Financial firms often rely on factor models to explain correlations among asset returns. These models are important for managing risk, for example by modeling the probability that many assets will simultaneously lose value. Yet after major events, e.g., COVID-19, analysts may reassess whether existing models continue to fit well: specifically, after accounting for the factor exposures, are the residuals of the asset returns independent? With this motivation, we introduce the mosaic permutation test, a nonparametric goodness-of-fit test for preexisting factor models. Our method allows analysts to use nearly any machine learning technique to detect model violations while provably controlling the false positive rate, i.e., the probability of rejecting a well-fitting model. Notably, this result does not rely on asymptotic approximations and makes no parametric assumptions. This property helps prevent analysts from unnecessarily rebuilding accurate models, which can waste resources and increase risk. We illustrate our methodology by applying it to the Blackrock Fundamental Equity Risk (BFRE) model. Using the mosaic permutation test, we find that the BFRE model generally explains the most significant correlations among assets. However, we find evidence of unexplained correlations among certain real estate stocks, and we show that adding new factors improves model fit. We implement our methods in the python package mosaicperm.

翻译：金融机构常依赖因子模型来解释资产收益间的相关性。这类模型对风险管理至关重要，例如通过建模多项资产同时贬值的概率。然而在重大事件（如COVID-19）发生后，分析师可能重新评估现有模型的拟合效果：具体而言，在考虑因子暴露后，资产收益的残差是否相互独立？基于此动机，我们提出镶嵌排列检验——一种针对既有因子模型的非参数拟合优度检验方法。该方法允许分析师使用几乎任何机器学习技术检测模型违规，同时可证明地控制假阳性率（即错误拒绝拟合良好模型的概率）。值得注意的是，这一结论无需渐近近似且无参数假设。该特性有助于防止分析师因非必要重建精确模型而浪费资源并增加风险。我们将该方法应用于贝莱德基础股票风险（BFRE）模型进行实证研究。通过镶嵌排列检验发现，BFRE模型通常能解释资产间最显著的相关性。但在某些房地产股票中观察到无法解释的相关性证据，并且添加新因子可改善模型拟合度。我们已在Python包mosaicperm中实现了该方法。