12 Pages Posted: 23 Apr 2012  

Peter Christoffersen

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

Date Written: November 19, 2008


This chapter surveys methods for backtesting risk models using the ex ante riskmeasure forecasts from the model and the ex post realized portfolio profit or loss. The risk measure forecast can take the form of a VaR, an Expected Shortfall, or a distribution forecast. The backtesting methods surveyed in this chapter can be seen as a final diagnostic check on the aggregate risk model carried out by the risk management team that constructed the risk model, or they can be used by external model-evaluators such as bank supervisors. Common for the approaches suggested is that they only require information on the daily ex ante risk model forecast and the daily ex post corresponding profit and loss. In particular, knowledge about the assumptions behind the risk model and its construction is not required.

Keywords: Value-at-Risk, expected shortfall, distribution, forecasting, model evaluation, testing, historical simulation

JEL Classification: G20

Suggested Citation

Christoffersen, Peter, Backtesting (November 19, 2008). 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

University of Aarhus - CREATES

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

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