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2016 | OriginalPaper | Buchkapitel

16. Expected Shortfall as a Response to Model Risk

verfasst von : James Ming Chen

Erschienen in: Postmodern Portfolio Theory

Verlag: Palgrave Macmillan US

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Abstract

Reducing the vulnerability of parametric VaR to model risk by improving its robustness addresses merely one threat to the reliability of VaR analysis. The most serious menace to VaR—and to the technique’s viability as the Basel Accords’ preferred approach to financial risk management—lies in VaR’s failure to satisfy the theoretical rigors demanded of “coherent” measures of risk.¹ The expected shortfall for any confidence interval, which is derived directly from VaR for that interval, is subadditive and coherent. VaR itself is not.² The allure of subadditivity and coherence supports Basel III’s embrace of expected shortfall as the international banking system’s preferred measure of market risk.

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Vorheriges Kapitel Comparing Student’s t-Distribution with the Logistic Distribution

Nächstes Kapitel Latent Perils: Stressed VaR, Elicitability, and Systemic Effects

See generally Sheppard, Chap. 13, supra note 31, at 522–524; Phillipe Artzner, Freddy Delbaen, Jean-Marc Eber & David Heath, Coherent Measures of Risk, 9 Math. Fin. 203–228 (1999).

See Chen, Chap. 13, supra note 7; Ziegel, Chap. 13, supra note 45.

See Basel II, Chap. 13, supra note 11, ¶ 718(lxxvi)(b)-(c), at 195.

See John Hull, Risk Management and Financial Institutions 189 (3d ed. 2012).

Id. at 190.

See Ruey S. Tsay, Lecture Note of Bus 41202, Spring 2013: Value at Risk, Expected Shortfall & Risk Management, at 5 (2013) (available at http://faculty.chicagobooth.edu/ruey.tsay/teaching/bs41202/sp2013/lec9-13.pdf).

See, e.g. Stuart A. Klugman, Harry H. Panjer & Gordon E. Willmot, Loss Models: From Data to Decisions 44–45 (4th ed. 2012); Julia Lynn Wirch, Raising Value at Risk, 3 N. Am. Actuarial J. 106–115 (1999).

See generally Roxy Peck & Jay L. Devore, Statistics: The Exploration and Analysis of Data 464–465 (2011); David Sheskin, Handbook of Parametric and Nonparametric Statistical Procedures 54 (2004).

See Sheppard, Chap. 13, supra note 31, at 522–24; Artzner, Delbaen, Eber & Heath, supra note 1.

On stochastic dominance rules, see generally Levy, CAPM in the 21st Century, Chap. 15, supra note 5, at 46–62; Haim Levy, Stochastic Dominance: Investment Decision Making Under Uncertainty 49–142 (2006); Vijay S. Bawa, Optimal Rules for Ordering Uncertain Prospects, 2 J. Fin. Econ. 95–121 (1975); Josef Hadar & William R. Russell, Rules for Ordering Uncertain Prospects, 59 Am. Econ. Rev. 25–34 (1969).

See Hull, supra note 4, at 189 (example 9.5).

McNeil, Frey & Embrechts, Chap. 14, supra note 7, at 239.

See Daníelsson, Chap. 13, supra note 35, at 1289.

See Anil Bangia, Francis X. Diebold, Til Schuermann & John D. Stroughair, Modeling Liquidity Risk, with Implications for Traditional Market Risk Measurement and Management (Dec. 21, 1998) (available at http://fic.wharton.upenn.edu/fic/papers/99/9906.pdf); Arnaud Bervas, Market Liquidity and Its Incorporation into Risk Management (2006) (available at http://www.banque-france.fr/fileadmin/user_upload/banque_de_france/publications/Revue_de_la_stabilite_financiere/etud2_0506.pdf).

See Robert N. McCauley, Patrick McGuire & Vladyslav Sushko, Global Dollar Credit: Links to US Monetary Policy and Leverage 1 n.7, 5, Bank for International Settlements Working Paper No. 483 (Jan. 2015) (available at http://www.bis.org/publ/work483.pdf).

Id. at 17.

See Jhuvesh Sobrun & Philip Turner, Bond Markets and Monetary Policy Dilemmas for the Emerging Markets 13, Bank of International Settlements Working Paper No. 508 (Aug. 2015) (available at http://www.bis.org/publ/work508.pdf).

McNeil, Frey & Embrechts, Chap. 14, supra note 7, at 240.

Id.

See Basel Committee on Banking Supervision, Messages from the Academic Literature on Risk Measurement for the Trading Book, at 17–20 (Jan. 31, 2011) (working paper no. 19) (available at http://www.bis.org/publ/bcbs_wp19.pdf) [hereinafter Messages from the Academic Literature].

See id. at 20–23.

See Basel Committee on Banking Supervision, Consultative Document: Fundamental Review of the Trading Book (May 3, 2012) (available at http://www.bis.org/publ/bcbs219.pdf).

Basel Committee on Banking Supervision, Consultative Document: Fundamental Review of the Trading Book: A Revised Market Risk Framework 5 (Oct. 2013) (available at http://www.bis.org/publ/bcbs265.pdf); see also id. at 18 (recommending adoption of expected shortfall in place of VaR and the incorporation of an “indirect” method of calculating maximum market stress over the observational period).

See supra 13.1, at 248.

See R. Tyrell Rockafellar & Stanislav Uryasev, Optimization of Conditional Value-at-Risk, 2:3 J. Risk 21–41 (Spring 2000).

Xiong & Idzorek, Chap. 14, supra note 9, at 23.

See generally Carlo Acerbi & Dirk Tasche, Expected Shortfall: A Natural Coherent Alternative to Value at Risk, 31 Econ. Notes 379–388 (2002); Messages from the Academic Literature, supra note 20; Ziegel, Chap. 13, supra note 45; https://en.wikipedia.org/wiki/Expected_shortfall. The information presented in this section is drawn from these sources.

See Ziegel, Chap. 13, supra note 45, at 2; cf. Messages from the Academic Literature, supra note 20, at 21.

See Messages from the Academic Literature, supra note 20, at 21.

See generally Carlo Acerbi & Dirk Tasche, On the Coherence of Expected Shortfall, 26 J. Banking & Fin. 1487–1503 (2002).

See Hull, supra note 4, at 190 (example 9.7).

To compute this indefinite integral, I enlisted Wolfram Alpha. See http://www.wolframalpha.com/input/?i=integrate+sqrt%286%29*sqrt%281%2Finversebetaregularized%282*x%2C3%2C1%2F2%29-1%29; http://www.wolframalpha.com/input/?i=integrate+sqrt%281%2Finversebetaregularized%282*x%2C3%2C1%2F2%29-1%29.

See http://www.wolframalpha.com/input/?i=integrate+sqrt%286%29*sqrt%281%2Finversebetaregularized%282*x%2C3%2C1%2F2%29-1%29+for+x%3D0+to+.01.

Titel: Expected Shortfall as a Response to Model Risk
verfasst von: James Ming Chen
Verlag: Palgrave Macmillan US
Buch: Postmodern Portfolio Theory
Print ISBN: 978-1-137-54463-6

Electronic ISBN: 978-1-137-54464-3

Copyright-Jahr: 2016
DOI: https://doi.org/10.1057/978-1-137-54464-3_16