arXiv:cond-mat/0402389v3 [cond-mat.stat-mech] 26 Sep 2006 An analysis of cross-correlations in an emerging market Diane Wilcox a,1 Tim Gebbie b a Dept. of Mathematics & Applied Mathematics, University of Cape Town, Rondebosch, 7700, South Africa b Futuregrowth Asset Management, Private Bag X6, Newlands, 7725, South Africa Abstract We apply random matrix theory to compare correlation matrix estimators C ob- tained from emerging market data. The correlation matrices are constructed from 10 years of daily data for stocks listed on the Johannesburg Stock Exchange (JSE) from January 1993 to December 2002. We test the spectral properties of C against random matrix predictions and find some agreement between the distributions of eigenvalues, nearest neighbour spacings, distributions of eigenvector components and the inverse participation ratios for eigenvectors. We show that interpolating both missing data and illiquid trading days with a zero-order hold increases agree- ment with RMT predictions. For the more realistic estimation of correlations in an emerging market, we suggest a pairwise measured-data correlation matrix. For the data set used, this approach suggests greater temporal stability for the lead- ing eigenvectors. An interpretation of eigenvectors in terms of trading strategies is given, as opposed to classification by economic sectors. Key words: Random matrices, Cross-correlations, Finance, Emerging markets PACS: 02.10.Yn, 05.40.Ca, 05.45.Tp, 87.23.Ge 1 Introduction Correlation matrices are common to problems involving complex interactions and the extraction of information from series of measured data. Our aim is to determine empirical correlations in price fluctuations of daily sampled price data of distinct shares in a reliable way. Our investigation is based on 10 years of daily data for 250-350 traded shares listed on the JSE Main Board from January 1993 to Dec 2002. Email addresses: diane@maths.uct.ac.za (Diane Wilcox), tim.gebbie@physics.org (Tim Gebbie). 1 Corresponding author. Preprint submitted to Elsevier Science 2 February 2008