We compare Value at Risk (VaR) and Expected Shortfall (ES) following a Stochastic Dominance (SD) approach frequently used to order distributions in terms of welfare and in portfolio selection. Basel Committee on Banking Supervision (BCBS) recommends bank risk managers to shift the current quantitative risk metrics system, based on Value-at-Risk (VaR), to Expected Shortfall (ES). “Welfare costs” of such a reform in terms of capital requirements and penalties are a central concern for risk managers and regulators. Policy makers’ concerns can be addressed with many different value functions. A uniform ranking analysis based on stochastic dominance is provided here as an effective tool for comparing distributions of daily capital requirement charges produced under different regulations. On the basis of empirical results, it is concluded that ES should be preferred by risk averse policy makers who favour larger but less volatile capital requirements, and reduces the sensitivity of capital charges to changes in the probability of default.

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Keywords Stochastic dominance, Welfare, 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)
Persistent URL hdl.handle.net/1765/97816
Series USC-INET Research Paper
Chang, C-L, Jiménez-Martín, J.A, Maasoumi, E, McAleer, M.J, & Pérez-Amaral, T. (2016). Choosing Expected Shortfall Over VaR in Basel III Using Stochastic Dominance (No. 16-05). USC-INET Research Paper. Retrieved from http://hdl.handle.net/1765/97816