Modeling the Cross Section of Stock Returns: A Model Pooling Approach

Abstract

The choice of an asset pricing model in applications such as performance evaluation or cost of capital estimation is an important problem for researchers and investors alike. Model selection is a commonly used strategy in this context, i.e., the choice of one model to the exclusion of the others. Such a strategy is inherently misguided when the true model is not available to the decision maker. This paper illustrates the advantages of a model pooling approach in contrast to model selection. Model pools of several asset pricing models including the CAPM, the Fama-French (1993) three-factor model, and the Carhart (1997) four-factor model are considered for the purpose of forming expectations (i.e., predictions) of the one-step-ahead returns for a cross section of stock portfolios. The optimal model pool weights are based on the well-known log predictive score criterion, a measure of the out-of-sample prediction performance track record of a model. Using a variety of test portfolios, the optimal pool of models is shown to consistently outperform the best individual model. In many cases the CAPM is inferior on a stand-alone basis and hence is discarded under the model selection approach. However, with model pooling the CAPM is in fact assigned a positive and significant weight when optimally combined with other models since it helps to improve the performance of the pool. The advantage of the model pooling approach over model selection and Bayesian model averaging is confirmed when performance is judged by an economic metric based on average cross-sectional pricing errors. Recently proposed models like the Pástor and Stambaugh (2003) and Chen and Zhang (2009) models generally fail to beat the optimal three-model pool that includes the CAPM, Fama-French and the Carhart models. This result suggests that the optimal pool of existing models is the relevant benchmark against which to evaluate new models in the literature.

Keywords: Asset Pricing Models, Model Pooling, Log Predictive Score, Return Prediction

JEL Classification: G12, C52, C53