Backtesting risk methodologies from one day to one year

Gilles Zumbach

Abstract

ABSTRACT

Market risk evaluation is nowadays routinely used, but surprisingly the performances of the various existing methodologies are poorly known. In this paper, we present a systematic backtesting study using 233 time series covering all geographic areas and asset classes, for time horizons ranging from one day to one year. The testing framework uses the probtiles and the relative exceedance fraction in order to compute convenient performance figures. The risk methodologies include the historical simulations, equal weight and RiskMetrics exponential moving average. Another methodology is new and has been designed specifically to deal with long risk horizons, up to one year. In particular, it captures correctly the long memory of the volatility dynamics as well as the fat tail distributions of the residuals. The results show that the new methodology outperforms systematically the existing ones at all risk horizons.