Bubbles, crashes and risk

A restricted-perceptions equilibrium exists in which risk-averse agents believe stock prices follow a random walk with a conditional variance that is self-fulfilling. When agents estimate risk, bubbles and crashes arise. These effects are stronger when agents allow for ARCH in excess returns. •An asset pricing model where agents forecast the conditional variance of a stock’s return.•Agents believe prices follow a random walk with a conditional variance that is self-fulfilling.•Agents estimate risk in real-time using a constant gain algorithm, bubbles and crashes can arise.•ARCH effects arise from updating risk, and effects are stronger when agents estimate an ARCH model.