Random matrix approach to cross correlations in financial data
(2002) In Physical Review E 65(6). Abstract
 We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate crosscorrelation matrices C of returns constructed from (i) 30min returns of 1000 US stocks for the 2yr period 19941995, (ii) 30min returns of 881 US stocks for the 2yr period 19961997, and (iii) 1day returns of 422 US stocks for the 35yr period 19621996. We test the statistics of the eigenvalues lambda(i) of C against a "null hypothesis"  a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [lambda(),lambda(+)] for the eigenvalues of random correlation matrices. We... (More)
 We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate crosscorrelation matrices C of returns constructed from (i) 30min returns of 1000 US stocks for the 2yr period 19941995, (ii) 30min returns of 881 US stocks for the 2yr period 19961997, and (iii) 1day returns of 422 US stocks for the 35yr period 19621996. We test the statistics of the eigenvalues lambda(i) of C against a "null hypothesis"  a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [lambda(),lambda(+)] for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matricesimplying a large degree of randomness in the measured crosscorrelation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. In addition, we find that these "deviating eigenvectors" are stable in time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Finally, we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/909787
 author
 Plerou, V; Gopikrishnan, P; Rosenow, B; Amaral, LAN; Guhr, Thomas ^{LU} and Stanley, HE
 organization
 publishing date
 2002
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Physical Review E
 volume
 65
 issue
 6
 publisher
 American Physical Society
 external identifiers

 wos:000176762900033
 scopus:33646976588
 ISSN
 1063651X
 DOI
 10.1103/PhysRevE.65.066126
 language
 English
 LU publication?
 yes
 id
 1af1ca0629e440d9a45fda035c9a438a (old id 909787)
 date added to LUP
 20080118 15:34:28
 date last changed
 20171210 04:31:01
@article{1af1ca0629e440d9a45fda035c9a438a, abstract = {We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate crosscorrelation matrices C of returns constructed from (i) 30min returns of 1000 US stocks for the 2yr period 19941995, (ii) 30min returns of 881 US stocks for the 2yr period 19961997, and (iii) 1day returns of 422 US stocks for the 35yr period 19621996. We test the statistics of the eigenvalues lambda(i) of C against a "null hypothesis"  a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [lambda(),lambda(+)] for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matricesimplying a large degree of randomness in the measured crosscorrelation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. In addition, we find that these "deviating eigenvectors" are stable in time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Finally, we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return.}, author = {Plerou, V and Gopikrishnan, P and Rosenow, B and Amaral, LAN and Guhr, Thomas and Stanley, HE}, issn = {1063651X}, language = {eng}, number = {6}, publisher = {American Physical Society}, series = {Physical Review E}, title = {Random matrix approach to cross correlations in financial data}, url = {http://dx.doi.org/10.1103/PhysRevE.65.066126}, volume = {65}, year = {2002}, }