Identifying Bull and Bear Markets in Stock Returns

Abstract

This paper uses a Markov switching model which incorporates duration dependence to capture nonlinear structure in both the conditional mean and variance of stock returns. The model sorts returns into a high return stable state and a low return volatile state. We label these as bull and bear markets respectively. The filter identifies all major stock market downturns in over 160 years of monthly data. We find that both bear and bull markets have declining hazard functions. Despite the declining hazards, the best market gains come at the start of a bull market. Moreover, allowing the conditional mean and volatility to vary with duration captures volatility clustering.