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We present new evidence on disaggregated profit and loss and VaR forecasts obtained from a large international commercial bank. Our dataset includes 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. We also collected the corresponding daily, 1-day ahead VaR forecasts for each business line. Given this rich dataset, we provide an integrated, unifying framework for assessing the accuracy of VaR forecasts. Our approach includes many existing backtesting techniques as special cases. In addition, we describe some new tests which are suggested by our framework. A thorough Monte Carlo comparison of the various methods is conducted to provide guidance as to which of these many tests have the best finite-sample size and power properties.

In this paper, we investigate how personal bankruptcy law affects small firms' access to credit. When a firm is unincorporated, its debts are personal liabilities of the firm's owner, so that lending to the firm is legally equivalent to lending to its owner. If the firm fails, the owner has an incentive to file for personal bankruptcy, since the firm's debts will be discharged and the owner is only obliged to use assets above an exemption level to repay creditors. The higher the exemption level, the greater is the incentive to file for bankruptcy. We show that supply of credit falls and demand for credit rises when non-corporate firms are located in states with higher bankruptcy exemptions. We test the model and find that, if small firms are located in states with unlimited rather than low homestead exemptions, they are more likely to be denied credit, they receive smaller loans and interest rates are higher. Results for non-corporate versus corporate firms suggest that lenders often disregard small firms' organizational status in making loan decisions.

Several authors have recently investigated the predictability of exchange rates by fitting a sequence of long-horizon error-correction equations. We show by means of a simulation study that, in small to medium samples, inference from this regression procedure depends on the null hypothesis that is used to generate empirical critical values. The standard assumption of a stationary error-correction term between exchange rates and fundamentals biases the results in favor of predictive power. Our results show that evidence of long-horizon predictability weakens when using empirical critical values generated under the more stringent null of no cointegration. Likewise, results are weakened using critical values generated under the null that exchange rates and fundamentals are generated by an unrestricted VAR with no integration restrictions. © 2000 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology

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...