Value-at-risk versus expected shortfall: A practical perspective

Value-at-Risk (VaR) has become a standard risk measure for financial risk management. However, many authors claim that there are several conceptual problems with VaR. Among these problems, an important one is that VaR disregards any loss beyond the VaR level. We call this problem the "tail risk". In this paper, we illustrate how the tail risk of VaR can cause serious problems in certain cases, cases in which expected shortfall can serve more aptly in its place. We discuss two cases: concentrated credit portfolio and foreign exchange rates under market stress. We show that expected shortfall requires a larger sample size than VaR to provide the same level of accuracy.