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Evaluating Value-at-Risk Models with Desk-Level Data

Department of Finance, University of Houston, Houston, Texas 77004
McGill University, Montreal, Quebec H3A 2T5, Canada; and CREATES, School of Economics and Management, University of Aarhus, DK-8000 Aarhus C, Denmark
Department of Economics, College of Management, North Carolina State University, Raleigh, North Carolina 27695
jberkowitz{at}uh.edu
peter.christoffersen{at}mcgill.ca
denis_pelletier{at}ncsu.edu

We present new evidence on disaggregated profit and loss (P/L) and value-at-risk (VaR) forecasts obtained from a large international commercial bank. Our data set includes the actual daily P/L generated by four separate business lines within the bank. All four business lines are involved in securities trading and each is observed daily for a period of at least two years. Given this unique data set, we provide an integrated, unifying framework for assessing the accuracy of VaR forecasts. We use a comprehensive Monte Carlo study to assess which of these many tests have the best finite-sample size and power properties. Our desk-level data set provides importance guidance for choosing realistic P/L-generating processes in the Monte Carlo comparison of the various tests. The conditional autoregressive value-at-risk test of Engle and Manganelli (2004) performs best overall, but duration-based tests also perform well in many cases.

Key Words: risk management; backtesting; volatility; disclosure
History: Received: July 30, 2007; accepted: October 24, 2008.