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Divergent estimation error in portfolio optimization and in linear regression

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Abstract

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and diverges for a critical value of this parameter. This divergence is the manifestation of an algorithmic phase transition, it is accompanied by a number of critical phenomena, and displays universality. As the structure of a large number of multidimensional regression and modelling problems is very similar to portfolio optimization, the scope of the above observations extends far beyond finance, and covers a large number of problems in operations research, machine learning, bioinformatics, medical science, economics, and technology.

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Authors and Affiliations

  1. Collegium Budapest, Institute for Advanced Study, Szentháromság u. 2, 1014, Budapest, Hungary

    I. Kondor

  2. Department of Physics of Complex Systems, Eötvös University, Pázmány Péter sétány 1/A, 1117, Budapest, Hungary

    I. Kondor & I. Varga-Haszonits

  3. Analytics Department of Fixed Income Division, Morgan Stanley, Budapest, Hungary

    I. Varga-Haszonits

Authors
  1. I. Kondor
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  2. I. Varga-Haszonits
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Correspondence to I. Kondor.

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Kondor, I., Varga-Haszonits, I. Divergent estimation error in portfolio optimization and in linear regression. Eur. Phys. J. B 64, 601–605 (2008). https://doi.org/10.1140/epjb/e2008-00060-x

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  • DOI: https://doi.org/10.1140/epjb/e2008-00060-x

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