We consider a model of the stock market with delegated portfolio management. All agents are rational: some trade for hedging reasons, some investors optimally contract with portfolio managers who may have stock-picking abilities, and portfolio managers trade optimally given the incentives provided by this contract. Managers try, but sometimes fail, to discover profitable trading opportunities. Although it is best not to trade in this case, their clients cannot distinguish "actively doing nothing," in this sense, from "simply doing nothing." Because of this problem: (i) some portfolio managers trade even though they have no reason to prefer one asset to another (noise trade). We also show that, (ii), the amount of such noise trade can be large compared to the amount of hedging volume. Perhaps surprisingly, (iii), noise trade may be Pareto-improving. Noise trade may be viewed as a public good. Results (i) and (ii) are compatible with observed high levels of turnover in securities markets. Result (iii) illustrates some of the possible subtleties of the welfare economics of financial markets.