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We propose a new market design for trading financial assets. The design combines three elements: (1) orders are downward-sloping linear demand curves with quantities expressed as flows; (2) markets clear in discrete time using uniform-price batch auctions; (3) traders may submit orders for portfolios of assets, expressed as arbitrary linear combinations with positive and negative weights. Thus, relative to the status quo design: time is discrete instead of continuous, prices and quantities are continuous instead of discrete, and traders can directly trade arbitrary portfolios. Clearing prices and quantities are shown to exist, with the latter unique, despite the wide variety of preferences that can be expressed via portfolio orders. Calculating prices and quantities is shown to be computationally feasible. Microfoundations for portfolio orders are provided. The proposal has six advantages over the current market design. Flow trading (1) eliminates sniping and the speed race, (2) avoids the complexities and inefficiencies caused by tick-size constraints, (3) reduces the cost and complexity of trading large quantities over time, (4) reduces the cost and complexity of trading portfolios, (5) reduces the cost and complexity of and Peter Cramton on market design academic advisor Carta on the design of a private equity exchange. S. Kyle consultant for U.S. government agencies on issues related to competition and efficiency in financial markets. a non-executive of U.S.-based asset management company. other relevant or material financial interests to this research. Budish Booth Cramton show that when the variance-covariance matrix is the same for all traders, each trader’s equilibrium price impact matrix is proportional to the variance-covariance matrix, which implies that all price impact matrices are positive semidefinite. It is left for future study to determine under what conditions the price impact matrix is positive semidefinite in a more general setting.