Adaptive Expectations and Stock Market Crashes

A theory is developed that explains how the stock market can crash in the absence of news about fundamentals, and why crashes are more common than frenzies. A crash occurs via the interaction of rational and naive investors. Naive traders believe in a simple (but reasonable) statistical model of stock prices: that prices follow a random walk with serially correlated volatility. They predict future volatility adaptively, as a weighted average of past squared price changes. In a crash, the naive traders lower their demand in response to the apparent increase in volatility. This lowers the risk bearing capacity of the market, so that the lower crash price clears the market. Unlike other explanations of market crashes, this mechanism is fundamentally asymmetric: the stock price cannot rise sharply, so frenzies or bubbles cannot occur.