Phase separation behavior in financial markets
ABSTRACT :
One of the spectacular examples of a complex system is the financial market, which displays rich correlation structures among price returns of different assets. The eigenvalue decomposition of a correlation matrix into partial correlations – market, group and random modes, enables identification of dominant stocks or “influential leaders†and sectors or “communitiesâ€. The correlation-based network of leaders and communities changes with time, especially during market events like crashes, bubbles, etc. Using the eigen-entropy measure, computed from the eigen-centralities (ranks) of different stocks in the correlation network, we extract information about the “disorder†(or randomness) in the market correlation and its different modes. The relative-entropy measures computed for these modes enable us to construct a “phase spaceâ€, where the different market events undergo “phase-separation†and display “order-disorder†transitions, as observed in critical phenomena in physics. We demonstrate these using the data from US S&P-500 and Japanese Nikkei-225 financial markets, over a 32-year period.