Value-at-risk: is lacking in sub-additivity just an annoying technicality?

摘要

Following the final revision of Basel II, Value-at-Risk (VaR) is becoming one of the most used risk measures for managing market and operational risks. Nevertheless, in recent years, some undesirable drawbacks in its use have been pointed out by academics. One of them is the so-called 'lacking in sub-additivity', which turns out to be not only an annoying technicality, but also the 'real culprit' of VaR misleading guide in capital allocation strategy. A number of numerical examples prove the fallacy of some common conjectures. Eventually, a risk measure, which is a revised version of the Expected Shortfall (ES), is suggested as a sound alternative.