The increasing availability of data and potential predictor variables poses new challenges to forecasters. The task of formulating a single forecasting model that can extract all the relevant information is becoming increasingly difficult in the face of this abundance of data. The two leading approaches to addressing this "embarrassment of riches" are philosophically distinct. One approach builds forecast models based on summaries of the predictor variables, such as principal components, and the second approach is analogous to forecast combination, where the forecasts from a multitude of possible models are averaged. Using several data sets we compare the performance of the two approaches in the guise of the diffusion index or factor models popularized by Stock and Watson and forecast combination as an application of Bayesian model averaging. We find that none of the methods is uniformly superior and that no method performs better than, or is outperformed by, a simple AR(p) process.