We study equilibrium returns in a continuous-time model where heterogeneous mean-variance investors trade subject to quadratic transaction costs. The unique equilibrium is characterized by a system of coupled but linear forward-backward stochastic differential equations. Explicit solutions obtain in a number of concrete settings. The corresponding liquidity premia compared to the frictionless case are mean reverting; they are positive if the more risk-averse agents are net sellers or if the asset supply expands over time.
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