The Ability to ''Outperform the Market'': Logical Foundations based on the Theory of Rational Beliefs

Is it theoretically legitimate for an investor to attempt to outperform the market index? Or is the investor simply deluding himself? The purpose of this paper is to apply the new Theory of Rational Beliefs (RB) to demonstrate the following result: Even when all agents have symmetric information, there exist three canonical strategies in an RB environment that make it theoretically legitimate to try to outperform the market. More specifically, while the three strategies that we will identify are not directly implied by RB theory which is a positive theory, the strategies are logically compatible with RB theory when interpreted in a normative manner from the standpoint of an individual agent attempting to exploit the existence of structural change in the environment. This is what we mean by the claim that the proposed strategies are «theoretically legitimate». Moreover, we propose that these three strategies are canonical in the sense that all theoretically legitimate strategies for outperforming the market (including all successful hedge fund strategies that we know of) are combinations of these three basic strategies.