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Quantum Computing Approach to Realistic ESG-Friendly Stock Portfolios

Author

Listed:
  • Francesco Catalano

    (Deutsche Börse AG, 60485 Frankfurt am Main, Germany)

  • Laura Nasello

    (Deutsche Börse AG, 60485 Frankfurt am Main, Germany)

  • Daniel Guterding

    (Technische Hochschule Brandenburg, Magdeburger Straße 50, 14770 Brandenburg an der Havel, Germany)

Abstract

Finding an optimal balance between risk and returns in investment portfolios is a central challenge in quantitative finance, often addressed through Markowitz portfolio theory (MPT). While traditional portfolio optimization is carried out in a continuous fashion, as if stocks could be bought in fractional increments, practical implementations often resort to approximations, as fractional stocks are typically not tradeable. While these approximations are effective for large investment budgets, they deteriorate as budgets decrease. To alleviate this issue, a discrete Markowitz portfolio theory (DMPT) with finite budgets and integer stock weights can be formulated, but results in a non-polynomial (NP)-hard problem. Recent progress in quantum processing units (QPUs), including quantum annealers, makes solving DMPT problems feasible. Our study explores portfolio optimization on quantum annealers, establishing a mapping between continuous and discrete Markowitz portfolio theories. We find that correctly normalized discrete portfolios converge to continuous solutions as budgets increase. Our DMPT implementation provides efficient frontier solutions, outperforming traditional rounding methods, even for moderate budgets. Responding to the demand for environmentally and socially responsible investments, we enhance our discrete portfolio optimization with ESG (environmental, social, governance) ratings for EURO STOXX 50 index stocks. We introduce a utility function incorporating ESG ratings to balance risk, return and ESG friendliness, and discuss implications for ESG-aware investors.

Suggested Citation

  • Francesco Catalano & Laura Nasello & Daniel Guterding, 2024. "Quantum Computing Approach to Realistic ESG-Friendly Stock Portfolios," Risks, MDPI, vol. 12(4), pages 1-20, April.
  • Handle: RePEc:gam:jrisks:v:12:y:2024:i:4:p:66-:d:1374534
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    References listed on IDEAS

    as
    1. Li, Han-Lin & Tsai, Jung-Fa, 2008. "A distributed computation algorithm for solving portfolio problems with integer variables," European Journal of Operational Research, Elsevier, vol. 186(2), pages 882-891, April.
    2. Jeffrey Cohen & Alex Khan & Clark Alexander, 2020. "Portfolio Optimization of 60 Stocks Using Classical and Quantum Algorithms," Papers 2008.08669, arXiv.org.
    3. Andrew D. King & Jack Raymond & Trevor Lanting & Richard Harris & Alex Zucca & Fabio Altomare & Andrew J. Berkley & Kelly Boothby & Sara Ejtemaee & Colin Enderud & Emile Hoskinson & Shuiyuan Huang & E, 2023. "Quantum critical dynamics in a 5,000-qubit programmable spin glass," Nature, Nature, vol. 617(7959), pages 61-66, May.
    4. Martin R. Young, 1998. "A Minimax Portfolio Selection Rule with Linear Programming Solution," Management Science, INFORMS, vol. 44(5), pages 673-683, May.
    5. Fernando García & Tsvetelina Gankova-Ivanova & Jairo González-Bueno & Javier Oliver & Rima Tamošiūnienė, 2022. "What is the cost of maximizing ESG performance in the portfolio selection strategy? The case of The Dow Jones Index average stocks," Entrepreneurship and Sustainability Issues, VsI Entrepreneurship and Sustainability Center, vol. 9(4), pages 178-192, June.
    6. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    7. N. J. Jobst & M. D. Horniman & C. A. Lucas & G. Mitra, 2001. "Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 489-501.
    8. Jeffrey Cohen & Alex Khan & Clark Alexander, 2020. "Portfolio Optimization of 40 Stocks Using the DWave Quantum Annealer," Papers 2007.01430, arXiv.org.
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