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Hybrid quantum-classical optimization for financial index tracking

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  • Samuel Fern'andez-Lorenzo
  • Diego Porras
  • Juan Jos'e Garc'ia-Ripoll

Abstract

Tracking a financial index boils down to replicating its trajectory of returns for a well-defined time span by investing in a weighted subset of the securities included in the benchmark. Picking the optimal combination of assets becomes a challenging NP-hard problem even for moderately large indices consisting of dozens or hundreds of assets, thereby requiring heuristic methods to find approximate solutions. Hybrid quantum-classical optimization with variational gate-based quantum circuits arises as a plausible method to improve performance of current schemes. In this work we introduce a heuristic pruning algorithm to find weighted combinations of assets subject to cardinality constraints. We further consider different strategies to respect such constraints and compare the performance of relevant quantum ans\"{a}tze and classical optimizers through numerical simulations.

Suggested Citation

  • Samuel Fern'andez-Lorenzo & Diego Porras & Juan Jos'e Garc'ia-Ripoll, 2020. "Hybrid quantum-classical optimization for financial index tracking," Papers 2008.12050, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2008.12050
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    References listed on IDEAS

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    1. Gilli, Manfred & Maringer, Dietmar & Schumann, Enrico, 2011. "Numerical Methods and Optimization in Finance," Elsevier Monographs, Elsevier, edition 1, number 9780123756626.
    2. Juan Francisco Monge, 2017. "Cardinality constrained portfolio selection via factor models," Papers 1708.02424, arXiv.org.
    3. Xiaojin Zheng & Xiaoling Sun & Duan Li & Jie Sun, 2014. "Successive convex approximations to cardinality-constrained convex programs: a piecewise-linear DC approach," Computational Optimization and Applications, Springer, vol. 59(1), pages 379-397, October.
    4. Beasley, J. E. & Meade, N. & Chang, T. -J., 2003. "An evolutionary heuristic for the index tracking problem," European Journal of Operational Research, Elsevier, vol. 148(3), pages 621-643, August.
    5. Rubén Ruiz-Torrubiano & Alberto Suárez, 2009. "A hybrid optimization approach to index tracking," Annals of Operations Research, Springer, vol. 166(1), pages 57-71, February.
    6. Gili Rosenberg & Poya Haghnegahdar & Phil Goddard & Peter Carr & Kesheng Wu & Marcos L'opez de Prado, 2015. "Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer," Papers 1508.06182, arXiv.org, revised Aug 2016.
    7. Abhinav Kandala & Antonio Mezzacapo & Kristan Temme & Maika Takita & Markus Brink & Jerry M. Chow & Jay M. Gambetta, 2017. "Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets," Nature, Nature, vol. 549(7671), pages 242-246, September.
    8. Iordanis Kerenidis & Anupam Prakash & D'aniel Szil'agyi, 2019. "Quantum Algorithms for Portfolio Optimization," Papers 1908.08040, arXiv.org.
    9. Roman Orus & Samuel Mugel & Enrique Lizaso, 2018. "Forecasting financial crashes with quantum computing," Papers 1810.07690, arXiv.org, revised Jun 2019.
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