We consider the problem of testing the presence of alpha in Linear Factor Pricing Models. We propose a robust spatial sign-based nonparametric test, which simultaneously alleviates two prominent difficulties encountered by most existing methods, respectively caused by the high dimensionality of the securities and the departure from normality of the distributions. We rigorously show that the proposed test has desired theoretical properties and demonstrate its superior performance via Monte Carlo

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... experiments. These results are established when the number of securities is larger than the time dimension of the return series, and the distribution of the securities belongs to the wide family of elliptically symmetric distributions, which extends the normal distribution to many well-known heavy-tailed distributions. We apply the test to the monthly returns on securities in some stock markets, and show more powerful results than existing tests.