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Multi-Objective Portfolio Optimization Using a Quantum Annealer

Author

Listed:
  • Esteban Aguilera

    (TNO, P.O. Box 96800, 2509 JE The Hague, The Netherlands)

  • Jins de Jong

    (TNO, P.O. Box 96800, 2509 JE The Hague, The Netherlands)

  • Frank Phillipson

    (TNO, P.O. Box 96800, 2509 JE The Hague, The Netherlands
    School of Business and Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands)

  • Skander Taamallah

    (Rabobank, P.O. Box 17100, 3500 HG Utrecht, The Netherlands)

  • Mischa Vos

    (Rabobank, P.O. Box 17100, 3500 HG Utrecht, The Netherlands)

Abstract

In this study, the portfolio optimization problem is explored, using a combination of classical and quantum computing techniques. The portfolio optimization problem with specific objectives or constraints is often a quadratic optimization problem, due to the quadratic nature of, for example, risk measures. Quantum computing is a promising solution for quadratic optimization problems, as it can leverage quantum annealing and quantum approximate optimization algorithms, which are expected to tackle these problems more efficiently. Quantum computing takes advantage of quantum phenomena like superposition and entanglement. In this paper, a specific problem is introduced, where a portfolio of loans need to be optimized for 2030, considering ‘Return on Capital’ and ‘Concentration Risk’ objectives, as well as a carbon footprint constraint. This paper introduces the formulation of the problem and how it can be optimized using quantum computing, using a reformulation of the problem as a quadratic unconstrained binary optimization (QUBO) problem. Two QUBO formulations are presented, each addressing different aspects of the problem. The QUBO formulation succeeded in finding solutions that met the emission constraint, although classical simulated annealing still outperformed quantum annealing in solving this QUBO, in terms of solutions close to the Pareto frontier. Overall, this paper provides insights into how quantum computing can address complex optimization problems in the financial sector. It also highlights the potential of quantum computing for providing more efficient and robust solutions for portfolio management.

Suggested Citation

  • Esteban Aguilera & Jins de Jong & Frank Phillipson & Skander Taamallah & Mischa Vos, 2024. "Multi-Objective Portfolio Optimization Using a Quantum Annealer," Mathematics, MDPI, vol. 12(9), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1291-:d:1382100
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    References listed on IDEAS

    as
    1. Stephen A. Rhoades, 1993. "The Herfindahl-Hirschman index," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue Mar, pages 188-189.
    2. Frank Phillipson, 2023. "Quantum Computing in Telecommunication—A Survey," Mathematics, MDPI, vol. 11(15), pages 1-18, August.
    3. Jeffrey Cohen & Alex Khan & Clark Alexander, 2020. "Portfolio Optimization of 60 Stocks Using Classical and Quantum Algorithms," Papers 2008.08669, arXiv.org.
    4. Miguel Lobo & Maryam Fazel & Stephen Boyd, 2007. "Portfolio optimization with linear and fixed transaction costs," Annals of Operations Research, Springer, vol. 152(1), pages 341-365, July.
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