The Estimation of Expected Shortfall in ETF Portfolios

This research evaluates the merit of the multivariate TGARCH-EVT-Copula model in forecasting Value at Risk and Expected Shortfall of a portfolio of Exchange Traded Funds by comparing the model with conventional benchmarks. The Value at Risk forecasts are tested using the standard Kupiec and Christoffersen tests, whereas the Expected Shortfall forecasts are tested using the state of the art testing method of Du & Escanciano (2017). Models that pass these tests are pairwise tested using the Diebold-Mariano framework with the comparative Fissler & Ziegel (2016) scoring function. The results show that including time-varying volatility improves the performance and that the multivariate TGARCH-EVT-Gaussian copula model is superior to the other models. It is also shown that multivariate modeling in combination with extreme value theory and TGARCH filtering improves the forecasting ability of ES.