Title: A theory of speculative bubbles and crashes

Abstract

The aim of this talk is to propose a new model of bubbles and crashes to elucidate a mechanism of bubbles and subsequent crashes. We consider an asset market in which the risky assets into two classes, the risky asset, and the risk-free asset are traded. Investors are divided into two groups of investors who have the different rationality on decision-making respectively. One is fundamentalists who maximize their expected utility of their wealth in the next period following their rational assessment of the fundamental values of risky assets. Another is speculators who maximize their random utility of binary choice: buying the bubble asset and holding the risk-free asst. The speculator’s behavior is modeled in a framework of the Ising spin model of statistical mechanics, which can be considered as a model of Keynse’s beauty contest metaphor. We demonstrate that (i) if speculators’ conformity effect (the extent that each noise-trader is influenced by the decisions of other speculators) is weak, then the market price converges to the fundamental price, so that the efficient market hypothesis holds, but that (ii) if speculators’ conformity effect is strong, then speculators’ herd behavior gives cause to a bubble, and their positive-feedback trading prolongs bubble, but a bubble is necessarily ended up with a crash. Furthermore, we describe that cycles of bubbles and crashes are repeated.