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arXiv · 0710.1855

Divergent estimation error in portfolio optimization and in linear regression

Imre Kondor·Istvan Varga-Haszonits
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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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Imre Kondor, Istvan Varga-Haszonits. 2007-10-09. Divergent estimation error in portfolio optimization and in linear regression. https://doi.org/10.1140/epjb/e2008-00060-x

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