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

Author

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  • Jingnan Chen

    (Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801)

  • Liming Feng

    (Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801)

  • Jiming Peng

    (Department of Industrial Engineering, University of Houston, Houston, Texas 77004)

  • Yinyu Ye

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

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.

Suggested Citation

  • Jingnan Chen & Liming Feng & Jiming Peng & Yinyu Ye, 2014. "Analytical Results and Efficient Algorithm for Optimal Portfolio Deleveraging with Market Impact," Operations Research, INFORMS, vol. 62(1), pages 195-206, February.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:1:p:195-206
    DOI: 10.1287/opre.2013.1222
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    References listed on IDEAS

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    Cited by:

    1. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.
    2. Hezhi Luo & Yuanyuan Chen & Xianye Zhang & Duan Li & Huixian Wu, 2020. "Effective Algorithms for Optimal Portfolio Deleveraging Problem with Cross Impact," Papers 2012.07368, arXiv.org, revised Jan 2021.
    3. Edirisinghe, Chanaka & Jeong, Jaehwan, 2019. "Indefinite multi-constrained separable quadratic optimization: Large-scale efficient solution," European Journal of Operational Research, Elsevier, vol. 278(1), pages 49-63.
    4. Hezhi Luo & Xianye Zhang & Huixian Wu & Weiqiang Xu, 2023. "Effective algorithms for separable nonconvex quadratic programming with one quadratic and box constraints," Computational Optimization and Applications, Springer, vol. 86(1), pages 199-240, September.
    5. Ningyuan Chen & Steven Kou & Chun Wang, 2018. "A Partitioning Algorithm for Markov Decision Processes with Applications to Market Microstructure," Management Science, INFORMS, vol. 64(2), pages 784-803, February.
    6. Yi Li & Ju’e Guo & Kin Keung Lai & Jinzhao Shi, 2022. "Optimal portfolio liquidation with cross-price impacts on trading," Operational Research, Springer, vol. 22(2), pages 1083-1102, April.
    7. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    8. Edirisinghe, Chanaka & Jeong, Jaehwan & Chen, Jingnan, 2021. "Optimal portfolio deleveraging under market impact and margin restrictions," European Journal of Operational Research, Elsevier, vol. 294(2), pages 746-759.
    9. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.

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