Choosing Expected Shortfall Over VaR in Basel III Using Stochastic Dominance

Abstract

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.