  This paper proposes a new procedure to validate the multi-factor pricing
theory by testing the presence of alpha in linear factor pricing models with a
large number of assets. Because the market's inefficient pricing is likely to
occur to a small fraction of exceptional assets, we develop a testing procedure
that is particularly powerful against sparse signals. Based on the
high-dimensional Gaussian approximation theory, we propose a simulation-based
approach to approximate the limiting null distribution of the test. Our
numerical studies show that the new procedure can deliver a reasonable size and
achieve substantial power improvement compared to the existing tests under
sparse alternatives, and especially for weak signals.
