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A new spin on optimal portfolios and ecological equilibria

Author

Listed:
  • Jerome Garnier-Brun

    (LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Michael Benzaquen

    (LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Stefano Ciliberti
  • Jean-Philippe Bouchaud

    (X - École polytechnique, Académie des sciences [Paris, France])

Abstract

We consider the classical problem of optimal portfolio construction with the constraint that no short position is allowed, or equivalently the valid equilibria of multispecies Lotka-Volterra equations, in the special case where the interaction matrix is of unit rank, corresponding to a single-resource MacArthur model. We compute the average number of solutions and show that its logarithm grows as N α , where N is the number of assets or species and α ≤ 2 3 depends on the interaction matrix distribution. We conjecture that the most likely number of solutions is much smaller and related to the typical sparsity m(N) of the solutions, which we compute explicitly. We also find that the solution landscape is similar to that of spin-glasses, i.e. very different configurations are quasi-degenerate. Correspondingly, "disorder chaos" is also present in our problem. We discuss the consequence of such a property for portfolio construction and ecologies, and question the meaning of rational decisions when there is a very large number "satisficing" solutions.

Suggested Citation

  • Jerome Garnier-Brun & Michael Benzaquen & Stefano Ciliberti & Jean-Philippe Bouchaud, 2021. "A new spin on optimal portfolios and ecological equilibria," Post-Print hal-03378915, HAL.
    • Handle: RePEc:hal:journl:hal-03378915
    DOI: 10.1088/1742-5468/ac21d9
    Note: View the original document on HAL open archive server: https://hal.science/hal-03378915
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    References listed on IDEAS

    as
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    7. Pierre-Alain Reigneron & Vincent Nguyen & Stefano Ciliberti & Philip Seager & Jean-Philippe Bouchaud, 2019. "The Case for Long-Only Agnostic Allocation Portfolios," Papers 1906.05187, arXiv.org.
    8. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679, arXiv.org.
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    Cited by:

    1. Jean Philippe Bouchaud & Matteo Marsili & Jean-Pierre Nadal, 2023. "Application of spin glass ideas in social sciences, economics and finance," Post-Print hal-04145594, HAL.
    2. Axel Pruser & Imre Kondor & Andreas Engel, 2021. "Aspects of a phase transition in high-dimensional random geometry," Papers 2105.04395, arXiv.org, revised Jun 2021.
    3. Jean-Philippe Bouchaud & Matteo Marsili & Jean-Pierre Nadal, 2023. "Application of spin glass ideas in social sciences, economics and finance," Papers 2306.16165, arXiv.org.

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    Keywords

    Spin-glasses; metastable states; cavity and replica method; quantitative finance; Markowitz portfolios; population dynamics;
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