Abstract
We review recent work on quantifying collective behavior among stocks by applying the conceptual framework of random matrix theory (RMT), developed in physics to describe the energy levels of complex systems. RMT makes predictions for “universal” properties that do not depend on the interactions between the elements comprising the system; deviations from RMT provide clues regarding system-specific properties. WE compare the statistics of the cross-correlation matrix C—whose elements C i,j are the correlation coefficients of price fluctuations of stock i and j — against a random matrix having the same symmetry properties. It is found that RMT methods can distinguish random and non-random parts of C. The non-random part of C which deviates from RMT results, provides information regarding genuine collective behavior among stocks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Campbell, A. W. Lo, and A. MacKinlay, The Econometrics of Financial Markets. Princeton University Press, 1997.
L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters, Phys. Rev. Lett. 83 (1999) 1467.
V. Plerou, P. Gopikrishnan, B. Rosenow, L. A. N. Amaral, and H. E. Stanley, Phys. Rev. Lett. 83 (1999) 1471.
S. Drozdz, F. Gruernmer, F. Ruf, and J. Speth, Physica A 287 (2000) 440.
J. D. Noh Phys. Rev. E 61 (2000) 5981.
M. Marsili. e-print cond-mat/0003241.
P. Gopikrishnan, B. Rosenow, V. Plerou, and H. E. Stanley, e-print cond-mat/0011145
V. Plerou, P. Gopikrishnan, L. A. N. Amaral, M. Meyer, and H. E. Stanley, Phys. Rev. E 60 (1999) 6519.
T. Lux, Applied Financial Economics 6 (1996) 463.
R. Muirhead, Aspects of Multivariate Statistical Theory. Wiley, New York, 1982.
F. J. Dyson, Revista Mexicana de Fisica 20 (1971) 231.
A. M. Sengupta and P. P. Mitra, Phys. Rev. E 60 (1999) 3389.
R. N. Mantegna Eur. Phys. J. B 11 (1999) 193.
G. Bonanno, F. Lillo, and R. N. Mantegna. e-print cond-mat/0009350.
P. C. Hohenberg and B. I. Halperin Rev. Mod. Phys. 49(1977) 435.
S.-K. Ma, Modern Theory of Critial Phenomena. Benjamin, Reading, Massachusetts, 1976.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Japan
About this paper
Cite this paper
Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Stanley, H.E. (2002). A Random Matrix Theory Approach to Quantifying Collective Behavior of Stock Price Fluctuations. In: Takayasu, H. (eds) Empirical Science of Financial Fluctuations. Springer, Tokyo. https://doi.org/10.1007/978-4-431-66993-7_5
Download citation
DOI: https://doi.org/10.1007/978-4-431-66993-7_5
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-66995-1
Online ISBN: 978-4-431-66993-7
eBook Packages: Springer Book Archive