Abstract

https://ssrn.com/abstract=2252463
 


 



Measuring Market Risk Under the Basel Accords: VaR, Stressed VaR, and Expected Shortfall


James Ming Chen


Michigan State University - College of Law

March 19, 2014

8 Aestimatio 184 (2014) -- Aestimatio, The IEB International Journal of Finance, volume 8, pp. 184-201 (2014)

Abstract:     
Each of the most recent accords of the Basel Committee on Banking Regulation, known as Basel II, 2.5, and II, has embraced a different primary measure of market risk in global banking regulation: traditional value-at-risk (VaR), stressed VaR, and expected shortfall. After introducing the mathematics of VaR and expected shortfall, this note will evaluate how well the reforms embraced by Basel 2.5 and III - stressed VaR and expected shortfall - have addressed longstanding regulatory concerns with traditional VaR.

Part I describes the calculation of VaR in its conventional form. For illustrative purposes, Part I will describe parametric VaR on a Gaussian distribution. Part II summarizes known weaknesses in VaR, from inherent model and estimation risk to VaR’s failure to perform under extreme economic stress and VaR’s failure to satisfy the theoretical constraints on “coherent” measurements of risk. Part III describes how to calculate expected shortfall as an extension of conditional VaR. It further describes how expected shortfall, but not VaR, provides a coherent measure of risk. Part III then reverses field. It explains how VaR, but not expected shortfall (or, for that matter, nearly every other general spectral measure of risk), satisfies the mathematical requirement of “elicitability.” Mathematical limitations on measures of risk therefore force regulators and bankers to choose between coherence and elicitability, between theoretically sound consolidation of diverse risks (on one hand) and reliable backtesting of risk forecasts against historical observations.

Number of Pages in PDF File: 18

Keywords: Value-at-risk, VaR, expected shortfall, coherence, elicitability, Basel

JEL Classification: G15, G28, G32


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Date posted: April 17, 2013 ; Last revised: April 23, 2014

Suggested Citation

Chen, James Ming, Measuring Market Risk Under the Basel Accords: VaR, Stressed VaR, and Expected Shortfall (March 19, 2014). 8 Aestimatio 184 (2014) -- Aestimatio, The IEB International Journal of Finance, volume 8, pp. 184-201 (2014). Available at SSRN: https://ssrn.com/abstract=2252463 or http://dx.doi.org/10.2139/ssrn.2252463

Contact Information

James Ming Chen (Contact Author)
Michigan State University - College of Law ( email )
318 Law College Building
East Lansing, MI 48824-1300
United States
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