The optimal method for determining the number of latent factors in a dataset is an unresolved problem in explanatory factor analysis. This article uses several of the most commonly cited methods to determine the number of relevant factors in developed equity markets, finding that there are typically between 10 and 20. The results of these tests are evaluated against the optimal number of factors for estimating realized correlations. The author concludes that the information criteria and random matrix theory approaches provide the best results. Notwithstanding these results, they find that filtered correlation matrixes provide only a marginal advantage over the sample correlation matrix when estimating correlations. The study then examines economic interpretations of the latent factors, which adds context to the evaluation of the number. Finally, the author compares the efficacy of the modeled correlations in an important real-world application: minimum variance portfolio construction.

中文翻译：

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股票回报的潜在因素：有多少，它们是什么？

确定数据集中潜在因素数量的最佳方法是解释性因素分析中未解决的问题。本文使用几种最常引用的方法来确定发达股票市场中相关因素的数量，发现通常在 10 到 20 个之间。这些测试的结果是根据用于估计已实现相关性的最佳因素数量进行评估的。作者得出结论，信息准则和随机矩阵理论方法提供了最好的结果。尽管有这些结果，但他们发现在估计相关性时，过滤的相关矩阵仅比样本相关矩阵提供边际优势。然后，该研究检查了对潜在因素的经济解释，这为数字的评估增加了背景。最后，