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The idea that extreme trading activity contains information about the future evolution of stock prices is investigated. We find that stocks experiencing unusually high (low) trading volume over a day or a week tend to appreciate (depreciate) over the course of the following month. We argue that this high-volume return premium is consistent with the idea that shocks in the trading activity of a stock affect its visibility, and in turn the subsequent demand and price for that stock. Return autocorrelations, firm announcements, market risk, and liquidity do not seem to explain our results.