Detecting Estimation Errors in Vaue at Risk

• Activity Number: 78
• Type: Contributed
• Date/Time: Monday, August 12, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Business & Economics Statistics Section*
• Author(s): Joe Sullivan*+ and Robert Brooks and Zachary Stoumbos
• Affiliation(s): Mississippi State University and University of Alabama and Rutgers University
• Keywords: GARCH ; Fourier Analysis ; Sequential Probability Ratio Test ; probatility transformation ; cumulative sum ; Exponentially Weighted Moving Average

Abstract

The value at risk (VaR) represents an attempt to summarize in a single number the total risk in a portfolio of financial assets. The VaR is appealing for senior management and regulators, because it reduces the risk management function to a single number. Numerically, the VaR is determined by the lower limit of a one-sided confidence interval for the change in the portfolio value over a specific period of time.

For the VaR to serve its intended function of summarizing the portfolio risk, the process of estimating the VaR must be accurate. In particular, the distribution for the change in portfolio value must be accurately estimated. We address two alternative settings for verifying this distribution. One is a daily assessment of the validity of the most recent of the estimated distributions, using a cumulative sum and a time window that varies adaptively with the data. The objective is to quickly signal if the estimation process is inaccurate, subject to a specified rate of false alarms. The other setting is a historical assessment using a fixed sample size.

We introduce several alternative assessment methods and consider their properties.