We live in a multivariate world, and effective modeling of financial portfolios, including their construction, allocation, forecasting, and risk analysis, simply is not possible without explicitly modeling the dependence structure of their assets. Dependence structure can drive portfolio results more than the combined effects of other parameters in investment and risk models, but the literature provides relatively little to define the finite-sample distributions of dependence measures under challenging, real-world financial data conditions. Yet this is exactly what is needed to make valid inferences about their estimates, and to use these inferences for essential purposes such as hypothesis testing, dynamic monitoring, realistic and granular scenario and reverse scenario analyses, and mitigating the effects of correlation breakdowns during market upheavals. This work develops a new and straightforward method, Nonparametric Angles-based Correlation (NAbC), for defining the finite-sample distributions of any dependence measure whose matrix of pairwise associations is positive definite (e.g. Pearsons, Kendalls, Spearmans, the Tail Dependence Matrix, and others). The solution remains valid under marginal asset distributions characterized by notably different and varying degrees of serial correlation, non-stationarity, heavy-tailedness, and asymmetry. Importantly, it provides p-values and confidence intervals at the matrix level, even when selected cells in the matrix are frozen, thus enabling flexible, granular, and realistic scenarios, reverse scenarios, and stress tests. Finally, when applied to directional dependence measures, NAbC enables accurate DAG recovery in causal modeling. NAbC stands alone in providing all of these capabilities simultaneously, and should prove to be a very useful means by which we can better understand and manage financial portfolios in our multivariate world.

翻译：我们生活在一个多元世界中，若不对资产间的依赖结构进行显式建模，金融投资组合的有效建模——包括其构建、配置、预测与风险分析——便无从实现。依赖结构对投资组合结果的影响可能超过投资与风险模型中其他参数的综合效应，然而现有文献在定义具有挑战性的现实金融数据条件下依赖度量的有限样本分布方面贡献甚微。而这正是对其估计值进行有效推断，并将这些推断用于假设检验、动态监测、现实且精细的情景与反向情景分析，以及缓解市场动荡期间相关性崩溃影响等关键目的所必需的。本研究提出了一种新颖而直接的方法——基于角度的非参数相关性（NAbC），用于定义任意其成对关联矩阵为正定的依赖度量（例如Pearson、Kendall、Spearman、尾部依赖矩阵等）的有限样本分布。该解决方案在资产边缘分布具有显著不同且变化程度的序列相关性、非平稳性、厚尾性与非对称性时依然有效。重要的是，它能在矩阵层面提供p值与置信区间，即使矩阵中部分选定单元格被固定，从而支持灵活、精细且现实的情景分析、反向情景分析与压力测试。最后，当应用于方向性依赖度量时，NAbC能够在因果建模中实现准确的DAG复原。NAbC是唯一能同时提供所有这些功能的方法，有望成为我们在多元世界中更好地理解与管理金融投资组合的强有力工具。