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We study the portfolio choice implications of leverage constrained banks, which need to deleverage in response to price shocks so to satisfy regulatory leverage requirements.  Banks select their asset holdings in order to minimize their expected execution costs, in a financial market consisting of multiple assets. Consistent with the classic theory of portfolio choice, diversification is optimal if each bank neglects the impact caused by the other agents' liquidation actions. If banks are heterogeneous in their leverage ratios, in equilibrium they reduce portfolio overlapping and seek diversity, at the expenses of sacrificing diversification benefits on the individual level. The bank's equilibrium allocation is not socially efficient. A benevolent social planner aiming for minimum deadweight losses from liquidation should provide banks with incentives to increase their diversity.