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A Stochastic Dominance Approach to Financial Risk Management Strategies

The Basel III Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one of a range of alternative risk models to forecast Value-at-Risk (VaR). The risk estimates from these models are used to determine the daily capital charges (DCC) and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realized losses exceed the estimated VaR. In this paper we define risk management in terms of choosing sensibly from a variety of risk models and discuss the optimal selection of financial risk models. A previous approach to model selection for predicting VaR proposed combining alternative risk models and ranking such models on the basis of average DCC. This method is based only on the first moment of the DCC distribution, supported by a restrictive evaluation function. In this paper, we consider uniform rankings of models over large classes of evaluation functions that may reflect different weights and concerns over different intervals of the distribution of losses and DCC. The uniform rankings are based on recently developed statistical tests of stochastic dominance (SD). The SD tests are illustrated using the prices and returns of VIX futures. The empirical findings show that the tests of SD can rank different pairs of models to a statistical degree of confidence, and that the alternative (recentered) SD tests are in general agreement.

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Paper provided by Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico in its series Documentos de Trabajo del ICAE with number 2014-08.

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Length: 33 pages
Date of creation: 2014
Date of revision: Apr 2014
Handle: RePEc:ucm:doicae:1408
Note: The authors are most grateful to Michael McAleer for many comments and suggestions. For financial support, the first author wishes to thank the National Science Council, Taiwan, and the second and fourth authors acknowledge the Ministerio de Economía y Competitividad and Comunidad de Madrid, Spain.
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  1. Linton, Oliver & Maasoumi, Esfandiar & Whang, Yoon-Jae, 2003. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," SFB 373 Discussion Papers 2003,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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  4. Oliver Linton & Kyungchul Song & Yoon-Jae Whang, 2009. "An improved bootstrap test of stochastic dominance," Economics Working Papers we094827, Universidad Carlos III, Departamento de Economía.
  5. Michael McAleer, 2009. "The Ten Commandments for Optimizing Value-at-Risk and Daily Capital Charges," CIRJE F-Series CIRJE-F-652, CIRJE, Faculty of Economics, University of Tokyo.
  6. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  7. Chan, Chia-Ying & de Peretti, Christian & Qiao, Zhuo & Wong, Wing-Keung, 2012. "Empirical test of the efficiency of the UK covered warrants market: Stochastic dominance and likelihood ratio test approach," Journal of Empirical Finance, Elsevier, vol. 19(1), pages 162-174.
  8. Michael McAleer & Juan-Ángel Jiménez-Martín & Teodosio Pérez-Amaral, 2011. "International Evidence on GFC-robust Forecasts for Risk Management under the Basel Accord," KIER Working Papers 757, Kyoto University, Institute of Economic Research.
  9. McAleer, Michael & Jimenez-Martin, Juan-Angel & Perez-Amaral, Teodosio, 2013. "GFC-robust risk management strategies under the Basel Accord," International Review of Economics & Finance, Elsevier, vol. 27(C), pages 97-111.
  10. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Michael McAleer & Teodosio Pérez-Amaral, 2011. "Risk Management of Risk under the Basel Accord: Forecasting Value-at-Risk of VIX Futures," KIER Working Papers 761, Kyoto University, Institute of Economic Research.
  11. Michael McAleer & Juan-Ángel Jiménez-Martín & Teodosio Pérez Amaral, 2012. "Has the Basel Accord Improved Risk Management During the Global Financial Crisis?," Documentos de Trabajo del ICAE 2012-26, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Oct 2012.
  12. McAleer, Michael & Chan, Felix & Marinova, Dora, 2007. "An econometric analysis of asymmetric volatility: Theory and application to patents," Journal of Econometrics, Elsevier, vol. 139(2), pages 259-284, August.
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  15. repec:dgr:uvatin:20130010 is not listed on IDEAS
  16. Pérignon, Christophe & Deng, Zi Yin & Wang, Zhi Jun, 2008. "Do banks overstate their Value-at-Risk?," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 783-794, May.
  17. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
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  19. Stephen G. Donald & Yu-Chin Hsu, 2012. "Improving the Power of Tests of Stochastic Dominance," IEAS Working Paper : academic research 12-A015, Institute of Economics, Academia Sinica, Taipei, Taiwan, revised May 2013.
  20. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  21. Egozcue, Martín & García, Luis Fuentes & Wong, Wing-Keung & Zitikis, Ricardas, 2011. "Do investors like to diversify? A study of Markowitz preferences," European Journal of Operational Research, Elsevier, vol. 215(1), pages 188-193, November.
  22. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
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