Dynamics of competition between collectivity and noise in the stock market

Detailed study of the financial empirical correlation matrix of the 30 companies which Deutsche Aktienindex (DAX) comprised during the period of the last 11 years, using the time window of 30 trading days, is presented. This allows clear identification of a nontrivial time-dependence of the resulting correlations. In addition, as a rule, the drawdowns are always accompanied by a sizable separation of one strong collective eigenstate of the correlation matrix which, at the same time, reduces the variance of the noise states. The opposite applies to drawups. In this case, the dynamics spreads more uniformly over the eigenstates which results in an increase of the total information entropy. Analogous study of the market corresponding to Daw Jones industrial average (DJIA) leads to similar conclusions. In the latter case, however, the correlations are weaker on average. One possible reason for this effect is that the market represented by DJIA is less susceptible to various external factors than the one represented by DAX.