Phase Transition in the S&P Stock Market

We analyze the stock prices of the S&P market from 1987 to 2012 with the covariance matrix of the firm returns determined in time windows of several years. The eigenvector belonging to the leading eigenvalue (market) exhibits in its long term time dependence a phase transition with an order parameter which can be interpreted within an agent model. From 1995 to 2005 the market is in an ordered state and after 2005 in a disordered state. We show that the influence of stocks on the market is changing and that this influence can be explained by trading volume and the stocks' beta