Hamburg 2001 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 26: Ökonophysik II
DY 26.4: Vortrag
Dienstag, 27. März 2001, 17:00–17:15, S 5.5
Random Matrix Theory and Econophysics — •B. Rosenow1,2, P. Gopikrishnan2, V. Plerou2, L.A.N. Amaral2, and H.E. Stanley2 — 1Insitut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany — 2Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA
Random Matrix Theory (RMT) is used in many branches of physics as a “zero information hypothesis”. It describes generic behavior of different classes of systems, while deviations from its universal predictions allow to identify system specific properties. We use methods of RMT to analyze the cross-correlation matrix C of stock price changes of the largest 1000 US companies. We find [1] that the statistics of most of the eigenvalues of the spectrum of C agree with the predictions of RMT, while there are deviations for some of the largest eigenvalues. We interpret these deviations as a system specific property, i.e. containing genuine informatin about correlations in the stock market. When analyzing the eigenvectors with deviating eigenvalues like quantum mechanical wave functions one finds that they are “localized” in different business sectors [2]. Using this information one can construct stable stock portfolios with an optimized ratio of return over risk.
[1] V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, and H.E. Stanley, Phys. Rev. Lett. 83, 1471(1999)
[2] P. Gopikrisnan, B. Rosenow, V. Plerou, and H.E. Stanley, cond-mat/0011145