Abstract
We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994–95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a few of the largest eigenvalues. The eigenvectors whose eigenvalues deviate from the random matrix bound contain information about business sectors and are stable in time. Finally, we demonstrate that the sectors we identify are useful for the practical goal of finding an investment which earns a given return without exposure to unnecessary risk.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J. Campbell, A.W. Lo, and A. MacKinlay (1997) The Econometrics of Financial Markets. Princeton University Press
E.J. Elton and M.J. Gruber (1995) Modern Portfolio Theory and Investment Analysis. J. Wiley, New York
V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, and H.E. Stanley (1999) Phys. Rev. Lett. 83: 1471
L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters (1999) Phys. Rev. Lett. 83: 1467
S. Drozdz, F. Gruemmer, F. Ruf, and J. Speth (2000) Physica A 287: 440
J.D. Noh (2000) Phys. Rev. E 61: 5981
P. Gopikrishnan, B. Rosenow, V. Plerou, and H.E. Stanley (2000) Identifying Business Sectors from Stock Price Fluctuations. eprint cond-mat/0011145
E.P. Wigner (1951) Ann. Math. 53: 36
T. Guhr, A. Müller-Groeling, and H. A. Weidenmüller (1998) Phys. Rep. 299: 190
F.J. Dyson (1971) Revista Mexicana de Física 20: 231;
A.M. Sengupta and P. P. Mitra (1999) Phys. Rev. E 60: 3389
T. Lux (1996) Appl. Fin. Econ. 6: 463;
V. Plerou, P. Gopikrishnan, L.A.N. Amaral, M. Meyer, and H.E. Stanley (1999) Phys. Rev. E 60: 6519;
U.A. Müller, M.M. Dacorogna, R.B. Olsen, O.V. Pictet, M. Schwarz, and C. Morgenegg (1990) J. Bank. Fin. 14: 1189
R.N. Mantegna (1999) Eur. Phys. J. B 11: 193; G. Bonnano, F. Lillo, and R.N. Mantegna (2000) e-print cond-mat/0009350
M. Marsili (2000) Data clustering and noise undressing of correlation matrices. eprint cond-mat/0003241
P. C. Hohenberg and B. I. Halperin (1977) Rev. Mod. Phys. 49: 435;
K. H. Fisher and J. A. Hertz (1991) Spin Glasses. Cambridge University Press, New York
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Japan
About this paper
Cite this paper
Rosenow, B., Gopikrishnan, P., Plerou, V., Stanley, H.E. (2002). Random Matrix Theory and Cross-Correlations of Stock Prices. In: Takayasu, H. (eds) Empirical Science of Financial Fluctuations. Springer, Tokyo. https://doi.org/10.1007/978-4-431-66993-7_4
Download citation
DOI: https://doi.org/10.1007/978-4-431-66993-7_4
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-66995-1
Online ISBN: 978-4-431-66993-7
eBook Packages: Springer Book Archive