Coherence Versus Elicitability in Measures of Market Risk

Abstract

The Basel II and III accords prescribe distinct measures of market risk in the trading book of regulated financial institutions. Basel II has embraced value-at-risk (VaR) analysis, while Basel III has suggested that VaR be replaced by a different measure of risk, expected shortfall. These measures of risk suffer from mutually irreconcilable flaws. VaR fails to satisfy the conditions required of coherent measures of risk. Conversely, expected shortfall fails the mathematical requirements for elicitability. Mathematical limitations therefore force a choice between theoretically sound aggregation of risks and reliable backtesting of risk forecasts against historical observations.

This research note is a condensed version of Measuring Market Risk Under Basel II, 2.5, and III: VaR, Stressed VaR, and Expected Shortfall, a full working paper posted at http://ssrn.com/abstract=2252463.

Keywords: Basel, Basel II, Basel III, value-at-risk, VaR, expected shortfall, risk, banking, coherence, elicitability