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.
We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled but linear forward-backward stochastic differential equations. Explicit solutions are obtained in a number of concrete settings. The sluggishness of the frictional portfolios makes the corresponding equilibrium returns mean-reverting. Compared to the frictionless case , expected returns are higher if the more risk-averse agents are net sellers or if the asset supply expands over time.
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