We study the behavior of a large trader with private information about the mean of an asset with a risky return. We argue that if the variability of the return is not too great, typically the trader will find it desirable to ensure that the market price does not reveal his information, that is, that a "pooling" equilibrium arises. Such an equilibrium has the advantage of avoiding the incentive constraints that arise in "separating" equilibria, where information can be inferred from prices. Thus the efficient market hypothesis may well fail if there is imperfect competition. Despite the uniformativeness of prices, the other (competitive) traders are also better off in the pooling equilibrium than in any separating equilibrium, again if one assumes limited variability.