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Divergent estimation error in portfolio optimization and in linear regression

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  • I. Kondor
  • I. Varga-Haszonits

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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Suggested Citation

  • I. Kondor & I. Varga-Haszonits, 2008. "Divergent estimation error in portfolio optimization and in linear regression," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 64(3), pages 601-605, August.
    • Handle: RePEc:spr:eurphb:v:64:y:2008:i:3:p:601-605
    DOI: 10.1140/epjb/e2008-00060-x
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    Cited by:

    1. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679, arXiv.org.
    2. Varga-Haszonits, Istvan & Caccioli, Fabio & Kondor, Imre, 2016. "Replica approach to mean-variance portfolio optimization," LSE Research Online Documents on Economics 68955, London School of Economics and Political Science, LSE Library.

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