Analytical Results and Efficient Algorithm for Optimal Portfolio Deleveraging with Market Impact
University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign - Department of Industrial and Enterprise Systems Engineering
University of Houston
June 13, 2013
Operations Research, Forthcoming
In this paper, we consider an optimal portfolio de-leveraging problem, where the objective is to meet specified debt/equity requirements at the minimal execution cost. Permanent and temporary price impact is taken into account. With no restrictions on the relative magnitudes of permanent and temporary price impact, the optimal de-leveraging problem reduces to a non-convex quadratic program with quadratic and box constraints. Analytical results on the optimal de-leveraging strategy are obtained. They provide guidance on how we liquidate a portfolio according to endogenous and exogenous factors. A Lagrangian method is proposed to solve the non-convex quadratic program numerically. By studying the breakpoints of the Lagrangian problem, we obtain conditions under which the Lagrangian method returns an optimal solution of the de-leveraging problem. When the Lagrangian algorithm returns a suboptimal approximation, we present upper bounds on the loss in equity caused by using such an approximation.
Number of Pages in PDF File: 19
Keywords: optimal de-leveraging, permanent and temporary price impact, non-convex quadratic program, Lagrangian method, break-point
JEL Classification: C61, G11
Date posted: August 28, 2013 ; Last revised: September 12, 2013
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