Backtesting and estimation error: value-at-risk overviolation rate

Abstract

Financial institutions and regulators use value-at-risk (VaR) and related measures as a tool for financial risk management. It is therefore critical to appropriately assess the quality of VaR forecasts and reporting. The VaR estimation error creates an additional source of imprecision. We show that even an unbiased estimator of VaR is likely to produce a systematic overviolation. We then propose an adjustment to account for the issue. A Monte Carlo study illustrates the overviolation problem and the effectiveness of the adjustment. An application to Fama–French portfolios returns series highlights the need to further account for tail behavior in the data. Applying the adjustment to the normal distribution performs relatively well for a less prudential level (5% VaR), but is unable to provide enough buffer to overcome the overviolation for more prudential levels (1% or 0.5%VaR). Using the empirical distribution for more prudential levels improves risk forecasts.