Forecasting the Collapse of Speculative Bubbles: An Empirical Investigation of the S&P 500 Composite Index

Abstract: In this paper we test for the presence of periodically partially collapsing, positive and negative, speculative bubbles in the S&P 500 Composite Index for the period 1888-2001. We extend existing regime-switching models of speculative behaviour by including abnormal volume as an indicator of the probable time of the bubble collapse. Abnormal volume is included as both a classifying variable that helps predict the probability of the bubble surviving, and as a factor of risk in the surviving state equation. Increased volume is considered a signal that market beliefs concerning the future of the bubble are changing. We show that abnormal volume is a significant predictor and classifier of returns. Furthermore, we examine the financial usefulness of the augmented model by studying the risk-adjusted profits of a trading rule formed using inferences from it. Use of the augmented model trading rule leads to higher risk adjusted returns than those obtained from employing existing models or a buy and hold strategy.