We propose a methodology for estimating and testing beta-pricing models when a large numberof assets is available for investment but the number of time-series observations is fixed. Wefirst consider the case of correctly specified models with constant risk premia, and then extendour framework to deal with time-varying risk premia, potentially misspecified models, firmcharacteristics, and unbalanced panels. We show that our large cross-sectional framework posesa serious challenge to common empirical findings regarding the validity of beta-pricing models.In the context of pricing models with Fama-French factors, firm characteristics are found toexplain a much larger proportion of variation in estimated expected returns than betas. (JELG12, C12, C52)