Rational expectations must not be expected to change. Hence, a rational expectation about a future random quantity follows a pure martingale until the uncertainty is resolved. This implies that the expectation itself could be non-stationary and, in fact, is non-stationary if the increments are iid. Most asset prices are functions of expectations about future quantities, so asset prices also could be non-stationary. This has consequences for tests based on prices rather than on returns.

Traditionally, volume has provided the link between trading activity and returns. We focus on a hitherto unexplored but intuitive measure of trading activity: the aggregate daily order imbalance, buy orders less sell orders, on the New York Stock Exchange. Order imbalance increases following market declines and vice versa, which reveals that investors are contrarians on aggregate. Order imbalances in either direction, excess buy or sell orders, reduce liquidity. Market-wide returns are strongly affected by contemporaneous and lagged order imbalances. Market returns reverse themselves after high-negative-imbalance, large-negative-return days. Even after controlling for aggregate volume and liquidity, market returns are affected by order imbalance.