Adaptive Expectations and Stock Market Crashes

Abstract

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. From time to time, the rational traders sharply lower their demand for stocks, causing prices to fall below fundamentals. This raises naive investors' assessment of future volatility. Since naive traders are risk averse, their demand for stocks falls. This lowers the market's risk-bearing ability after the crash. Anticipating this, a rational trader has no incentive to bid up prices on the day of the crash. Unlike other explanations of market crashes, this mechanism is fundamentally asymmetric: the price of stocks cannot exceed fundamentals, so frenzies or bubbles cannot occur.

Keywords: Stock market crashes, adaptive expectations