This paper discusses some of the challenges faced by a policy treatment of speculative trading that is motivated by differences in beliefs. The first challenge is philosophical. Suppose two investors prefer to speculate with each other, under the common knowledge that they are motivated to trade purely by a difference in beliefs (unconditional probability assessments). In the absence of third-party costs, are there conditions under which society should try to prevent them from doing so? The second challenge is the existence of a rationale for a policy based on beliefs, as distinct from other determinants of risk preferences. The third challenge is the ability of enforcement agencies to monitor the distinction between belief-motivated trade and trade motivated by more obvious welfare-enhancing activities, such as hedging, liquidity provision, or acquiring payoff-relevant information.