We analyze a multi-period model of trading with differentially informed traders, liquidity traders, and a market maker. Each informed trader's initial information is a noisy estimate of the long-term value of the asset, and the different signals received by informed traders can have a variety of correlation structures. With this setup, informed traders not only compete with each other for trading profits, they also learn about other traders' signals from the observed order flow. Our work suggests that the initial correlation among the informed traders' signals has a significant effect on the informed traders' profits and the informativeness of prices.