Robustness and sensitivity analysis of risk measurement procedures

Rama Cont (1, 2) , Romain Deguest (2) , Giacomo Scandolo (3)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 Center for Financial Engineering, Columbia University
3 DIMAD - Dipartimento di Matematica per le Decisioni

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 introduce a rigorous framework for studying the robustness of risk measurement procedures and their sensitivity to changes in the data set. Our results point to a conflict between subadditivity and robustness of risk measurement procedures and show that the same risk measure may exhibit quite different sensitivities depending on the estimation procedure used. Our results illustrate in particular that using recently proposed risk measures like CVaR/ expected shortfall lead to a less robust risk measurement procedure than historical Value at Risk. We also propose alternative risk measurement procedures which possess the robustness property.

Keywords: robust statistics; risk measure; influence function; sensitivity analysis; risk management; robust statistics

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]; Statistical Finance [q-fin.ST]; Risk Management [q-fin.RM]

Rama Cont, Romain Deguest, Giacomo Scandolo. Robustness and sensitivity analysis of risk measurement procedures. Quantitative Finance, 2010, 10 (6), pp.593 - 606. ⟨10.1080/14697681003685597⟩. ⟨hal-00413729⟩