Quantifying stock return distributions in financial markets

Being able to quantify the probability of large price changes in stock markets is of crucial importance in understanding financial crises that affect the lives of people worldwide. Large changes in stock market prices can arise abruptly, within a matter of minutes, or develop across much longer time scales. Here, we analyze a dataset comprising the stocks forming the Dow Jones Industrial Average at a second by second resolution in the period from January 2008 to July 2010 in order to quantify the distribution of changes in market prices at a range of time scales. We find that the tails of the distributions of logarithmic price changes, or returns, exhibit power law decays for time scales ranging from 300 seconds to 3600 seconds. For larger time scales, we find that the distributions tails exhibit exponential decay. Our findings may inform the development of models of market behavior across varying time scales.FB acknowledges the support of UK EPSRC EP/E501311/1. HSM and TP acknowledge the support of the Research Councils UK Grant EP/K039830/1. HES acknowledges the support of IARPA and NSF (grants 1411158 and 1452061). (EP/E501311/1 - UK EPSRC; EP/K039830/1 - Research Councils UK; IARPA; 1411158 - NSF; 1452061 - NSF; 1231220 - Engineering and Physical Sciences Research Council; EP/K039830/1 - Engineering and Physical Sciences Research Council)Published versio