Value at Risk: On the Stability and Forecasting of the Variance-covariance Matrix

Over the past decade value at risk (VaR) has become the most widely used technique for the quantification of market-risk exposure. VaR is a measure of the potential loss that may occur from adverse moves in market prices (interest rates, exchange rates, equity prices and so forth). The capacity for a VaR measure to accurately predict future risk exposures depends upon the forecasts of the volatility of market rates and the correlations between the various market rates (that is, the variance-covariance matrix) incorporated into the VaR model. In this paper we first present the results of tests of the stability of the variances, covariances and correlations for exchange rates and Australian interest rates. Secondly, we assess the performance of several time-series models that may be used to forecast the variance-covariance matrix. In particular three models for the variance-covariance matrix are considered: equally weighted historical variances and covariances, exponentially weighted averages of historical variances and generalised autoregressive conditional heteroskedasticity (GARCH). We conclude that simple models perform as well as their more sophisticated GARCH counterparts.