Extracting bull and bear markets from stock returns∗

Traditional methods used to partition the market index into bull and bear regimes often sort returns ex post based on a deterministic rule. We model the entire return distribution; two states govern the bull regime and two govern the bear regime, allowing for rich and heterogeneous intra-regime dynamics. Our model can capture bear market rallies and bull market corrections. A Bayesian estimation approach accounts for parameter and regime uncertainty and provides probability statements regarding future regimes and returns. Applied to 123 years of data our model provides superior identification of trends in stock prices. ∗The authors are grateful for comments from seminar participants at Brock University, McMaster University, and the Econometrics Workshop at the Rimini Centre for Economic Analysis and to the Social Sciences and Humanities Research Council of Canada for financial support. †Department of Economics, University of Toronto and RCEA, [email protected] ‡Rotman School of Management, University of Toronto and CIRANO, [email protected] §Department of Economics, University of Toronto, [email protected]