A new method for estimating Value-at-Risk of Brady bond portfolios

Value-at-Risk (VAR) statistics are often calculated via a variance-covariance matrix methodology. While simple to implement, such an approach ignores the well documented fact that high-frequency financial data tend to substantially deviate from the Gaussian distribution. This feature is particularly pronounced in country spread data (over treasuries) for emerging markets. This study addresses the problem of estimating VAR statistics for Brady bond portfolios by using a modified GARCH(1,1) model with a superimposed 'jump' innovation which affects not only instantaneous spreads but subsequent volatilities. This approach incorporates the stochastic volatility feature of ARCH models, while allowing for occasional large shocks to country spreads that persist over time. This new methodology is evaluated by estimating one-day, one-week and one-month VAR measures on a daily basis for several risk tolerance levels for spread-driven returns of sample portfolios. The introduction of a persistent 'jump' component improves upon the risk 'confidence intervals' estimated by both standard GARCH(1,1) and rolling variance-covariance methods. However, this result is not homogeneous across countries. Our methodology deals with multiple-country portfolios without the computationally problematic large number of parameters of standard Multivariate ARCH models, instead of parametrically estimating cross-country correlations, we extract them from each country's individual "non-jump" standardized innovations on a rolling basis. Furthermore, our results also show that by allowing the jump frequencies to depend on variables such as contagion effects, the accuracy of VAR estimates may be improved. All model parameters are re-estimated daily using prior historical data. Therefore our testing is performed out-of-sample.