Choosing expected shortfall over VaR in Basel III using stochastic dominance

Abstract

In this paper we use stochastic dominance to evaluate the consequences of moving from Value-at-Risk (VaR) to Expected Shortfall (ES) from a policy maker's perspective. In particular, we compare VaR at the 99% level (VaR99) and ES at the 97.5% level (ES97.5). We contemplate VaR99 and ES97.5 as two alternative risk metrics according to the capital adequacy bank regulation, as suggested by Basel III. Moving from VaR99 to ES97.5 will have effects in terms of the quantity and quality of the capital required to banks. According to the Basel Committee on Banking Supervision (2013, page 18):“the Committee believes that moving to a confidence level of 97.5% (relative to the 99th percentile confidence level for the current VaR measure) is appropriate.”Stochastic dominance of the capital requirement distribution after the change in bank regulations, as suggested by Basel III, over the capital requirement under the old regulation, implies that a policy maker with any positive marginal utility of capital requirements (and a negative second derivative for risk aversion) would prefer it. SD tests examines if the rankings of outcomes are utility function specific, or uniform, over all decision makers with preferences in the class considered.