Abstract

This article proposes a methodology that can be used to parameterize stress test scenarios using the conditional probability distributions that are commonly used in VaR calculations. This new approach allows for a complete characterization of the value change distribution of a portfolio in a stress scenario. Statistical evidence demonstrates that the proposed loss exposure measure is substantially more accurate than the stress exposure measures that financial institutions commonly use.

The results also suggest, contrary to popular perception, that historical VaR risk factor covariances and the assumption of conditional normality can be used to construct reasonably accurate loss exposure estimates in many stressful market environments.

Introduction

Value at Risk, or VaR, is a commonly accepted methodology for measuring the loss magnitudes associated with rare ‘tail’ events in financial markets. On occasion, either to satisfy management interest or for regulatory compliance, it becomes necessary to quantify the magnitude of the losses that might accrue under events less likely than those analyzed in a standard VaR calculation.

The procedures used to quantify potential loss exposures under such special circumstances are often called a ‘stress test’. While this term is commonly used by risk managers and financial institution regulators, there is no accepted definition of what constitutes a stress test. There is even less published information about how best to accomplish a stress test of a trading portfolio or mark-to-market balance sheet.

Given the nature of institutions, it is impossible to document the specific details about how they actually conduct stress tests.