This article considers tests of alpha in linear factor pricing models when the number of securities, N, is much larger than the time dimension, T, of the individual return series. We focus on class of tests that are based on Student’s t-tests of individual securities which have a number of advantages over the existing standardized Wald type tests, and propose a test procedure that allows for non-Gaussianity and general forms of weakly cross-correlated errors. It does not require estimation of an invertible error covariance matrix, it is much faster to implement, and is valid even if N is much larger than T. We also show that the proposed test can account for some limited degree of pricing errors allowed under Ross’s arbitrage pricing theory condition. Monte Carlo evidence shows that the proposed test performs remarkably well even when T = 60 and N = 5000. The test is applied to monthly returns on securities in the S&P 500 at the end of each month in real time, using rolling windows of size 60. Statistically significant evidence against Sharpe–Lintner capital asset pricing model and Fama–French three and five factor models are found mainly during the period of Great Recession (2007M12–2009M06).

中文翻译：

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大量证券的线性因子定价模型中的 Alpha 测试

本文考虑了当证券数量 N 远大于单个回报序列的时间维度 T 时线性因子定价模型中的 alpha 测试。我们专注于基于学生对单个证券的 t 检验的测试类别，与现有的标准化 Wald 类型测试相比具有许多优势，并提出了一种允许非高斯性和一般形式的弱交叉相关的测试程序错误。它不需要估计可逆误差协方差矩阵，实施起来要快得多，并且即使 N 远大于 T 也是有效的。我们还表明，所提出的测试可以解释 Ross 允许的某些有限程度的定价误差套利定价理论条件。