Analytical results and efficient algorithm for optimal portfolio deleveraging with market impact

Jingnan Chen, Liming Feng, Jiming Peng, Yinyu Ye

Research output: Contribution to journalArticle

Abstract

In this paper, we consider an optimal portfolio deleveraging 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 deleveraging problem reduces to a nonconvex quadratic program with quadratic and box constraints. Analytical results on the optimal deleveraging 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 nonconvex 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 deleveraging problem. When the Lagrangian algorithm returns a suboptimal approximation, we present upper bounds on the loss in equity caused by using such an approximation.

Original languageEnglish (US)
Pages (from-to)195-206
Number of pages12
JournalOperations Research
Volume62
Issue number1
DOIs
StatePublished - Jan 1 2014

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Keywords

  • Breakpoint
  • Lagrangian method
  • Nonconvex quadratic program
  • Optimal deleveraging
  • Permanent and temporary price impact

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research

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