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：本文提出一种新方法，通过检验大量资产的线性因子定价模型中是否存在Alpha，来验证多因子定价理论。由于市场定价失效可能仅发生在少量异常资产上，我们开发了一种对稀疏信号特别有效的检验程序。基于高维高斯逼近理论，我们提出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，新方法在稀疏备择假设下，尤其是针对弱信号，能够实现合理的检验尺寸并显著提升检验功效。