Dissecting financial markets: Sectors and states
  By analyzing a large data set of daily returns with data clustering technique, we identify economic sectors as clusters of assets with a similar economic dynamics. The sector size distribution follows Zipf's law. Secondly, we find that patterns of daily market-wide economic activity cluster into classes that can be identified with market states. The distribution of frequencies of market states shows scale-free properties and the memory of the market state process extends to long times ($\sim 50$ days). Assets in the same sector behave similarly across states. We characterize market efficiency by analyzing market's predictability and find that indeed the market is close to being efficient. We find evidence of the existence of a dynamic pattern after market's crashes. 
Matteo Marsili