Excess covariance and dynamic instability in a multi-asset model

The presence of excess covariance in financial price returns is an accepted empirical fact: the price dynamics of financial assets tend to be more correlated than their fundamentals would justify. We propose an intertemporal equilibrium multi-assets model of financial markets with an explicit and endogenous price dynamics. The market is driven by an exogenous stochastic process of dividend yields paid by the assets that we identify as market fundamentals. The model is rather flexible and allows for the coexistence of different trading strategies. The evolution of assets price and traders' wealth is described by a high-dimensional stochastic dynamical system. We identify the equilibria of the model consistent with a baseline assumption of procedural rationality. We show that these equilibria are characterized by excess covariance in prices with respect to the dividend process. Moreover, we show that in equilibrium there is a positive expected marginal profit in choosing more risky portfolios. As a consequence, the evolutionary pressure generates a trend towards more remunerative strategies, which, in turn, increase the variance of prices and the dynamic instability of the system.