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Estimating Portfolio Risk with Product Copulas: A GARCH-EVT Approach Applied to Financial Data
Marcel Steinborn, Eckhard Liebscher
Hochschule Merseburg, Germany
This talk introduces a sophisticated GARCH-EVT-Copula framework designed to enhance portfolio risk estimation for multi-asset portfolios. We specically address the limitations of the traditional Markowitz mean-variance model, which often fails to account for extreme market events and tail dependencies. Our approach integrates a Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model to capture time-varying volatility with Extreme Value Theory (EVT) for modeling heavy-tailed distributions.
A key innovation presented is the application of product copulas to model the intricate, non-linear dependencies among four diverse nancial indices: the MSCI World IMI, ICE BofAML Global Government Index, HFRX Global Hedge Fund Index, and Swiss Re Global Unhedged CAT Bond Performance Index. Product copulas prove particularly eective in capturing asymmetric dependencies and non-normal characteristics, leading to signicantly more accurate Value-at-Risk (VaR) estimations.
Our empirical analysis demonstrates the superior performance of the product copula framework compared to traditional models, particularly regarding its resilience during the 2008 nancial crisis and its ecacy in equal risk contribution portfolios.
