Market Panics: Correlation Dynamics, Dispersion and Tails

Lisa Borland

The financial crisis of 2008 prompted us to explore statistical signatures of market panic. In particular, we focus on the properties of the cross-sectional distribution of returns and propose a model for the cross-sectional dynamics. On daily timescales, we find a significant anti-correlation between dispersion and cross-sectional kurtosis such that dispersion is high but kurtosis is low in times of panic, and vice versa in normal times. This appears counter-intuitive at first, because times of panic have wild returns, so-called “black swans” (Taleb 2007) and rare events, which are typically associated with fat-tailed distributions (high kurtosis). We also find that the co-movement of stock returns increases in times of panic. In order to model these dynamics, we have proposed (Borland 2009) a joint stochastic process to describe the behaviour of stocks across time as well as their interactions at each point in time. The basic idea is a simple model of self-organisation, such that there occurs a spontaneous phase transition to a highly correlated state at the onset of panic. We quantify this with a simple statistic, s, the normalised sum of signs of returns on a given day, which