  We study properties of the cross-sectional distribution of returns. A
significant anti-correlation between dispersion and cross-sectional kurtosis is
found such that dispersion is high but kurtosis is low in panic times, and the
opposite in normal times. The co-movement of stock returns also increases in
panic times. We define a simple statistic $s$, the normalized sum of signs of
returns on a given day, to capture the degree of correlation in the system. $s$
can be seen as the order parameter of the system because if $s= 0$ there is no
correlation (a disordered state), whereas for $s \ne 0$ there is correlation
among stocks (an ordered state). We make an analogy to non-equilibrium phase
transitions and hypothesize that financial markets undergo self-organization
when the external volatility perception rises above some critical value.
Indeed, the distribution of $s$ is unimodal in normal times, shifting to
bimodal in times of panic. This is consistent with a second order phase
transition. Simulations of a joint stochastic process for stocks use a multi
timescale process in the temporal direction and an equation for the order
parameter $s$ for the dynamics of the cross-sectional correlation. Numerical
results show good qualitative agreement with the stylized facts of real data,
in both normal and panic times.
