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Choosing Expected Shortfall over VaR in Basel III Using Stochastic Dominance

Author

Listed:
  • Chia-Lin Chang

    (National Chung Hsing University, Taichung, Taiwan)

  • Juan-Ángel Jiménez-Martín

    (Complutense University of Madrid, Spain)

  • Esfandiar Maasoumi

    (Emory University, USA)

  • Michel McAleer

    (National TsingHua University, Taiwan; Erasmus School of Economics, Erasmus University Rotterdam, and Tinbergen Institute, the Netherlands; Complutense University of Madrid, Spain)

  • Teodosio Pérez-Amaral

    (Complutense University of Madrid, Spain)

Abstract

Bank risk managers follow the Basel Committee on Banking Supervision (BCBS) recommendations that recently proposed shifting the quantitative risk metrics system from Value-at-Risk (VaR) to Expected Shortfall (ES). The Basel Committee on Banking Supervision (2013, p. 3) noted that: “a number of weaknesses have been identified with using VaR for determining regulatory capital requirements, including its inability to capture tail risk”. The proposed reform costs and impact on bank balances may be substantial, such that the size and distribution of daily capital charges under the new rules could be affected significantly. Regulators and bank risk managers agree that all else being equal, a “better” distribution of daily capital charges is to be preferred. The distribution of daily capital charges depends generally on two sets of factors: (1) the risk function that is adopted (ES versus VaR); and (2) their estimated counterparts. The latter is dependent on what models are used by bank risk managers to provide for forecasts of daily capital charges. That is to say, while ES is known to be a preferable “risk function” based on its fundamental properties and greater accounting for the tails of alternative distributions, that same sensitivity to tails can lead to greater daily capital charges, which is the relevant (that is, controlling) practical reference for risk management decisions and observations. In view of the generally agreed focus in this field on the tails of non-standard distributions and low probability outcomes, an assessment of relative merits of estimated ES and estimated VaR is ideally not limited to mean variance considerations. For this reason, robust comparisons between ES and VaR will be achieved in the paper by using a Stochastic Dominance (SD) approach to rank ES and VaR.

Suggested Citation

  • Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Esfandiar Maasoumi & Michel McAleer & Teodosio Pérez-Amaral, 2015. "Choosing Expected Shortfall over VaR in Basel III Using Stochastic Dominance," Tinbergen Institute Discussion Papers 15-133/III, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20150133
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    References listed on IDEAS

    as
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    Cited by:

    1. Stephan Eckstein & Michael Kupper & Mathias Pohl, 2018. "Robust risk aggregation with neural networks," Papers 1811.00304, arXiv.org.
    2. repec:gam:jrisks:v:6:y:2018:i:2:p:61-:d:150249 is not listed on IDEAS

    More about this item

    Keywords

    Stochastic dominance; Value-at-Risk; Expected Shortfall; Optimizing strategy; Basel III Accord;

    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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