Beyond their importance from the regulatory policy point of view, Value-at-Risk (VaR) and Expected Shortfall (ES) play an important role in risk management, portfolio allocation, capital level requirements, trading systems, and hedging strategies. However, due to the curse of dimensionality, their accurate estimation and forecast in large portfolios is quite a challenge. To tackle this problem, two procedures are proposed. The first one is based on a filtered historical simulation method in which high-dimensional conditional covariance matrices are estimated via a general dynamic factor model with infinite-dimensional factor space and conditionally heteroscedastic factors; the other one is based on a residual-based bootstrap scheme. The two procedures are applied to a panel with concentration ratio close to one. Backtesting and scoring results indicate that both VaR and ES are accurately estimated under both methods, which both outperform the existing alternatives.

除了从监管政策的角度来看其重要性之外，风险价值（VaR）和预期缺口（ES）在风险管理、投资组合配置、资本水平要求、交易系统和对冲策略中发挥着重要作用。然而，由于维数灾难，它们在大型投资组合中的准确估计和预测是一个相当大的挑战。为了解决这个问题，提出了两种程序。第一个基于过滤历史模拟方法，其中通过通用动态因子具有无限维因子空间和条件异方差因子的模型；另一种是基于残差引导方案。这两个程序应用于浓度比接近1的面板。回测和评分结果表明，这两种方法都可以准确估计 VaR 和 ES，并且都优于现有替代方法。