Jumps in Cross-sectional Rank and Expected Returns: a Mixture Model

We propose a new nonlinear time series model of expected returns based on the dynamics of the crosssectional rank of realized returns. We model the joint dynamics of a sharp jump in the cross-sectional rank and the asset return by analyzing (1) the marginal probability distribution of a jump in the cross-sectional rank within the context of a duration model, and (2) the probability distribution of the asset return conditional on a jump, for which we specify different dynamics depending upon whether or not a jump has taken place. As a result, the expected returns are generated by a mixture of normal distributions weighted by the probability of jumping. The model is estimated for the weekly returns of the constituents of the SP500 index from 1990 to 2000, and its performance is assessed in an out-of-sample exercise from 2001 to 2005. Based on the one-step-ahead forecast of the mixture model we propose a trading rule, which is evaluated according to several forecast evaluation criteria and compared to 18 alternative trading rules. We find that the proposed trading strategy is the dominant rule by providing superior risk-adjusted mean trading returns and accurate value-at-risk forecasts. Copyright  2008 John Wiley & Sons, Ltd.