Abstract: We consider the problem of testing the presence of alpha in linear factor pricing models. We propose a robust spatial sign-based nonparametric test that simultaneously alleviates two prominent difficulties encountered by most existing methods, namely, those 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 using Monte Carlo 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 family of elliptically symmetric distributions, which extends the normal distribution to many well-known heavy-tailed distributions. We apply the proposed test to the monthly returns on securities in stock markets, showing that it outperforms existing tests.

Key words and phrases: Elliptical symmetric distribution, high dimensionality, linear factor pricing models, robust test for alpha, S&P's 500 securities.