Time-Inconsistency of VaR and Time-Consistent Alternatives
8 Pages Posted: 5 Mar 2008
Date Written: November 2007
We show that VaR (value-at-risk) is not time-consistent and discuss examples where this leads to dynamically inconsistent behavior. Then we propose two time-consistent alternatives to VaR. The first one is a composition of one-period VaR's. It has some of the theoretical drawbacks of static VaR and should be used with care in situations where financial positions are not normally distributed or in models with complex dependence structures. The second one is a composition of average VaR's. It is a time-consistent coherent risk measure and provides good results in any situation.
Keywords: time-consistency, value at risk, composed value at risk, composed average value at risk
JEL Classification: D81, G18
Suggested Citation: Suggested Citation