Credible value-at-risk

Peter Mitic

Abstract

Some value-at-risk (VaR) calculations yield extremely large results, which are often rejected on the grounds that they are inconsistent with the operational loss profile of the organization concerned. Therefore, an informal limit has effectively been placed on VaR. Hitherto, the concept of a “maximum” VaR has rarely been considered. In this paper, we propose an objective and simple process to determine whether or not a calculated VaR is “too large”, and thereby give a precise definition of “too large” in this context. A simple decision process, using a constant multiplier of the annualized sum of losses, is proposed to reject distributions that produce extremely high VaR values. This decision process works in conjunction with a bootstrap to also reject distributions that produce very low VaR values. Together, they determine whether or not a calculated VaR value is “credible”. A practical guide to using the combined procedures is given, along with a discussion of potential problems and viable solutions to those problems.