Emissions trading schemes on entity level are becoming more and more important in the context of controlling greenhouse gases. The directive on a Europe-wide trading scheme is a prime example. Prior to the start of such a scheme, a number of design features have to be agreed upon. Regarding the allocation of allowances, a distribution that is (almost) free of charge has been the method of choice. An aspect that has interestingly attracted little attention thus far is the question of how to allocate emission rights over time, i.e. in single, subsequent periods that exist in real trading schemes. In this paper, different allocation options are applied to the electricity sector. A power market that mirrors reality with five different types of power plants (hydro, nuclear, lignite, coal and gas) is simulated over two periods. On the demand side, three different load curves are assumed (winter, summer, transition). For each demand curve different elasticities are analysed. Supply and demand are matched on an hourly basis. The allocation is either based on absolute emissions or on a generation benchmark. The base period / generation metric is either constant or updated over time. Thus, four different allocation options exist. It turns out that the electricity sector as a whole gains from the introduction of the instrument. Its aggregated gross margin is considerably higher with an allocation based on a constant period / generation metric. It is thus the preferred allocation option. This result contradicts other recent studies that assumed completely inelastic demand. Single plant operators may, however, win or lose in terms of the net financial impact. On the installation level, preferences regarding the different allocation scheme are a function of the fuel used.