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 addresses six concerns with the current market design: (1) sniping and the speed race; (2) the complexities and inefficiencies caused by tick-size constraints; (3) the cost and complexity of trading large quantities over time, (4) of trading portfolios, and (5) of providing liquidity in correlated assets; (6) fairness and transparency of optimal execution.