A limiting theory for estimating and testing linear asset-pricing models with a large number of assets and a fixed time-series sample size is presented. The focus of the paper is on the modified ordinary least squares estimator of the ex-post risk premia proposed by Shanken (1992). We derive the asymptotic distribution of this estimator and show how its limiting variance can be consistently estimated. In addition, we characterize the asymptotic distribution of a cross-sectional test of the fundamental asset-pricing relation. Finally, we show how our results can be extended to deal with an unbalanced panel. The practical relevance of our findings is demonstrated using Monte Carlo simulations and an empirical application to asset-pricing models with traded risk factors. Our analysis suggests that the market, size, and value factors are often priced in the cross-section of NYSE-AMEX-NASDAQ individual stock returns. Overall, we cannot reject the null of zero risk premia for the profitability and investment factors of Fama and French (2015). Joint with Valentina Raponi, Cesare Robotti, and Paolo Zaffaroni. All of us are from Imperial College London.