Learning about risk and return: A simple model of bubbles and crashes

This paper demonstrates that an asset pricing model with least-squares learning can lead to bubbles and crashes as endogenous responses to the fundamentals driving asset prices. When agents are risk-averse they need to make forecasts of the condi-tional variance of a stock’s return. Recursive updating of both the conditional variance and the expected return implies several mechanisms through which learning impacts stock prices. Extended periods of excess volatility, bubbles and crashes arise with a frequency that depends on the extent to which past data is discounted. A central role is played by changes over time in agents ’ estimates of risk. JEL Classifications: G12; G14; D82; D83 Key Words: Risk, asset pricing, bubbles, adaptive learning. Thus, this vast increase in the market value of asset claims is in part the indirect result of investors accepting lower compensation for risk. Such an increase in market value is too often viewed by market participants as structural and permanent... Any onset of increased investor caution elevates risk premiums and, as a consequence, lowers asset values and promotes the liquidation of the debt that supported higher asset prices. This is the reason that history has not dealt kindly with the aftermath of protracted periods of low risk premiums