Index cohesive force analysis of the U.S. stock market

The 2007-2009 financial crisis, and its fallout, has strongly emphasized the need to define new ways and measures to study and assess the dynamics of financial markets. The S & P500 dynamics during 4/1999-4/2010 is investigated in terms of the index cohesive force (ICF - the balance between the stock correlations and the partial correlations after subtraction of the index contribution). We found a rapid market transition at the end of 2001 from a flexible state of low ICF into a stiff (nonflexible) state of high ICF that is prone to market systemic collapses. The stiff state is also marked by strong effect of the market index on the stock-stock correlations as well as bursts of high stock correlations reminiscence of epileptic brain activity. Finally, we make use of the recently introduced stock dependency networks to uncover changes in the market structure following the transition at the end of 2001. This analysis sheds new light on the origin and nature of the current crisis. The new approach is likely to be applicable to other classes of complex systems from gene networks to the human brain.