Financial firms often rely on fundamental factor models to explain correlations among asset returns and manage risk. Yet after major events, e.g., COVID-19, analysts may reassess whether existing risk models continue to fit well: specifically, after accounting for a set of known 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 can leverage modern machine learning techniques to detect model violations while provably controlling the false positive rate, i.e., the probability of rejecting a well-fitting model, without making asymptotic approximations or parametric assumptions. This property helps prevent analysts from unnecessarily rebuilding accurate models, which can waste resources and increase risk. To illustrate our methodology, we apply the mosaic permutation test to the BlackRock Fundamental Equity Risk (BFRE) model. Although the BFRE model generally explains the most significant correlations among assets, 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：金融机构通常依赖基础因子模型来解释资产收益间的相关性并管理风险。然而，在重大事件（如新冠疫情）发生后，分析师可能需要重新评估现有风险模型是否仍保持良好的拟合效果：具体而言，在考虑一组已知因子暴露后，资产收益的残差是否保持独立？基于此动机，我们提出镶嵌置换检验——一种针对既有因子模型的非参数拟合优度检验方法。本方法能够利用现代机器学习技术检测模型偏差，同时可证明地控制误报率（即拒绝拟合良好模型的概率），无需依赖渐近近似或参数假设。这一特性有助于避免分析师对准确模型进行不必要的重建，从而减少资源浪费并降低风险。为展示方法的应用，我们将镶嵌置换检验应用于贝莱德基础股票风险（BFRE）模型。尽管BFRE模型总体上能解释资产间最显著的相关性，但我们发现某些房地产股票存在未解释的相关性证据，并通过添加新因子展示了模型拟合度的提升。本方法已在Python软件包mosaicperm中实现。