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Spin models of markets inspired by physics models of magnetism, as the Isingmodel, allow for the study of the collective dynamics of interacting agents ina market. The number of possible states has been mostly limited to two (buy orsell) or three options. However, herding effects of competing stocks and thecollective dynamics of a whole market may escape our reach in the simplestmodels. Here I study a q-spin Potts model version of a simple Ising marketmodel to represent the dynamics of a stock market index in a spin model. As aresult, a self-organized gain-loss asymmetry in the time series of an indexvariable composed of stocks in this market is observed.

A q-spin Potts model of markets: Gain-loss asymmetry in stock indices as an emergent phenomenon