Time-Inconsistency of VaR and Time-Consistent Alternatives

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