Equilibrium Returns with Transaction Costs

Bruno Bouchard (1) , Masaaki Fukasawa (2) , Martin Herdegen (3) , Johannes Muhle-Karbe (4)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Osaka University [Osaka]
3 University of Warwick [Coventry]
4 University of Michigan [Ann Arbor]

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.

Mots clés: equilibrium; liquidity premium; FBSDEs; transaction costs

Domaines: Probabilités [math.PR]; Finance quantitative [q-fin.CP]

Bruno Bouchard, Masaaki Fukasawa, Martin Herdegen, Johannes Muhle-Karbe. Equilibrium Returns with Transaction Costs. Finance and Stochastics, 2018, 22 (3), pp.569-601. ⟨hal-01569408v3⟩