Divergent estimation error in portfolio optimization and in linear regression
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
Published online: 8 February 2008
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.
PACS: 02.50.Tt – Inference methods / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.65.Gh – Economics; econophysics, financial markets, business and management
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008