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In a one-period model of market making with many exogenously informed traders, we first show that the variance of prices and expected.trading volume depend on the public information released at the start of trading. This is accomplished by representing beliefs with elliptically countoured distributions, for which the form of optimal decision rules does not depend on the specific distribution used. Second, if the model is altered so that the decision to become informed is made endogenous, then the decision rules of the market-maker and infomed traders depend on the public information. Third, in a multiperiod model with many informed traders and long-lived private information, recursion formulas similar to those of Kyle (1985) hold for all elliptically contoured distributions, trading volume is autocorrelated, and, unless per period liquidity trading is bounded.away from zero as new trading periods are added, informed traders' profits vanish. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.