Random magnets and correlations of stock price fluctuations

Abstract

Random magnets provide a paradigm for the study of competing interactions and frustration in physics. Here, we suggest that this paradigm is also useful for the study and explanation of correlations between stock price changes of di erent companies: it (i) provides for a mechanism to explain the origin of correlations, (ii) allows to understand the occurrence of power-law correlations in the time series of highly correlated eigenmodes, and (iii) is a useful framework for the analysis of optimal investment strategies where the knowledge of (anti-)correlations is an important prerequisite for the reduction of risk. The theoretical analysis of a physical system often starts by setting up a Hamiltonian describing both the dynamics of the basic constituents and the interactions between them. Then, one proceeds to calculate correlation functions relating physical observables to the microscopic Hamiltonian and compares them to experimental data. This procedure is possible because one has an a priori idea about the description of the system. The situation is di erent when describing economical systems, as there exists no microscopic theory which is applicable to all types of systems. For this reason, an inductive procedure starting with the analysis of empirical correlation function is more adequate. After getting an intuition for the system under consideration, one can proceed

Market structure explained by pairwise interactions

“…We choose this data-based approach to avoid the use of any particular microscopic schemes (e.g. trader-agent-based rules, a priori unknown) which are difficult to assess experimentally or to avoid any analogy (even if some of such models are valuable [8]). The reason is that, even if one does not know the underlying microscopic processes, the macroscopic collective behaviors can still be described by an effective model.…”

Statistical pairwise interaction model of stock market

“…In this view, the spin-glass paradigm seems to be a seducing candidate to explain the market structure. Spin glasses were already applied to finance but with the restricting assumption that the market dynamics follows the soft-spins Langevin dynamics [8]. There are also Ising like models which are agent-based models with specific rules such as "do what your neighbours do" or more complex dynamical rules [9,10,11].…”

Mean-variance model based on filters of minimum spanning tree

“…For example, Pafka & Kondor (2002 propose noisy covariance matrices and portfolio optimization. Rosenow et al (2002) propose random magnets and correlations of stock price fluctuations, whereas Plerou et al (2002) propose a random matrix approach to cross-correlations in financial data. Basalto et al (2005) propose clustering stock market companies via chaotic map synchronization.…”