Heterogeneous Investment Horizons in a Simple Asset Pricing Model

In this paper we study the dynamics of a simple asset pricing model describing the trading activity of heterogeneous agents in a ''stylized'' market. The economy in the model contains two assets: a bond with risk-less return and a dividend paying security. The price of the security is determined through Walrasian mechanism. Traders are speculators described as expected utility maximizers with heterogeneous beliefs about future prices and with heterogeneous estimation of risk. In particular, we consider traders who base their investment decision on different time horizons and we analyze the effect of these differences on the price dynamics. Under suitable parameterization, the stock no-arbitrage ``fundamental'' price can emerge as a stable fixed point of the model dynamics. For different parameterizations, however, the market shows cyclical or chaotic price dynamics with speculative bubbles and crashes. We find that the sole heterogeneity of agents with respect to their time horizons is not enough to guarantee the instability of the fundamental price and the emergence of non-trivial price dynamics. However, if different groups of agents are characterized by different trading behaviors, the introduction of heterogeneous investment horizons can decrease the stability region of the ``fundamental'' fixed point. The role of time horizons results different for different trade behaviors and, in general, depends on the whole ecology of agents' beliefs.