A general randomized test for Alpha

The test is based on equation-by-equation estimation, using a <i>randomized</i> 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 <i>N</i> and <i>T</i> 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 to several existing tests.