Abstract This paper analyzes how an investor who is convinced that he can “beat the market” should behave when the equilibrium price process is endogenous. The investor's optimal portfolio is shown to consist of three components: (1) a tangency portfolio, (2) a hedge portfolio against changes in the market's valuation of securities, and (3) a hedging position against changes in the divergence between the investor's and the market's beliefs. The sign and magnitude of this third component will depend on investor preferences and on the divergence in the investor's and the market's quality of information. A numerical example illustrates that the effect of heterogeneous beliefs on optimal portfolio allocations can be significant. JEL classification codes: G11, G14.