A noisy rational expectations model of asset trading is extended to incorporate costs of information acquisition and expectation formation. Because of the information costs, how much information to acquire becomes an important decision. Agents make this decision by choosing an expectations strategy about the future value of information. Because expectation formation is costly, agents often choose strategies that are simpler (and thus cheaper) than rational expectations. The model's dynamics can be expressed in terms of the market precision, which represents the amount of information acquired by the average agent. Under certain conditions, market precision follows an unstable and highly irregular time path. This irregularity directly affects observable market quantities. In particular, simulated time series for return volatility and trading volume display a copersistence similar to that found in actual financial data.