Symmetry Breaking in Stock Demand

Scale-free distributions and correlation functions found in financial data are reminiscent of the scale invariance of physical observables in the vicinity of a critical point. Here, we present empirical evidence for a transition phenomenon, accompanied by a symmetry breaking, in the investors' demand for stocks. We study the volume imbalance $\Omega$ -- difference between the number of shares traded in buyer-initiated and seller-initiated trades in a time interval $\Delta t$ -- conditioned on $\Sigma$ which is defined as the local first moment of $\Omega$ in $\Delta t$. We find that the conditional distribution $P(\Omega | \Sigma)$ undergoes a qualitative change in behavior as $\Sigma$ increases beyond a critical threshold $\Sigma_c$. For $\Sigma <\Sigma_c$, $P(\Omega|\Sigma)$ displays a maximum at $\Omega=0$, i.e., trades in $\Delta t$ are equally likely to be buyer initiated or seller initiated. For $\Sigma > \Sigma_c$, $\Omega=0$ becomes a local minimum and two new maxima $\Omega_{+}$ and $\Omega_{-}$ appear at non-zero values of $\Omega$, i.e., trades in $\Delta t$ are either predominantly buyer initiated or predominantly seller initiated. We interpret these results using a Langevin equation with multiplicative noise.