We propose a nonparametric method to study which characteristics provide incremental information for the cross-section of expected returns. We use the adaptive group LASSO to select characteristics and to estimate how selected characteristics affect expected returns nonparametrically. Our method can handle a large number of characteristics and allows for a flexible functional form. Our implementation is insensitive to outliers. Many of the previously identified return predictors don’t provide incremental information for expected returns, and nonlinearities are important. We study our method’s properties in simulations and find large improvements in both model selection and prediction compared to alternative selection methods.

We propose a simple and computationally attractive method to deal with missing data in in cross-sectional asset pricing using conditional mean imputations and weighted least squares, cast in a generalized method of moments (GMM) framework. This method allows us to use all observations with observed returns; it results in valid inference; and it can be applied in nonlinear and high-dimensional settings. In simulations, we find it performs almost as well as the efficient but computationally costly GMM estimator. We apply our procedure to a large panel of return predictors and find that it leads to improved out-of-sample predictability.

We propose a new methodology for forming arbitrage portfolios that utilizes the information contained in firm characteristics for both abnormal returns and factor loadings. The methodology gives maximal weight to risk-based interpretations of characteristics’ predictive power before any attribution is made to abnormal returns. We apply the methodology to simulated economies and to a large panel of U.S. stock returns. The methodology works well in our simulation and when applied to stocks. Empirically, we find the arbitrage portfolio has (statistically and economically) significant alphas relative to several popular asset pricing models and annualized Sharpe ratios ranging from 1.31 to 1.66.