Journal of Operational Risk

Credible value-at-risk

Peter Mitic

  • The annualised sum of losses (sum of all losses, S, divided by the number of years spanned by those losses y) is a significant driver of value-at-risk.
  • If VaR exceeds 7.33*S/y, it is “too big”, and an alternative distribution should be sought.
  • The multiplier 7.33 should be considered a guideline. A good way to remember the multiplier is to swap the “three” and the “seven” in the simple approximation for Pi: π ~ 31/7 →71/3

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.

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