A new spin on optimal portfolios and ecological equilibria

Jerome Garnier-Brun, Michael Benzaquen (), Stefano Ciliberti and Jean-Philippe Bouchaud ()
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Jerome Garnier-Brun: LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Michael Benzaquen: LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Jean-Philippe Bouchaud: X - École polytechnique - IP Paris - Institut Polytechnique de Paris, Académie des sciences [Paris, France]

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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.

Keywords: Spin-glasses; metastable states; cavity and replica method; quantitative finance; Markowitz portfolios; population dynamics (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-fmk
Note: View the original document on HAL open archive server: https://hal.science/hal-03378915v1
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Citations: View citations in EconPapers (3)

Published in Journal of Statistical Mechanics: Theory and Experiment, 2021, 2021 (9), pp.093408. ⟨10.1088/1742-5468/ac21d9⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03378915

DOI: 10.1088/1742-5468/ac21d9

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