Emission trading has become recently more and more import in environmental regulation. In the context of controlling greenhouse gas emissions, the directive on a Europewide trading scheme for large immobile sources may be perceived as one of the most important milestones in recent years. Prior to its start, however, a number of very specific design features have to be agreed upon. In the political discussion, the question of how to allocate emission rights is considered as one of the most important issues. So far, a distribution (almost) free of charge is the option of choice. An aspect that has interestingly attracted little attention in the past is the question of how to allocate emission rights over time. This may for example be done on the basis of a constant reference metric, as for example emissions in a certain fixed year, or on the basis of a rolling metric as for example emissions in the previous year. The following paper analyses four different allocation options in multi-period emissions trading that are currently discussed in the European context. The four options are applied for the electricity sector. A power market close to reality with five different types of power plants (hydro, nuclear, lignite, coal and gas) is simulated over two periods. The paper distinguishes between a market effect of emissions trading on the one hand and compliance costs for meeting the emission reduction obligation on the other. The market effect results from a price increase which is due to the fact that opportunity costs for using allowances, though received free of charge, must be considered. However, only compliance costs and not opportunity costs materialise as costs in the profit and loss account of utilities. It turns out that the electricity sector as a whole gains from the introduction of the instrument due to the increase of the electricity price. With regard to the different allocation options, it is found that utilities have different preferences depending on the fuel used.