Adaptive Expectations and Stock Market Crashes

A theory is developed that explains how the stock market can crash inthe absence of news about fundamentals, and why crashes are more commonthan frenzies. A crash occurs via the interaction of rational and naive investors.Naive traders believe in a simple (but reasonable) statistical modelof stock prices: that prices follow a random walk with serially correlatedvolatility. They predict future volatility adaptively, as a weighted averageof past squared price changes. We assume an initial round of trading thatestablishes a baseline price for the stock. In the next round, the price eitherremains near the baseline level or, with a small probability, "crashes" to alower level. If the price crashes, the naive traders lower their demand inresponse to the apparent increase in volatility. This lowers the risk bearingcapacity of the market, so that the lower crash price clears the market.Unlike other explanations of market crashes, this mechanism is fundamentallyasymmetric: the stock price cannot rise sharply, so frenzies or bubblescannot occur.[...]