This paper considers the possibility of static and dynamic speculation when traders have rational expectations. Its central theme is that, unless traders have different priors or are able to obtain insurance in the market, speculation relies on inconsistent plans, and thus is ruled out by rational expectations. Its main contribution lies in the integration of the rational expectations equilibrium concept into a model of dynamic asset trading and in the study of the speculation created by potential capital gains. Price bubbles and their martingale properties are examined. It is argued that price bubbles rely on the myopia of traders and that they disappear if traders adopt a truly dynamic maximizing behavior.