We propose a new market design for trading financial assets. The design allows traders to directly trade any user-defined linear combination of assets. Orders for such portfolios are expressed as downward-sloping piecewise-linear demand curves with quantities as flows (shares/second). Batch auctions clear all asset markets jointly in discrete time. Market-clearing prices and quantities are shown to exist, despite the wide variety of preferences that can be expressed. Calculating prices and quantities is shown to be computationally feasible. Microfoundations are provided to show that traders can implement optimal strategies using portfolio orders. The proposal has several advantages over the status quo.

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