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.

翻译：本文提出了一种新方法，通过在线性因子定价模型中检验大量资产中Alpha的存在性，以验证多因子定价理论。由于市场低效定价可能仅出现在少数异常资产中，我们开发了一种对稀疏信号尤其有效的检验程序。基于高维高斯近似理论，我们提出了一种基于模拟的方法来近似检验的极限零分布。数值研究表明，与现有检验方法相比，新程序在稀疏备择假设下能够保持合理的检验水平并实现显著的势提升，尤其是在弱信号情境下。