### Abstract

In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Lévy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Lévy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Lévy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.

Original language | English |
---|---|

Title of host publication | Acta Physica Polonica B |

Pages | 4747-4763 |

Number of pages | 17 |

Volume | 34 |

Edition | 10 |

Publication status | Published - Oct 2003 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Acta Physica Polonica B*(10 ed., Vol. 34, pp. 4747-4763)

**Lévy matrices and financial covariances.** / Burda, Zdzislaw; Jurkiewicz, Jerzy; Nowak, Maciej A.; Papp, G.; Zahed, Ismail.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Acta Physica Polonica B.*10 edn, vol. 34, pp. 4747-4763.

}

TY - CHAP

T1 - Lévy matrices and financial covariances

AU - Burda, Zdzislaw

AU - Jurkiewicz, Jerzy

AU - Nowak, Maciej A.

AU - Papp, G.

AU - Zahed, Ismail

PY - 2003/10

Y1 - 2003/10

N2 - In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Lévy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Lévy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Lévy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.

AB - In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Lévy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Lévy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Lévy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.

UR - http://www.scopus.com/inward/record.url?scp=0142196720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142196720&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0142196720

VL - 34

SP - 4747

EP - 4763

BT - Acta Physica Polonica B

ER -