Robustness and Sensitivity Analysis of Risk Measurement Procedures
Columbia University Center for Financial Engineering, Financial Engineering Report No. 2007-06
33 Pages Posted: 24 Jan 2008 Last revised: 19 Apr 2010
Date Written: January 1, 2008
Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a "risk measure" which summarizes the risk of the portfolio. We define the notion of "risk measurement procedure", which includes both of these steps, and study the robustness of risk measurement procedures and their sensitivity to a change in the data set. After introducing a rigorous definition of 'robustness' of a risk measurement procedure, we illustrate the presence of a conflict between subadditivity and robustness of risk measurement procedures. We propose a measure of sensitivity for risk measurement procedures and compute the sensitivity function of various examples of risk estimators used in financial risk management, showing that the same risk measure may exhibit quite different sensitivities depending on the estimation procedure used. Our results illustrate in particular that using historical Value at Risk leads to a more robust procedure for risk measurement than recently proposed alternatives like CVaR. We also propose other risk measurement procedures which possess the robustness property.
Keywords: risk measure, Value at Risk, statistical estimation, robustness
JEL Classification: C13, G10
Suggested Citation: Suggested Citation