A structural Garch model: an application to portfolio risk management

Abstract

The primary objective of this study is to decompose the conditional covariance matrix of a system of variables. A structural GARCH model is proposed which makes use of existing multivariate GARCH (MGARCH) models to decompose the covariance matrix. The variables analysed in the study are the All Share index (ALSI) on the Johannesburg stock exchange, the South African Rand/US Dollar exchange rate (R/$) and the South African 90- day Treasury bill interest rate (Tbill). The contemporaneous structural parameters in the system of endogenous variables are identified using heteroscedasticity. Although the structural parameters of the system of variables hold important and interesting information, it is not the main focus of this study. Identifying the structural parameters can be seen as a necessary condition to decompose the conditional variance covariance matrix into an endogenous and exogenous part. The contribution of the study is twofold. The first contribution is methodological in nature, while the second is empirical. The study proposes a methodology that utilises two multivariate GARCH models to decompose the time-varying conditional covariance matrix of a system of assets, without imposing unnecessary constraints on the system. In doing so more information is obtained from decomposing the covariance matrix than what is available from existing or traditional multivariate GARCH models. The information allows the investor to analyse the structural relationships between variables in the system in both the first and the second moments. On an empirical level, the study analyses the structural relationship between financial variables in the South African economy using high-frequency data. The methodology utilised allows for consistent and efficient estimates of the structural contemporaneous relationships between these variables. The study also decomposes the volatility of each individual variable as well as the volatility between the variables. More information is gained on what drives the volatility of these variables, i.e. is volatility generated within the system, alternative to volatility generated from structural innovations or latent factors outside the system. The study finally shows how the information can be utilised in a portfolio management context.