Eur. Phys. J. B 64, 601-605 (2008)
https://doi.org/10.1140/epjb/e2008-00060-x

Divergent estimation error in portfolio optimization and in linear regression

¹ Collegium Budapest, Institute for Advanced Study, Szentháromság u. 2, 1014 Budapest, Hungary
² Department of Physics of Complex Systems, Eötvös University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
³ Analytics Department of Fixed Income Division, Morgan Stanley, Budapest, Hungary

Corresponding authors: ^a kondor@colbud.hu - ^b Istvan.Varga-Haszonits@morganstanley.com

Received: 5 October 2007
Published online: 8 February 2008

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.