Learning and Stock Market Volatility

Introducing learning into a standard asset pricing model improves considerably its empirical performance. In a model of learning where today's stock price is determined by the expectation of tomorrow's stock price, the dynamics of expectations and actual price are such that the market has inertia. If the market has been increasing it will have a tendency to increase further, thereby generating large and persistent deviations of asset prices from fundamental values. For overvalued asset prices the model predicts the possibility of sudden and strong price decreases, i.e., 'stock market crashes', but no symmetric stock market increases in the presence of undervalued asset prices. These features emerge even though the deviations of agents' price expectations from perfectly rational return forecasts would be hard to detect given available sample sizes. Using a calibrated asset pricing model with habit persistence and learning, we can match the following quarterly U.S. asset pricing facts: the mean and volatility of stock returns; the mean, volatility, and autocorrelation of the price dividend ratio; and the average bond returns (equity premium). Consistent with empirical studies, the learning model also predicts that the price dividend ratio has predictive power for stock returns over the medium term (but not the short-term) and is unrelated to future fundamentals. The same model under rational expectations generates insufficient volatility and auto-correlation of the price dividend ratio and implies that the price dividend ratio is unrelated to future stock returns. The learning and rational expectations models both predict too much volatility of the short-term real interest rate, although the learning model performs somewhat better on this account.