Phase-transition–like behaviour of information measures in financial markets

We apply measures based on information theory to the analysis of day close equity prices traded on US stock markets over the 13-year interval from 1995 up until after the market crash of September 2008. We show that the mutual information between prices provides insight into the changing relationships between equities over a time period which includes three known market crashes and two events which have not previously been included in this type of study, one of which is related to the sub-prime meltdown starting in 2007. Specifically, the mutual information around market crashes shows behaviour typical of the phase transitions studied in condensed-matter physics, however similar but more extended peaks in mutual information are also observed at other times not associated with any known market crashes.