Cognitive Bias in Financial Markets

The biases, briefly

Standard finance assumes traders form unbiased expectations from all available information. Kahneman and Tversky's behavioural research found something different: people weight losses roughly twice as heavily as equivalent gains (loss aversion), cling to an initial reference price when judging whether a new price is cheap or expensive (anchoring), and copy the actions of others rather than acting on independent analysis, especially under uncertainty (herding). None of these are irrational in isolation — anchoring on a recent price is a reasonable shortcut when full information is costly to gather — but in aggregate, across thousands of interacting traders, they produce price dynamics that a rational-expectations model cannot.

Two kinds of trader

The workhorse model here, in the tradition of Brock and Hommes (1998), splits the trading population into fundamentalists, who believe price reverts toward a computable fair value and trade against any deviation, and chartists (trend followers), who extrapolate whatever the recent price move has been, betting it continues. Crucially, the population is not fixed: each period, traders re-evaluate which strategy has been more profitable recently and switch accordingly, weighted by a parameter that controls how sensitive the switching is to a performance gap.

How a bubble forms in the model

demand_fund   = beta * (fair_value - price)        // pulls toward fair value
demand_chart  = gamma * (price - price_lag)         // pushes with the trend

price_next = price + eta * ( w_fund * demand_fund + w_chart * demand_chart )

w_fund, w_chart : fractions of traders using each rule this period,
                  updated by relative recent profitability

When chartists briefly outperform — which happens by chance even in a fair market — more traders switch to trend-following, which itself pushes the trend further, which makes chartists look even more profitable, and so on. This positive feedback is what a bubble is, mechanically: a self-reinforcing majority of trend-followers pushing price away from fundamental value. The bubble ends when the gap grows large enough that fundamentalist demand (which grows with the size of the deviation) overwhelms the chartist push, or when a shock reverses the recent trend and flips the switching logic into a self-reinforcing decline — the crash.

The stylized facts this reproduces

Real financial returns share several statistical regularities that a simple random walk does not: fat tails (extreme moves are far more common than a normal distribution predicts), volatility clustering (large moves tend to be followed by more large moves, of either sign), and near-zero autocorrelation in returns themselves despite strong autocorrelation in their magnitude. A switching fundamentalist-chartist model reproduces all three qualitatively from nothing more exotic than the two trading rules above plus a switching mechanism — no fat-tailed news shocks need to be assumed, because the feedback loop itself manufactures the fat tail.

What this does and does not explain

The model is deliberately stylized: it says nothing about which specific asset will bubble next or when a particular crash will occur, because the switching dynamics are chaotic and sensitive to initial conditions in the same way weather is. What it does explain is why bubbles and crashes are a structural feature of markets populated by people using simple, individually reasonable heuristics, rather than requiring irrationality, fraud or external shocks as a trigger — the shock can just as easily be an ordinary run of luck for one trading strategy over another.

Frequently asked questions

Try it live

Everything above runs in your browser — open Cognitive Bias in Financial Markets and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.