state.

The Russian default was the grain of sand. It prompted a handful of funds to reduce risk, which moved prices against everyone holding the crowded positions, which prompted more funds to reduce risk, which moved prices further. The convergence trades did not converge. They diverged, all at once, for everybody.

The system did not move smoothly from stable to unstable. It held, and held, and then transitioned — fast, and all at once. The mechanism that transmits phase transitions through a market has a name — liquidity — and it is important enough to be the subject of its own piece.

In Section One, the observer effect was described as a general feature of complex systems. In markets, this feature is unusually strong, and it has a name. George Soros calls it reflexivity, and it has been the core of how he has explained his own approach to markets for forty years.

The standard model treats a market price as an estimate of an underlying value that exists independently of the estimate. Reflexivity says the relationship runs both ways. The price does not just reflect the fundamentals — it changes them. A company whose share price is rising can raise capital more cheaply, attract better staff, win customers who read the share price as a signal of quality, and use its valuable shares to acquire competitors. The rising price has improved the actual business.

The same loop runs in reverse. A falling price raises a company’s cost of capital, unsettles its staff, worries its customers and lenders, and can in time damage the business badly enough to justify the very fall that started the process.

A market is not a system the investor observes from outside. It is a system the investor is inside, contributing to, and changing by participating in. That is not a philosophical nicety. It is a structural fact with consequences for everything that follows.

Markets adapt because the agents in them learn. When a reliable pattern is discovered — a pricing anomaly, a profitable strategy, a factor that predicts returns — investors move to exploit it, and the act of exploiting it changes it. A market is not a fixed puzzle that yields to a solution. It is a puzzle that changes its shape in response to being solved.

Markets are path-dependent because their history constrains their present. The relationships between asset classes, the behaviour of inflation, the response of policymakers to a downturn — none of these are constants. They are the products of a particular history. An investor who builds a model on data from one regime and runs it unchanged into the next is mistaking a snapshot of one phase of a complex system for a permanent law of how the system works.

A diagnosis is only useful if it changes what you do. If markets are complex adaptive systems — which they are — then a number of things follow directly for the investor. None of them is a technique or a trick. They are closer to a change of posture: a different way of standing in relation to the market, better matched to what the market actually is.

That is the shape of the answer complexity gives you. Not a better prediction, but a better perspective. Avoiding catastrophic error matters more than precision. This is not pessimism; it is calibrating to the system.

That leaves one question open. If a market cannot be modelled precisely, what kind of working model should you build instead — and how should you hold it? That is the subject of the companion piece.