Backtesting Value-at-Risk Based on Tail Losses

32 Pages Posted: 5 Dec 2007 Last revised: 10 Nov 2008

See all articles by Woon K. Wong

Woon K. Wong

IMRU, Cardiff Business School

Date Written: November 2, 2008


Extreme losses caused by leverage and financial derivatives highlight the need to backtest Value-at-Risk (VaR) based on sizes of tail losses, for the risk measure disregards losses beyond the VaR boundary and there is no formal statistical analysis required for stress testing. While Basel II backtests VaR by counting the number of exceptions, this paper proposes to use saddlepoint technique to backtest VaR by summing the tail losses. Monte Carlo simulations show that the technique is very accurate and powerful even for small samples. The proposed backtest finds substantial downside tail risks in S&P 500, and that risk models which account for jumps, skewed and fat-tailed distributions fail to capture the tail risk during the 1987 stock market crash. Finally, the saddlepoint technique is used to derive a multiplication factor for risk capital requirement that is responsive to sizes of tail losses.

Keywords: Value-at-Risk, tail risk, backtesting, risk management, risk capital

JEL Classification: G10, G18, G32

Suggested Citation

Wong, Woon K., Backtesting Value-at-Risk Based on Tail Losses (November 2, 2008). Available at SSRN: or

Woon K. Wong (Contact Author)

IMRU, Cardiff Business School ( email )

Cardiff CF10 3EU
United Kingdom

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