Duration Dependence in Stock Prices: An Analysis of Bull and Bear Markets

Abstract

This paper investigates the presence of bull and bear market states in stock price dynamics. A new definition of bull and bear market states based on sequences of stopping times tracing local peaks and troughs in stock prices is proposed. Duration dependence in stock prices is investigated through posterior mode estimates of the hazard function in bull and bear markets. We find that the longer a bull market has lasted, the lower is the probability that it will come to a termination. In contrast, the longer a bear market has lasted, the higher is its termination probability. Interest rates are also found to have an important effect on cumulated changes in stock prices: increasing interest rates are associated with an increase in bull market hazard rates and a decrease in bear market hazard rates.