On the Value at Risk Forecasting of the Market Risk for Large Portfolios based on Dynamic Factor Models with Multivariate GARCH Specifications

Abstract: Market risk is the risk of capital loss due to unexpected changes in market prices. One risk measure used to estimate market risk is Value at Risk (VaR). The common historical simulation methodology of VaR forecasting usually does not capture the time-varying volatilities associated with financial data. Therefore, dynamic factor models (DFM) are employed to improve VaR forecasting. The paper’s main focus is to use different volatility model specifications in the DFM to evaluate which is the most appropriate for VaR forecasting. The volatility models considered are the Constant Conditional Correlation (CCC-) GARCH, the Dynamic Conditional Correlation (DCC-) GARCH, and the corrected Dynamic Conditional Correlation (cDCC-) GARCH. The method is applied to an empirical dataset consisting of Swedish large-cap stocks between 2017-2021 where two different portfolios are used, the equally- and the value-weighted portfolio. The data purposefully includes the COVID-19 pandemic such that the models can be compared during less- and more volatile periods. The method is further evaluated in a simulation study where randomized portfolio weights are used. It is found that the VaR forecasts produced by the three different model specifications are similar throughout the entire sample. Therefore the most restricted volatility model (CCC-GARCH) is recommended.