Rational Infinitely-lived Asset Prices Must Be Non-stationary

Rational expectations must not be expected to change. Hence, a rational expectation about a future random quantity must follow 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. Acknowledgement The author is grateful for stimulating discussions with Stephen Ross and for helpful comments from John Cochrane, Robert Geske, Jun Liu, and Eduardo Schwartz.