A Three-Regime Model of Speculative Behaviour: Modelling the Evolution of Bubbles in the S&P 500 Composite Index

In this paper we examine whether a three-regime model that allows for dormant, explosive and collapsing speculative behaviour can explain the dynamics of the S&P 500 Composite Index for the period 1888-2001. We extend existing two-regime models of speculative behaviour by including a third regime that allows for a bubble to grow at a steady growth rate, and examine whether other variables, beyond the deviation of actual prices from fundamental values can help predict the level and the generating state of returns. We propose abnormal volume as an indicator of the probable time of the bubble collapse and thus include abnormal volume in the state and the classifying equations of the surviving regime in the explosive state. We show that abnormal volume is a significant predictor and classifier of returns. Furthermore, we find that the spread of the 6-month average actual returns above the 6-month average fundamental returns can help predict when a bubble will enter the explosive state. Finally, we examine the financial usefulness of the three-regime model by studying the risk-adjusted profits of a trading rule formed using inferences from it. Use of the three-regime model trading rule leads to higher risk adjusted returns and end of period wealth than those obtained from employing existing models or a buy and hold strategy.