# Random matrix approach to cross correlations in financial data.

@article{Plerou2002RandomMA, title={Random matrix approach to cross correlations in financial data.}, author={Vasiliki Plerou and P. Gopikrishnan and Bernd Rosenow and Luis A. Nunes Amaral and Thomas Guhr and Harry Eugene Stanley}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2002}, volume={65 6 Pt 2}, pages={ 066126 } }

We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994-1995, (ii) 30-min returns of 881 US stocks for the 2-yr period 1996-1997, and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962-1996. We test the statistics of the eigenvalues lambda(i) of C against a…

## Figures and Tables from this paper

## 787 Citations

Random Matrix Application to Correlations Among Volatility of Assets

- Economics
- 2013

In this paper, we apply tools from the random matrix theory (RMT) to estimates of correlations across volatility of various assets in the S&P 500. The volatility inputs are estimated by modeling…

Correlation and volatility in an Indian stock market: A random matrix approach

- Economics
- 2007

Abstract.We examine the volatility of an Indian stock market in terms of
correlation of stocks and quantify the volatility using the random
matrix approach. First we discuss trends observed in the…

Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

- Computer Science
- 2013

Statistical properties of cross-correlation in the Korean stock market

- Economics
- 2011

Abstract.
We investigate the statistical properties of the cross-correlation
matrix between individual stocks traded in the Korean stock market
using the random matrix theory (RMT) and observe how…

COMPARING TEHRAN STOCK EXCHANGE AS AN EMERGING MARKET WITH A MATURE MARKET BY RANDOM MATRIX APPROACH

- Computer Science
- 2011

Analyzing the components of the deviating eigenvectors by Inverse Participation Ratio, leads us to know that the largest eigenvalue corresponds to an influence common to the whole market, as well as showing distinct industries, whose identities corresponds to the structure of the Iran business environment.

Volatility of an Indian stock market : A random matrix approach

- Economics
- 2005

We examine volatility of an Indian stock market in terms of aspects like participation, synchronization of stocks and quantification of volatility using the random matrix approach. Volatility pattern…

Random matrix theory and cross-correlations in global financial indices and local stock market indices

- Economics
- 2013

We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock…

The Information Content of the Financial Cross Correlation Matrix: Evidence from Shanghai Stock Exchange

- Computer Science2008 International Conference on Information Management, Innovation Management and Industrial Engineering
- 2008

This work uses methods of random matrix theory (RMT) to investigate the information content of the cross correlation matrix C of Shanghai stock exchange (SSE) and finds that, SSE has a particularly high value of the largest eigenvalues of 209.26, which is about 89 times larger than the theorical upper bound.

Fe b 20 04 An analysis of Cross-correlations in South African Market data

- Mathematics
- 2004

We apply random matrix theory (RMT) to the analysis of an emerging market. In particular we analyse correlation matrices C constructed from 10 years of daily data for stocks listed on the…

Random Matrix Theory Analysis of Cross-Correlation in the Nigerian Stock Exchange

- Economics
- 2017

These preliminary results on the dynamics of asset price correlations in the NSE are important for improving risk-return trade-offs associated with Markowitz’s portfolio optimization in the stock exchange, which is achieved by cleaning up the correlation matrix.

## References

SHOWING 1-10 OF 77 REFERENCES

An Introduction to Econophysics: Correlations and Complexity in Finance

- Physics, Economics
- 1999

Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.

Aspects of Multivariate Statistical Theory

- MathematicsWiley Series in Probability and Statistics
- 1982

Tables. Commonly Used Notation. 1. The Multivariate Normal and Related Distributions. 2. Jacobians, Exterior Products, Kronecker Products, and Related Topics. 3. Samples from a Multivariate Normal…

Portfolio Theory and Capital Markets

- Economics
- 1970

William Sharpe's influential Portfolio Theory and Capital Management is as relevant today as when it was first published in 1970. McGraw-Hill is proud to reintroduce tiffs hard-to-Find classic in its…

Theory of Financial Risk

- Environmental Science
- 1997

403,828. Gravity-separation-apparatus. ZOLLINGER, J., 33, Green Grove Road, Wayside, New Jersey, U.S.A. Feb. 13, 1933, No. 4377. Convention date, June 2, 1932. [Class 46.] Solid matter is removed…

Modern portfolio theory and investment analysis

- Economics
- 1981

An update of a classic book in the field, Modern Portfolio Theory examines the characteristics and analysis of individual securities as well as the theory and practice of optimally combining…

Phys

- Rev. E 60, 1390 (1999); Y. Liu, P. Cizeau, M. Meyer, C.-K. Peng, and H. E. Stanley, Physica A 245, 437 (1997); P. Cizeau, Y. Liu, M. Meyer, C.-K. Peng, and H. E. Stanley, Physica A 245, 441
- 1997

Phys

- Rev. Lett. 83, 1469
- 1999

Phys

- Rep. 299, 190
- 1998

Phys

- Rev. Lett. 69, 1093 (1992); 71, 412 (1993); Int. J. Mod. Phys. B 8, 3795 (1994); A. D. Mirlin and Y. V. Fyodorov, J. Phys. A: Math. Gen. 26, L551 (1993); E. P. Wigner, Ann. Math. 62, 548
- 1955

Investments

- EconomicsCanadian Medical Association journal
- 1924

The author argues that during Russia's new industrialization, it would be a mistake to relay on foreign investments. Instead, the domestic accumulation fund must be increased as much as possible.