We provide a model in which irrational investors trade based upon considerations that have no inherent connection to fundamentals. However, trading activity affects market prices, and because of feedback from security prices to cash flows, the irrational trades influence underlying cash flows. As a result, irrational investors can, in some situations, earn positive expected profits. These expected profits are not market compensation for bearing risk, and can exceed the expected profits of rational informed investors. Although the trading of irrational investors cause prices to deviate from fundamental values, stock prices follow a random walk.