Predicting Tail Risks by a Markov Switching MGARCH Model with Varying Copula Regimes

Abstract

To improve the dynamic assessment of risks of speculative assets, we apply a Markov switching MGARCH approach to portfolio forecasting. More specifically, we take advantage of the flexible Markov switching copula multivariate GARCH (MS-C-MGARCH) model of Fülle and Herwartz (2021). As an empirical illustration we take the perspective of a risk averse agent and employ the suggested model for assessments of future risks of portfolios composed of a high yield equity index (S&P 500) and two safe-haven investment instruments (i.e. Gold and U.S. Treasury Bond Futures). We follow recent suggestions to employ the expected shortfall as a prime assessment of tail risks. To accurately evaluate the merits of the new model, we back test the risk forecasting for daily returns over 10 years for heterogeneous market environments including, for example, the COVID-19 pandemic. We find that the MS-C-MGARCH model outperforms benchmark volatility models (MGARCH, C-MGARCH) in predicting both value-at-risk and expected shortfall. The superiority of the MS-C-MGARCH model becomes even stronger when the share of comparably risky assets in the portfolio is relatively large.

Keywords: Copula, MGARCH, Markov Switching, Forecasting, VaR, Expected Shortfall

JEL Classification: C32, C58, G11, G17, G32