Quantifying meta-correlations in financial markets

Financial markets are modular multi-level systems, in which the relationships between the individual components are not constant in time. Sudden changes in these relationships significantly affect the stability of the entire system, and vice versa. Our analysis is based on historical daily closing prices of the 30 components of the Dow Jones Industrial Average (DJIA) from March 15th, 1939 until December 31st, 2010. We quantify the correlation among these components by determining Pearson correlation coefficients, to investigate whether mean correlation of the entire portfolio can be used as a precursor for changes in the index return. To this end, we quantify the meta-correlation - the correlation of mean correlation and index return. We find that changes in index returns are significantly correlated with changes in mean correlation. Furthermore, we study the relationship between the index return and correlation volatility - the standard deviation of correlations for a given time interval. This parameter provides further evidence of the effect of the index on market correlations and their fluctuations. Our empirical findings provide new information and quantification of the index leverage effect, and have implications to risk management, portfolio optimization, and to the increased stability of financial markets. Copyright (C) EPLA, 2012