Analysis of Collective Behavior of Iran Banking Sector by Random Matrix Theory

Raei, Reza; Namaki, Ali; Vahabi, Hanie

doi:10.22034/ijf.2019.111729

Document Type : Original Article

Authors

¹ Prof., Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran.

² Assistant Prof., Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran.

³ MSc., Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran.

https://doi.org/10.22034/ijf.2019.111729

Abstract

Banked based financial sector of Iran leads us to focus on the banking industry and its components. One of the important aspects of this industry is its coupling structure. In this paper, we have analyzed the collective behavior of Iran banking sector by Random Matrix Approach (RMT). This technique is useful for splitting the information part of the correlation matrix from the random region. This research confirms good compliance with random matrix predictions. By removing the market mode of the system the average of the banking cross-correlation matrix changes. Then, by calculation of the participation ratio, node participation ratio and relative participation ratios of these banks, it is shown that the collective behavior of the system is so fragile. Also, by applying local and global perturbations on the banking sector, it is shown that this system is very sensitive to the global perturbation and the mean value of cross-correlations decreases rapidly that means some banks have crucial effects in the market.

Keywords

20.1001.1.26766337.2019.3.4.3.4

References

Wigner, E. P. (1951, October). On the statistical distribution of the widths and spacings of nuclear resonance levels. In Mathematical Proceedings of the Cambridge Philosophical Society (Vol. 47, No. 4, pp. 790-798). Cambridge University Press.

N. F. Johnson, P. Je_eries, P. M. Hui, et al., Financial market complexity, OUP Catalogue (2003).

Stanley, H. E., & Mantegna, R. N. (2000). An introduction to econophysics. Cambridge University Press, Cambridge.

A. Namaki, A. Shirazi, R. Raei, G. Jafari, Network analysis of a financial market based on genuine correlation and threshold method, Physica A: Statistical Mechanics and its Applications 390 (21-22) (2011) 3835-3841.

Albert, R., Jeong, H., & Barabási, A. L. (2000). Error and attack tolerance of complex networks. nature, 406(6794), 378-382.

Bouchaud, J. P., & Potters, M. (2000). Theory of financial risks (Vol. 4). From Statistical Physics to Risk Management: Cambridge University Press, Cambridge.

Namaki, A., Raei, R., & Jafari, G. R. (2011). Comparing Tehran stock exchange as an emerging market with a mature market by random matrix approach. International Journal of Modern Physics C, 22(04), 371-383.

Namaki, A., Jafari, G. R., & Raei, R. (2011). Comparing the structure of an emerging market with a mature one under global perturbation. Physica A: Statistical Mechanics and its Applications, 390(17), 3020-3025.

Namaki, A., Raei, R., Asadi, N., & Hajihasani, A. (2019). Analysis of Iran Banking Sector by Multi-Layer Approach. Iranian Journal of Finance, 3(1), 73-89.

Li, S., Xu, T., & He, J. (2016). Determination of collective behavior of the financial market. SpringerPlus, 5(1), 1-9.

Peron, T. D. M., & Rodrigues, F. A. (2011). Collective behavior in financial markets. EPL (Europhysics Letters), 96(4), 48004.

Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L. A. N., & Stanley, H. E. (1999). Universal and nonuniversal properties of cross-correlations in financial time series. Physical review letters, 83(7), 1471.

Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L. A. N., & Stanley, H. E. (2001). Collective behavior of stock price movements—a random matrix theory approach. Physica A: Statistical Mechanics and its Applications, 299(1-2), 175-180.

Lim, G., Kim, S., Kim, J., Kim, P., Kang, Y., Park, S., ... & Kim, K. (2009). Structure of a financial cross-correlation matrix under attack. Physica A: Statistical Mechanics and its Applications, 388(18), 3851-3858.

Laloux, L., Cizeau, P., Bouchaud, J. P., & Potters, M. (1999). Noise dressing of financial correlation matrices. Physical review letters, 83(7), 1467.

Utsugi, A., Ino, K., & Oshikawa, M. (2004). Random matrix theory analysis of cross-correlations in financial markets. Physical Review E, 70(2), 026110.

Plerou, V., Gopikrishnan, P., Amaral, L. A. N., Meyer, M., & Stanley, H. E. (1999). Scaling of the distribution of price fluctuations of individual companies. Physical review e, 60(6), 6519.

Mobarhan, N. S., Saeedi, A., Roodposhti, F. R., & Jafari, G. R. (2016). Network trending; leadership, followership and neutrality among companies: A random matrix approach. Physica A: Statistical Mechanics and its Applications, 462, 858-863.

Mantegna, R. N., & Stanley, H. E. (1999). Introduction to econophysics: correlations and complexity in finance. Cambridge university press.

Mehta, M. L. (2004). Random matrices, volume 142 of Pure and Applied Mathematics.

Guhr, T., Müller–Groeling, A., & Weidenmüller, H. A. (1998). Random-matrix theories in quantum physics: common concepts. Physics Reports, 299(4-6), 189-425.

Saeedian, M., Jamali, T., Kamali, M. Z., Bayani, H., Yasseri, T., & Jafari, G. R. (2019). The emergence of the world-stock-market network. Physica A: Statistical Mechanics and its Applications, 526, 120792.

Podobnik, B., Wang, D., Horvatic, D., Grosse, I., & Stanley, H. E. (2010). Time-lag cross-correlations in collective phenomena. EPL (Europhysics Letters), 90(6), 68001.

Jamali, T., & Jafari, G. R. (2015). Spectra of empirical autocorrelation matrices: A random-matrix-theory–inspired perspective. EPL (Europhysics Letters), 111(1), 10001.

Gopikrishnan, P., Plerou, V., Amaral, L. A. N., Meyer, M., & Stanley, H. E. (1999). Scaling of the distribution of fluctuations of financial market indices. Physical Review E, 60(5), 5305.

Bell, R. J., & Dean, P. (1970). Atomic vibrations in vitreous silica. Discussions of the Faraday Society, 50, 55-61.

Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L. A. N., Guhr, T., & Stanley, H. E. (2002). Random matrix approach to cross-correlations in financial data. Physical Review E, 65(6), 066126.

Pan, R. K., & Sinha, S. (2007). Collective behavior of stock price movements in an emerging market. Physical Review E, 76(4), 046116.

Cattell, R. B. (1943). The description of personality: Basic traits resolved into clusters. The journal of abnormal and social psychology, 38(4), 476.

Ward Jr, J. H. (1963). Hierarchical grouping to optimize an objective function. Journal of the American statistical association, 58(301), 236-244.

Analysis of Collective Behavior of Iran Banking Sector by Random Matrix Theory

References

References

Volume 3, Issue 4October 2019Pages 60-75

Volume 3, Issue 4
October 2019
Pages 60-75