We develop a simple financial market model in which speculators rely on trend following, contrarian and fundamental trading rules to determine their orders. Speculators’ probabilistic rule selection behavior, the only type of randomness in our model, depends on past and future performance indicators. Despite its simplicity, our model possesses a remarkable ability to match a number of important stylized facts of financial markets. For a large number of speculators, however, the model’s intrinsic noise vanishes and its dynamics is driven by an analytically-tractable four-dimensional nonlinear map. An in-depth investigation of this map offers valuable insights into the model’s functioning