Temporal evolution of financial-market correlations.

We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible with uncorrelated random price changes. We then identify the principal components of these correlation matrices and demonstrate that a small number of components accounts for a large proportion of the variability of the markets that we consider. We characterize the time-evolving relationships between the different assets by investigating the correlations between the asset price time series and principal components. Using this approach, we uncover notable changes that occurred in financial markets and identify the assets that were significantly affected by these changes. We show in particular that there was an increase in the strength of the relationships between several different markets following the 2007-2008 credit and liquidity crisis.

[1]  T. Guhr,et al.  RANDOM-MATRIX THEORIES IN QUANTUM PHYSICS : COMMON CONCEPTS , 1997, cond-mat/9707301.

[2]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[3]  E. Elton,et al.  Economic News and Bond Prices: Evidence from the U.S. Treasury Market , 2001, Journal of Financial and Quantitative Analysis.

[4]  Bertrand Melenberg,et al.  Common Factors in International Bond Returns , 2000 .

[5]  Christophe Pérignon,et al.  Why common factors in international bond returns are not so common , 2007 .

[6]  Y. Abu-Mostafa,et al.  Decision Technologies for Financial Engineering: Proceedings of the Fourth International Conference on Neural Networks in the Capital Markets (NNCM '96) , 1998 .

[7]  M. Stephanov,et al.  Random Matrices , 2005, hep-ph/0509286.

[8]  A. Refenes.  Neural Networks in the Capital Markets , 1994 .

[9]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[10]  Francis X. Diebold,et al.  Real-Time Price Discovery in Global Stock, Bond and Foreign Exchange Markets , 2006 .

[12]  Eshel Ben-Jacob,et al.  RMT Assessments of the Market Latent Information Embedded in the Stocks' Raw, Normalized, and Partial Correlations , 2009 .

[13]  Nick S. Jones,et al.  Dynamic communities in multichannel data: an application to the foreign exchange market during the 2007-2008 credit crisis. , 2008, Chaos.

[14]  Anirvan M. Sengupta,et al.  Distributions of singular values for some random matrices. , 1997, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  S. Ross.  The arbitrage theory of capital asset pricing , 1976 .

[16]  L. Guttman.  Some necessary conditions for common-factor analysis , 1954 .

[17]  Dalibor S. Eterovic,et al.  Separating the Wheat from the Chaff: Understanding Portfolio Returns in an Emerging Market , 2012 .

[18]  Paul R. Kleindorfer,et al.  The Network Challenge: Strategy, Profit, and Risk in an Interlinked World , 2009 .

[19]  George Sugihara,et al.  Complex systems: Ecology for bankers , 2008, Nature.

[20]  Raj Kumar Pan,et al.  Collective behavior of stock price movements in an emerging market. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  M. Heyer,et al.  Application of Principal Component Analysis to Large-Scale Spectral Line Imaging Studies of the Interstellar Medium , 1997 .

[22]  Eric R. Ziegel,et al.  Analysis of Financial Time Series , 2002, Technometrics.

[23]  S. Ross,et al.  Economic Forces and the Stock Market , 1986 .

[24]  Donald A. Jackson.  STOPPING RULES IN PRINCIPAL COMPONENTS ANALYSIS: A COMPARISON OF HEURISTICAL AND STATISTICAL APPROACHES' , 1993 .

[25]  Leonidas Sandoval Junior,et al.  Correlation of financial markets in times of crisis , 2011, 1102.1339.

[26]  S. Goldhor.  Ecology , 1964, The Yale Journal of Biology and Medicine.

[27]  M. Bianchi,et al.  Bank of England Working Paper No.50 , 2013 .

[28]  J. Kwapień,et al.  World currency exchange rate cross-correlations , 2007, 0708.4347.

[29]  Zijun Wang,et al.  The Stock-Bond Correlation and Macroeconomic Conditions: One and a Half Centuries of Evidence , 2008 .

[30]  Richard Kershaw,et al.  Finance , 1892, Handbooks in operations research and management science.

[31]  Lingfeng Li.  Macroeconomic Factors and the Correlation of Stock and Bond Returns , 2002 .

[32]  Paul Geladi,et al.  Principal Component Analysis , 1987, Comprehensive Chemometrics.

[33]  Gregory Connor,et al.  Performance Measurement with the Arbitrage Pricing Theory: A New Framework for Analysis , 1985 .

[34]  Paul H. Malatesta.  インタビュー "Journal of Financial and Quantitative Analysis" 編集長Paul Malatesta教授 , 2005 .

[35]  J. Bouchaud,et al.  Noise Dressing of Financial Correlation Matrices , 1998, cond-mat/9810255.

[36]  Diane Wilcox,et al.  An analysis of cross-correlations in an emerging market , 2007 .

[37]  D. Reich,et al.  Principal components analysis corrects for stratification in genome-wide association studies , 2006, Nature Genetics.

[38]  T. Andersen.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1998, Econometric Theory.

[39]  P. Lane,et al.  The Drivers of Financial Globalization , 2008 .

[40]  Ruey S. Tsay,et al.  Analysis of Financial Time Series: Tsay/Analysis of Financial Time Series , 2005 .

[41]  V. Plerou,et al.  Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series , 1999, cond-mat/9902283.

[42]  Resul Eryigit,et al.  Cross correlations in an emerging market financial data , 2007 .

[43]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[44]  K. Kaski,et al.  Dynamics of market correlations: taxonomy and portfolio analysis. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  V. Plerou,et al.  Random matrix approach to cross correlations in financial data. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  D. Villemin,et al.  Chemometrics and Intelligent Laboratory Systems 24 (J994J )17-128 , 1994 .

[47]  Hawoong Jeong,et al.  Systematic analysis of group identification in stock markets. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  A. Bucciol,et al.  Risk Aversion and Portfolio Choice , 2008 .

[49]  Ericka Stricklin-Parker,et al.  Ann , 2005 .