We refine the approximate factor model of asset returns by distinguishing between strong factors, whose sum of squared factor betas grow at the same rate as the number of assets, and semi-strong factors, whose sum of squared factor betas grow to infinity, but at a slower rate. We develop a test statistic for strength of factors based on the cross-sectional mean-square of regression-estimated betas. We also describe an adjusted version of the test statistic to differentiate semi-strong factors from strong factors. We apply the methodology to daily equity returns to characterize some pre-specified factors as strong or semi-strong.

中文翻译：

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资产回报的半强因素

我们通过区分强因子和半强因子（其因子 beta 的平方和以与资产数量相同的速度增长）和半强因子（其因子 beta 的平方和增长到无穷大，但在较慢的速度。我们基于回归估计 beta 的横截面均方开发了因子强度的检验统计量。我们还描述了检验统计量的调整版本，以区分半强因素和强因素。我们将该方法应用于每日股票收益，以将一些预先指定的因素描述为强或半强。