RiskTech Forum

EDHEC: Robust Risk Estimation And Hedging: A Reverse Stress Testing Approach

Posted: 1 October 2014  |  Source: EDHEC


Abstract

Traditional risk modeling using Value-at-Risk (VaR) is widely viewed as ill equipped for dealing with tail risks. As a result, scenario-based portfolio stress testing is increasingly being promoted as central to the risk management process. A recent innovation in portfolio stress testing endorsed by regulators, called reverse stress testing, is intended to identify economic scenarios that will threaten a financial firm’s viability, but do so without injecting the manager’s cognitive biases into stress scenario specification. While the idea is intuitively appealing, no template has been provided to operationalize the idea. Some first steps in developing reverse stress testing approaches have begun to appear in the literature. Complexity and computational intensity appear to be important issues. A more subtle issue appearing in this emerging research is the relationship among the concepts of likelihood, plausibility, and representativeness. In this paper, we propose a novel method for reverse stress testing. The process starts with a multivariate normal distribution and uses Principal Components Analysis (PCA) along with Gram-Schmidt orthogonalization to determine scenarios leading to a specified loss level. The approach is computationally efficient. The method includes the maximum likelihood scenario, maximizes (a definition of) representativeness of the scenarios chosen, and measures the plausibility of each scenario. In addition, empirical results for sample portfolios show this method can provide new information beyond VaR and standard stress testing analyses.

Stress Testing and Reverse Stress Testing

Stress testing’s aim is to elucidate the level of portfolio loss under the condition that a specified event occurs (i.e., a conditional loss forecast). This contrasts with the risk measure known as Value-at-Risk, which defines a level of portfolio loss expected to be exceeded with a specified probability (a quantile of a forecast loss distribution of a specific form). Over the last fifteen years, the use of stress testing has gained ever-wider currency, fuelled by perceived failings of Value-at-Risk and other traditional risk models under extreme events.1

Stress testing is thought to complement traditional risk models by focusing on events that are not represented in traditional risk forecasts, either because they are absent from or underrepresented in the historical record. Thus a stress test, unlike a quantile forecast, it is not defined in relation to all possible states of the world and their estimated probabilities. This claim may be overstated, however, as stress testing covariance matrices may actually confound the conditional loss forecast with the statistical density forecast.2

In addition to the conceptual problems just alluded to, stress testing also entails design obstacles as a risk forecasting technique. One of the most troublesome is the subjective nature of the specified shocks. Indeed, this is especially important in cases in which shocks are not explicitly set by regulators (which is common only in the banking industry), e.g., under company-generated stress scenarios in the US, as required under the Dodd-Frank Act. It is not easy to demonstrate that a particular stress testing scenario, specifically the magnitude of the various stress shocks, have been chosen unbiasedly and represent risks relevant to the financial firm’s decision making. In other words, plausibility and relevance must be demonstrated, with the emphasis on plausibility. Reverse stress testing has as its main motivation the goal of overcoming this particular objection.

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