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Robustness and sensitivity analysis of risk measurement procedures

Robustness and sensitivity analysis of risk measurement procedures 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’ that 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 the 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 such as CVaR/expected shortfall leads to a less robust risk measurement procedure than historical Value-at-Risk. We also propose alternative risk measurement procedures that possess the robustness property. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantitative Finance Taylor & Francis

Robustness and sensitivity analysis of risk measurement procedures

Quantitative Finance , Volume 10 (6): 14 – Jun 1, 2010
14 pages

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References (33)

Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1469-7696
eISSN
1469-7688
DOI
10.1080/14697681003685597
Publisher site
See Article on Publisher Site

Abstract

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’ that 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 the 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 such as CVaR/expected shortfall leads to a less robust risk measurement procedure than historical Value-at-Risk. We also propose alternative risk measurement procedures that possess the robustness property.

Journal

Quantitative FinanceTaylor & Francis

Published: Jun 1, 2010

Keywords: Risk management; Risk measurement; Coherent risk measures; Law invariant risk measures; Value-at-Risk; Expected shortfall

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