Analytical Results and Efficient Algorithm for Optimal Portfolio Deleveraging with Market Impact

Operations Research, Forthcoming

19 Pages Posted: 28 Aug 2013 Last revised: 12 Sep 2013

Jingnan Chen

University of Illinois at Urbana-Champaign

Liming Feng

University of Illinois at Urbana-Champaign - Department of Industrial and Enterprise Systems Engineering

Jiming Peng

University of Houston

Yinyu Ye

Independent

Date Written: June 13, 2013

Abstract

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.

Keywords: optimal de-leveraging, permanent and temporary price impact, non-convex quadratic program, Lagrangian method, break-point

JEL Classification: C61, G11

Suggested Citation

Chen, Jingnan and Feng, Liming and Peng, Jiming and Ye, Yinyu, Analytical Results and Efficient Algorithm for Optimal Portfolio Deleveraging with Market Impact (June 13, 2013). Operations Research, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2316893

Jingnan Chen (Contact Author)

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

Liming Feng

University of Illinois at Urbana-Champaign - Department of Industrial and Enterprise Systems Engineering ( email )

104 S. Mathews Avenue
Urbana, IL 61801
United States

Jiming Peng

University of Houston ( email )

Houston, TX 77204
United States

Yinyu Ye

Independent

No Address Available

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