How Accurate are Value-at-Risk Models at Commercial Banks

Abstract

In recent years, the trading accounts at large commercial banks have grown substantially and become progressively more diverse and complex. We provide descriptive statistics on the trading revenues from such activities and on the associated Value-at-Risk forecasts internally estimated by banks. For a sample of large bank holding companies, we evaluate the performance of banks' trading risk models by examining the statistical accuracy of the VaR forecasts. Although a substantial literature has examined the statistical and economic meaning of Value-atRisk models, this article is the first to provide a detailed analysis of the performance of models actually in use.Keywords: market risk, portfolio models, value-at-risk, volatility Correspondence: Berkowitz: (949) O'Brien: (202) 452-2384, e-mail: jmobrien@frb.gov. We gratefully acknowledge the support and comments of Jim Embersit and Denise Dittrich of the Federal Reserve Board's Division of Supervision and Regulation, Philippe Jorion, Matt Pritsker, Mike Gibson, Hao Zhou, colleagues at the Federal Reserve Board and the New York Fed. The comments and suggestions of an anonymous referee were especially helpful in improving the paper. The opinions expressed do not necessarily represent those of the Federal Reserve Board or its staff. 1In recent years, the trading accounts at large commercial banks have grown rapidly and become progressively more complex. To a large extent, this reflects the sharp growth in the over-the-counter derivatives markets, in which commercial bank are the principal dealers. In order to manage market risks, major trading institutions have developed large scale risk measurement models. While approaches may differ, all such models measure and aggregate market risks in current positions at a highly detailed level. The models employ a standard risk metric, Value-at-Risk (VaR), which is a lower tail percentile for the distribution of profit and loss (P&L). VaR models have been sanctioned for determining market risk capital requirements for large banks by U.S. and international banking authorities through the 1996 Market Risk Amendment to the Basle Accord. Spurred by these developments, VaR has become a standard measure of financial market risk that is increasingly used by other financial and even nonfinancial firms as well.The general acceptance and use of large scale VaR models has spawned a substantial literature including statistical descriptions of VaR and examinations of different modeling issues and approaches (for a survey and analysis see Jorion (2001)). Yet, because of their proprietary nature, there has been little empirical study of risk models actually in use, their VaR output, or indeed the P&L distributions of trading firms. For the most part, VaR analyses in the public domain have been limited to comparing modeling approaches and implementation procedures using illustrative portfolios (e.g., Beder (1995), Hendricks (1996), Marshall and Siegel (1997), Pritsker (1997)). 1In this paper, we provide the first direct evidence on...

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