This paper develops a new estimation procedure for characteristic-based factor models of stock returns. We treat the factor model as a weighted additive nonparametric regression model, with the factor returns serving as time-varying weights and a set of univariate nonparametric functions relating security characteristic to the associated factor betas. We use a time-series and cross-sectional pooled weighted additive nonparametric regression methodology to simultaneously estimate the factor returns and characteristic-beta functions. By avoiding the curse of dimensionality, our methodology allows for a larger number of factors than existing semiparametric methods. We apply the technique to the three-factor FamaFrench model, Carhart's four-factor extension of it that adds a momentum factor, and a five-factor extension that adds an own-volatility factor. We find that momentum and own-volatility factors are at least as important, if not more important, than size and value in explaining equity return comovements. We test the multifactor beta pricing theory against a general alternative using a new nonparametric test.