Motivated by these issues, we perform the first multi-model analysis of vortex splits and displacements using historical simulations from 13 stratosphere-resolving models in the fifth Coupled Model Intercomparison Project (CMIP5). The two-dimensional vortex state is quantified using the centroid and aspect ratio moment diagnostics. A wide range of biases are found in the 'most likely' state of the vortex, and these are strongly correlated with biases in the frequency of vortex splits and displacements. This suggests that an improvement in the simulated average state of the vortex leads to an improvement in the representation of extremes. In agreement with observational results, almost all models show vortex splits to be barotropic and displacements to be baroclinic. This is consistent with resonance of the barotropic mode being the dominant mechanism behind vortex splits. The surface annular mode response to vortex splits and displacements is found to be similar, but there are also consistent differences in the surface response which do not project onto the annular mode. We discuss possible mechanisms which may lead to these differences.