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.

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Keywords Stochastic dominance, Value-at-Risk, Expected Shortfall, Optimizing strategy, Basel III Accord
JEL Financing Policy; Capital and Ownership Structure (jel G32), Portfolio Choice; Investment Decisions (jel G11), Financial Forecasting (jel G17), Forecasting and Other Model Applications (jel C53), Time-Series Models; Dynamic Quantile Regressions (jel C22)
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Series Econometric Institute Research Papers
Note The first author wishes to thank the National Science Council, Taiwan, the second and fifth authors acknowledge the Ministerio de Ciencia y Tecnología of Spain through the research project ECO2012-31941 and Comunidad de Madrid, and the fourth author is grateful to the National Science Council, Taiwan and the Australian Research Council.
Chang, C-L, Jiménez-Martín, J.A, Maasoumi, E, & McAleer, M.J. (2015). Choosing Expected Shortfall over VaR in Basel III Using Stochastic Dominance (No. EI2015-38). Econometric Institute Research Papers. Retrieved from