Physica A 390 (2011) 3020–3025 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Comparing the structure of an emerging market with a mature one under global perturbation A. Namaki a , G.R. Jafari b,∗ , R. Raei a a Department of Financial Management, Faculty of Management, University of Tehran, Tehran, Iran b Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran article info Article history: Received 14 October 2010 Received in revised form 15 March 2011 Available online 15 April 2011 Keywords: Random matrix theory Financial market Global perturbation abstract In this paper we investigate the Tehran stock exchange (TSE) and Dow Jones Industrial Average (DJIA) in terms of perturbed correlation matrices. To perturb a stock market, there are two methods, namely local and global perturbation. In the local method, we replace a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series, whereas in the global method, we reconstruct the correlation matrix after replacing the original return series with Gaussian-distributed time series. The local perturbation is just a technical study. We analyze these markets through two statistical approaches, random matrix theory (RMT) and the correlation coefficient distribution. By using RMT, we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks. We find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with Gaussian-distributed time series, the mean values of correlation coefficients, the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the RMT prediction fall sharply in both markets. By comparing these two markets, we can see that the DJIA is more sensitive to global perturbations. These findings are crucial for risk management and portfolio selection. © 2011 Elsevier B.V. All rights reserved. 1. Introduction The global financial system is composed of a large variety of markets, which exist across different geographic locations and in which a broad range of financial products are traded. Despite the diversity of markets and products that are traded, price changes of assets often respond to the same economic events and market news [1–3]. There are many reasons for us wanting to know about correlations in price movements. The most familiar motivation is for risk management and portfolio optimization purposes, because, when the prices of the assets held in the portfolio are correlated, large changes in the value of a portfolio are more likely to happen [4–7]. Basically, price fluctuations stems from an imbalance between the buy and sell orders placed by investors. This imbalance is mainly due to the heterogeneity of investors in expecting future returns [8]. The results of previous works have emphasized the complexity of financial markets [9–15]. In essence, the stock market is an example of a complex system consisting of many interacting components [8,13,14]. The price fluctuations among many stocks have complicated relationships. Lately, many researchers have investigated stock markets by establishing the corresponding stock correlation networks, of which the vertices are the stocks and edges between vertices are the price fluctuation relationships of stocks [11,12,16–20]. So, the analysis of the correlation matrix of financial networks has been an important issue in the econophysics discipline [21–27]. That means, a correlation matrix contains a complicated structure ∗ Corresponding author. Tel.: +98 21 29902773; fax: +98 21 22412889. E-mail address: g_jafari@sbu.ac.ir (G.R. Jafari). 0378-4371/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2011.04.004