Rare Events and Return Predictability in a Regime Switching Setting

Inspired by the recent literature on rare events and their impact on asset prices, we investigate the return predictability properties of a set of variables related to the risk of tail events extracted from equity market information and measures based on credit spreads. Our variables outperform traditional variables in terms of fit at the monthly prediction horizon. We employ both a linear model as well as a model allowing for structural breaks to obtain a better understanding of the nature of the predictability relationship. We find evidence for pronounced changes in the way the predictor variables relate to future realized returns between normal times and states of crisis, supporting theoretical models that accommodate these changes. The out-of-sample investigations show that when allowing the transition probabilities to depend on a crisis related variable, the regime switching model yields more precise forecasts than any linear model or naive forecasting method considered here. However, the regime switching models do not have a general advantage over linear models due to the difficulties in forecasting the correct future state for longer forecasting horizons, as structural breaks tend to occur suddenly