Comparison of approaches for value-at-risk estimation of foreign exchange portfolios

In this paper historical performance of eleven approaches for estimation of one-day 95% value-at-risk is evaluated. Random sample of 1000 foreign exchange portfolios consisting of positions in EUR and USD with CZK as a base currency was considered. Since foreign exchange portfolio consists of linear instruments, historical simulation and the variance-covariance method for VaR estimation were investigated. Performance of all approaches was evaluated using seven performance criteria. With minimal degree of simplification we can say that variance-covariance method using exponentially weighted averages with is the best approach. This approach produces risk estimates which are systematically lowest ones and with high time volatility. It also achieves perfect coverage (95 %) and the highest correlation between risk measure and absolute value of the outcome. RiskMetrics variance-covariance approach was dominant in spite of violation of normality assumption.