When traders follow each other instead of fundamentals, prices detach from reality.
Markets go parabolic every few years: tulips, railroads, dot-coms, housing, crypto. The mechanism is structural — a feedback loop between price and behavior.
A bubble doesn't require irrational people. It needs a system where participants' actions feed back into the signals they act on: rising prices attract buyers, buying raises prices, and small perturbations amplify into departures from reality.
Fundamentalists compare price to underlying value: buy below, sell above. They tether price to reality.
Chartists buy on rising trends and sell on falling ones, ignoring underlying value. They follow the loudest signal — the price itself.
Starting with 20% chartists, price tracks fundamental value. Push the chartist slider above 60% and the blue line detaches, sometimes overshooting wildly before snapping back — that snap-back is a crash.
Figure 1. Asset price driven by a mix of fundamentalists and chartists. The fundamental value drifts slowly. With few chartists the price tracks it. With many, it does not.
Bubbles are not shapeless. They follow a recognizable arc. The sequence goes roughly like this:
Stealth. Smart money enters early. The price begins to drift above fundamental value, but the move is small enough that most participants ignore it.
Awareness. The trend becomes visible. Chartists pile in. Media coverage begins. The price rise accelerates.
Mania. Everyone is buying. The narrative justifies any price. Skeptics are dismissed. The deviation from fundamental value becomes extreme.
Blow-off. Some event or simply exhaustion tips the balance. The price peaks and begins to fall. Chartists are still buying the dip, so the drop is choppy at first.
Capitulation. Trend-followers capitulate. Selling feeds selling. The price crashes back toward fundamental value, often overshooting to the downside.
Click the chart to inject a shock. Click high to hype, click low to panic-sell.
Figure 2. Bubble phases detected in real time. The sentiment bar shows aggregate trader behavior: green for buying, red for selling, and gray for holding.
Real traders switch strategies. A fundamentalist watching neighbors get rich from trend-following starts trend-following too. This is herding.
Herding is locally rational but globally destructive. Copying a profitable neighbor is reasonable, but when everyone copies, the strategy stops working — price is then supported only by the feedback loop.
In the network below, blue nodes are fundamentalists and orange nodes are chartists. Agents flip their strategy based on what their neighbors are doing and how profitable that strategy has been recently. This can be described by a transition probability $P_{i \to j}$ influenced by local neighbor sentiment and profit gaps.
Figure 3. Strategy contagion on a network. Clusters of chartists form, amplify price swings, and collapse when fundamentalists profit from the reversion.
The mechanism isn't specific to any market — it's a property of any system where participants watch and imitate each other.