Statistical physics model for the collective price fluctuations of portfolios

A statistical physics model for the collective price changes of stock portfolios is propose; it is an analogue to the spin glass model for a disordered magnetic system. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is expressed by long-range spin-spin interactions as in the Sherrington-Kirkpatrick model of spin glass (D. Sherrington and S. Kirkpatrick, 1975). The interaction coefficients between two stocks are determined by empirical data using fluctuation-response theorem. Our theory is applied to price changes of stocks in the Dow-Jones industrial portfolio. Monte Carlo simulations are performed based on the model. The resultant probability distributions of magnetization show good agreement with empirical data.