Dynamic instability in a phenomenological model of correlated assets

Abstract

We show that financial correlations exhibit a non-trivial dynamic behavior.\nWe introduce a simple phenomenological model of a multi-asset financial market,\nwhich takes into account the impact of portfolio investment on price dynamics.\nThis captures the fact that correlations determine the optimal portfolio but\nare affected by investment based on it. We show that such a feedback on\ncorrelations gives rise to an instability when the volume of investment exceeds\na critical value. Close to the critical point the model exhibits dynamical\ncorrelations very similar to those observed in real markets. Maximum likelihood\nestimates of the model's parameter for empirical data indeed confirm this\nconclusion, thus suggesting that real markets operate close to a dynamically\nunstable point.\n