How to Identify and Forecast Bull and Bear Markets?

The state of the equity market, often referred to as a bull or a bear market, is of key importance for financial decisions and economic analyses. Its latent nature has led to several methods to identify past and current states of the market and forecast future states. These methods encompass semi-parametric rule-based methods and parametric regime-switching models. We compare these methods by new statistical and economic measures that take into account the latent nature of the market state. The statistical measure is based directly on the predictions, while the economic mea- sure is based on the utility that results when a risk-averse agent uses the predictions in an investment decision. Our application of this framework to the S&P500 shows that rule-based methods are preferable for (in-sample) identification of the market state, but regime-switching models for (out-of-sample) forecasting. In-sample only the direction of the market matters, but for forecasting both means and volatilities of returns are important. Both the statistical and the economic measures indicate that these differences are significant.