Revisiting the Duration Dependence in the US Stock Market Cycles

Abstract

There is a big controversy among both investment professionals and academics regarding the question of how the probability that a bull or bear market terminates depends on its age. Using more than two centuries of data on the broad US stock market index, in this paper we revisit the duration dependence in bull and bear markets. We find that for both bull and bear markets the duration dependence is a nonlinear function of the state age. Our results suggest that the duration dependence in bear markets is strictly positive. For 93% of bull markets the duration dependence is also positive. Only about 7% of the bull markets, those with the longest durations, do not exhibit positive duration dependence. We also compare a few selected theoretical distributions in describing the duration dependence in bull and bear markets. We find that the gamma distribution most often provides the best fit to both the survivor and hazard functions of bull and bear markets. However, our results reveal that none of the selected distributions correctly describes the right tail of the hazard functions.