[en] We use large N-body simulations and empirical scaling relations between dark matter halos, galaxies, and supermassive black holes (SMBBHs) to estimate the formation rates of SMBBH binaries and the resulting low-frequency stochastic gravitational wave background (GWB). We find this GWB to be relatively insensitive ($\lesssim <!--\; ???\; -->10\mathrm{\%<!--\; \%\; -->}$) to cosmological parameters, with only slight variation between wmap5 and Planck cosmologies. We find that uncertainty in the astrophysical scaling relations changes the amplitude of the GWB by a factor of ∼2. Current observational limits are already constraining this predicted range of models. We investigate the Poisson variance in the amplitude of the GWB for randomly generated populations of SMBBHs, finding a scatter of order unity per frequency bin below 10 nHz, and increasing to a factor of ∼10 near 100 nHz. This variance is a result of the rarity of the most massive binaries, which dominate the signal, and acts as a fundamental uncertainty on the amplitude of the underlying power law spectrum. This Poisson uncertainty dominates at $\gtrsim <!--\; ???\; -->20$ nHz, while at lower frequencies the dominant uncertainty is related to our poor understanding of the astrophysical scaling relations, although very low frequencies may be dominated by uncertainties related to the final parsec problem and the processes which drive binaries to the gravitational wave dominated regime. Cosmological effects are negligible at all frequencies.