Forecasting Value-at-Risk and Expected Shortfall in Large Portfolios: A General Dynamic Factor Model Approach

Abstract

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. Unfortunately, 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, being one of them 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, and the other one based on a residual-based bootstrap scheme. The 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 our methods, which outperforms alternative approaches available in the literature.