Symmetry Breaking in Stock Demand

Abstract

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 $Ω$ -- difference between the number of shares traded in buyer-initiated and seller-initiated trades in a time interval $Δt$ -- conditioned on $Σ$ which is defined as the local first moment of $Ω$ in $Δt$. We find that the conditional distribution $P(Ω| Σ)$ undergoes a qualitative change in behavior as $Σ$ increases beyond a critical threshold $Σ_c$. For $Σ<Σ_c$, $P(Ω|Σ)$ displays a maximum at $Ω=0$, i.e., trades in $Δt$ are equally likely to be buyer initiated or seller initiated. For $Σ> Σ_c$, $Ω=0$ becomes a local minimum and two new maxima $Ω_{+}$ and $Ω_{-}$ appear at non-zero values of $Ω$, i.e., trades in $Δt$ are either predominantly buyer initiated or predominantly seller initiated. We interpret these results using a Langevin equation with multiplicative noise.

5 pages, 4 figures (two-column format, revtex)