The existence of some 2 billion unused EU Allowances (EUAs) at the end of Phase II of the EU's Emissions Trading System (EU ETS) has sparked considerable debate about structural shortcomings of the EU ETS. At the same time, there has been a surprising lack of interest in one possible explanation of this accumulation of EUAs: the theory of intertemporal permit trading, i.e. allowance banking. In this paper we adapt basic banking theory to the case of a smoothly declining cap such as that in the EU ETS. We show that it is rational for agents to decrease emissions beyond the constraint imposed by the cap initially, accumulating an allowance bank and then drawing it down in the interest of minimizing abatement cost over time. Having laid out the theory, we carry out a set of simulations for a reasonable range of key parameters, calibrated to the EU ETS, to illustrate the effects of intertemporal optimization of abatement decisions on optimal time paths of emissions and allowance prices. We also explore the effect of an unexpected change in counterfactual emissions. We conclude that bank accumulation as the result of intertemporal abatement cost optimization should be considered at least a partial explanation when evaluating the current discrepancy between the cap and observed emissions in the EU ETS.