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A Stochastic Dominance Approach to the Basel III Dilemma: Expected Shortfall or VaR?

Author

Listed:
  • Chang, C-L.
  • Jiménez-Martín, J.A.
  • McAleer, M.J.
  • Pérez-Amaral, T.
Abstract
__Abstract__ The Basel Committee on Banking Supervision (BCBS) (2013) recently proposed shifting the quantitative risk metrics system from Value-at-Risk (VaR) to Expected Shortfall (ES). The BCBS (2013) noted that “a number of weaknesses have been identified with using VaR for determining regulatory capital requirements, including its inability to capture tail risk” (p. 3). For this reason, the Basel Committee is considering the use of ES, which is a coherent risk measure and has already become common in the insurance industry, though not yet in the banking industry. While ES is mathematically superior to VaR in that it does not show “tail risk” and is a coherent risk measure in being subadditive, its practical implementation and large calculation requirements may pose operational challenges to financial firms. Moreover, previous empirical findings based only on means and standard deviations suggested that VaR and ES were very similar in most practical cases, while ES could be less precise because of its larger variance. In this paper we find that ES is computationally feasible using personal computers and, contrary to previous research, it is shown that there is a stochastic difference between the 97.5% ES and 99% VaR. In the Gaussian case, they are similar but not equal, while in other cases they can differ substantially: in fat-tailed conditional distributions, on the one hand, 97.5%-ES would imply higher risk forecasts, while on the other, it provides a smaller down-side risk than using the 99%-VaR. It is found that the empirical results in the paper generally support the proposals of the Basel Committee.

Suggested Citation

  • Chang, C-L. & Jiménez-Martín, J.A. & McAleer, M.J. & Pérez-Amaral, T., 2015. "A Stochastic Dominance Approach to the Basel III Dilemma: Expected Shortfall or VaR?," Econometric Institute Research Papers EI2015-14, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:78155
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    References listed on IDEAS

    as
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    Cited by:

    1. Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & Maasoumi, Esfandiar & McAleer, Michael & Pérez-Amaral, Teodosio, 2019. "Choosing expected shortfall over VaR in Basel III using stochastic dominance," International Review of Economics & Finance, Elsevier, vol. 60(C), pages 95-113.
    2. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Esfandiar Maasoumi & Michael McAleer & Teodosio Pérez-Amaral, 2015. "A Stochastic Dominance Approach to the Basel III Dilemma: Expected Shortfall or VaR?," Documentos de Trabajo del ICAE 2015-16, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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    More about this item

    Keywords

    Stochastic dominance; Value-at-Risk; Expected Shortfall; Optimizing strategy; Basel III Accord;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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