We develop a noisy rational expectations model of financial trade featuring investors who acquire information and trade at a range of different frequencies. In the model, a restriction on high-frequency trading lowers the efficiency of prices at high frequencies but increases the efficiency of prices at low frequencies. In a particular equilibrium of the model, investors specialize into trading at individual frequencies. High- and low-frequency investors coexist, trade with each other, and make money from each other. The model matches key features of financial markets: investors endogenously specialize into strategies distinguished by frequency; volume is disproportionately driven by high-frequency traders; and the portfolio holdings of informed investors forecast returns at the same frequencies as those at which they trade.