In the ongoing quest for improved seismic design codes, there is currently substantial focus on risk‐targeted design, which aims to achieve more uniform seismic risk across code‐compliant buildings. Such an approach has already been adopted in ASCE 7, which uses lognormal fragility functions, with a single assumed value for dispersion, to generate uniform risk spectra. One challenge to this approach is that fragility functions have been shown to vary depending on the site being considered. This article, therefore, explores the extent to which site location influences the dispersion of fragility functions through the study of inelastic single‐degree‐of‐freedom systems. Twenty‐four different sites across New Zealand are considered so that a diverse range of seismic hazard settings, including multiple tectonic region types, are examined. The resulting dispersion values for the cases examined range from 0.14 to 0.29 and they are shown to be influenced by both the spectral shape and variance of the target spectra used for ground motion selection. The study is then extended to the consideration of scenario‐based seismic risk analysis. It is shown that fragility functions derived using ground motions selected on the basis of probabilistic seismic hazard analysis are, in theory, not suitable for use in scenario‐based risk analyses. The potential ramifications of this work on other risk‐targeted design methods are also discussed. Overall, this work sheds important light on the importance and potential implications of site dependence for what concerns risk‐targeted design.