Closed-Form Multi-Factor Copula Models With Observation-Driven Dynamic Factor Loadings

We develop new multi-factor dynamic copula models with time-varying factor loadings and observation-driven dynamics. The new models are highly flexible, scalable to high dimensions, and ensure positivity of covariance and correlation matrices. A closed-form likelihood expression allows for straightforward parameter estimation and likelihood inference. We apply the new model to a large panel of 100 U.S. stocks over the period 2001–2014. The proposed multi-factor structure is much better than existing (single-factor) models at describing stock return dependence dynamics in high-dimensions. The new factor models also improve one-step-ahead copula density forecasts and global minimum variance portfolio performance. Finally, we investigate different mechanisms to allocate firms into groups and find that a simple industry classification outperforms alternatives based on observable risk factors, such as size, value, or momentum.

本研究开发了一种新型的多因子动态Copula模型，该模型具备时变因子负载和观测驱动的动态特性。新模型具有高度灵活性，可扩展至高维空间，并确保协方差和相关性矩阵的正定性。闭式似然表达式使得参数估计和似然推断变得简便。我们将该模型应用于2001至2014年间100只美国股票的大面板数据。所提出的多因子结构在描述高维股票回报依赖动态方面，相较于现有的（单因子）模型具有显著优势。新的因子模型还提升了单步预测的Copula密度估计以及全球最小方差投资组合的表现。最终，我们探讨了不同的机制以将公司分配至不同的组别，并发现简单的行业分类在性能上优于基于可观察风险因子（如规模、价值或动量）的替代方案。