Estimating Portfolio Risk with Product Copulas: A GARCH-EVT Approach Applied to Financial Data

This study introduces a sophisticated GARCH-EVT-Copula framework to enhance portfolio risk estimation for multi-asset portfolios. It specifically addresses the limitations of the traditional Markowitz mean-variance model, which is often insensitive to extreme market events. Our approach integrates a Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model to capture time-varying volatility with Extreme Value Theory (EVT) for modeling tail events. A key innovation is the application of product copulas to model the intricate, non-linear dependencies among four diverse financial indices: the MSCI World Investable Market Index, ICE BofAML Global Government Index, HFRX Global Hedge Fund Index, and Swiss Re Global Unhedged CAT Bond Performance Index. The use of product copulas is particularly effective in capturing the asymmetric dependencies and non-normal distributions characteristic of financial data, leading to a more accurate estimation of risk measures like Value-at-Risk (VaR). Our empirical analysis demonstrates the superior performance of product copula models compared to traditional copula models, with significant improvements in VaR estimation accuracy across various confidence levels. This finding is further validated by their resilience during the 2008 financial crisis and their efficacy in an equal risk contribution portfolio. This research not only advances the theoretical framework of risk management but also provides a more robust and effective methodology for investors seeking to develop resilient multi-asset portfolio strategies.