<div> We propose a methodology to test for the null hypothesis that the alphas of a panel of asset returns are jointly equal to zero in a linear factor pricing model with observable and tradable factors - that is, the&nbsp;<span>null of zero alpha. The test is based on equation-by-equation estimation, using a randomized version of the estimated alphas, which only requires rates of convergence. The distinct features of the proposed methodology are that it does not require the estimation of any covariance matrix, and that it allows for both N and T to pass to infinity, with the former possibly faster than the latter. Further, unlike extant approaches, the procedure can accommodate conditional heteroskedasticity, non-Gaussianity, and strong cross-sectional dependence in the error terms. We also propose a derandomized decision rule to choose in favor or against the correct specification of a linear factor pricing model. Monte Carlo simulations show that the test has satisfactory properties and it compares favorably </span><span>to several existing tests. The usefulness of the testing procedure is illustrated through an application of linear factor pricing models to the constituents of the S&amp;P 500.</span> </div>