Backtesting Value-at-Risk: A Duration-Based Approach

27 Pages Posted: 20 Jul 2003

See all articles by Peter Christoffersen

Peter Christoffersen

University of Toronto - Rotman School of Management; Copenhagen Business School; Aarhus University - CREATES

Denis Pelletier

North Carolina State University - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: January 31, 2003


Financial risk model evaluation or backtesting is a key part of the internal model's approach to market risk management as laid out by the Basle Commitee on Banking Supervision (1996). However, existing backtesting methods such as those developed in Christoffersen (1998), have relatively small power in realistic small sample settings. Methods suggested in Berkowitz (2001) fare better, but rely on information such as the shape of the left tail of the portfolio return distribution, which is often not available. By far the most common risk measure is Value-at-Risk (VaR), which is defined as a conditional quantile of the return distribution, and it says nothing about the shape of the tail to the left of the quantile. Our contribution is the exploration of a new tool for backtesting based on the duration of days between the violations of the VaR. The chief insight is that if the VaR model is correctly specified for coverage rate, p, then the conditional expected duration between violations should be a constant 1/p days. We suggest various ways of testing this null hypothesis and we conduct a Monte Carlo analysis which compares the new tests to those currently available. Our results show that in realistic situations, the duration based tests have better power properties than the previously suggested tests. The size of the tests is easily controlled using the Monte Carlo technique of Dufour (2000).

Suggested Citation

Christoffersen, Peter and Pelletier, Denis, Backtesting Value-at-Risk: A Duration-Based Approach (January 31, 2003). Available at SSRN: or

Peter Christoffersen (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5P 3C4
416-946-5511 (Phone)

Copenhagen Business School

Solbjerg Plads 3
Frederiksberg C, DK - 2000

Aarhus University - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C

Denis Pelletier

North Carolina State University - Department of Economics ( email )

Raleigh, NC 27695-8110
United States

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