The objective of this paper is to run a forecasting competition of different parametric volatility time series models to estimate Value-at-Risk (VaR) and Expected Shortfall (ES) within the Portuguese Stock Market. This work is also intended to bring new insights about the methods used throughout this exercise. Finally, we want to relate the timing of the exceptions (extreme losses surpassing the VaR) with events at the firm level and with national/international economic conditions.

For these purposes, a number of models from the General Autoregressive Conditional Heteroscedasticity (GARCH) class are used with different distribution functions for the innovations, in particular, Normal, Student-t and Generalized Error Distribution (GED) and corresponding skewed versions. The GARCH models are also used in conjunction with the Generalized Pareto Distribution through the use of extreme value theory.

The performance of these different models to forecast 1% and 5% VaR and ES for 1-day, 5-days and 10-days horizons are analyzed for a set of companies traded in the EURONEXT Lisbon stock exchange. The results obtained for the VaRs and ESs are evaluated with backtesting procedures based on a number of statistical tests and compared with the use of different loss functions.

The final results are analyzed in several dimensions. Preliminary analysis show that the use of extreme value theory generally leads to better results, especially for low values of alpha. This is more evident in the case of the statistical backtests dealing with ES. Moreover, skewed distributions generally do not seem to perform better than their centered counterparts