Testing, Comparing, and Combining Value-at-Risk Measures

27 Pages Posted: 16 Nov 1999

See all articles by Peter Christoffersen

Peter Christoffersen

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

Jinyong Hahn

Atsushi Inoue

Southern Methodist University

Date Written: October 1, 1999

Abstract

Value-at-Risk (VaR) has emerged as the standard tool for measuring and reporting financial market risk. Currently, more than eighty commercial vendors offer enterprise or trading risk management systems which report VaR-like measures. Risk managers are therefore often left with the daunting task of having to choose from this plethora of risk measures. Accordingly, this paper develops framework for answering the following questions about VaRs: 1) How can a risk manager test that the VaR measure at hand is properly specified, given the history of asset returns? 2) Given two different VaR measures, how can the risk manager compare the two and pick the best in a statistically meaningful way? Finally, 3) how can the risk manager combine two or more different VaR measures in order to obtain a single statistically superior measure? The usefulness of the methodology is illustrated in an application to daily returns on the S&P500. In the application, competing VaR measures are calculated from either historical or option-price based volatility measures, and the VaRs are then tested and compared.

JEL Classification: G10, C22, C53

Suggested Citation

Christoffersen, Peter and Hahn, Jinyong and Inoue, Atsushi, Testing, Comparing, and Combining Value-at-Risk Measures (October 1, 1999). Available at SSRN: https://ssrn.com/abstract=192150 or http://dx.doi.org/10.2139/ssrn.192150

Peter Christoffersen (Contact Author)

University of Toronto - Rotman School of Management ( email )

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

Copenhagen Business School

Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark

Aarhus University - CREATES

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

Atsushi Inoue

Southern Methodist University ( email )

Dallas, TX 75275
United States

No contact information is available for Jinyong Hahn

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