Improving Accuracy and Precision of Value-at-Risk Forecasts

Abstract

As Value-at-Risk (VaR) forecasts are quantile estimates, in this paper we employ a resampling technique alternative to bootstrap, the jackknife method. The delete-d jackknife is specifically designed for non-smooth statistics such as the quantile and produces unbiased statistics because it resamples from the original distribution rather than from the empirical distribution as in the bootstrap. Unlike previous studies that only take into consideration the uncertainty of VaR forecasts arising from the estimation of conditional volatilities of returns, we also account for the uncertainty resulted from the estimation of the conditional quantiles of the simulated return series by using the median unbiased quantile estimator. Applied to five proxy portfolios for managed funds in Australia, the proposed technique is shown to have modest improvement over the other eight benchmark models in terms of statistical and regulatory tests, but it provides much more accurate VaR forecasts based on statistical loss measures. In particular, considerable improvement is achieved in forecast precision.