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(eng): We examine the complexity of financial returns generated by popular agent-based models through studying multifractal properties of such time series. Specifically, we are interested in the sensitivity of the models to their parameter settings and whether some patterns emerge in the connection between complexity and a specific type of parameter. We find that (i) herding behavior mostly boosts the model complexity as measured by multifractality, (ii) various in-built stabilizing factors increase model complexity, while (iii) the role of the intensity of choice, the number of agents, as well as the chartists’ representation have rather model-specific effects. Finally, the core feature driving the model complexity seems to be the implementation of a switching mechanism governing agents’ interactions. The heterogeneous set of nine analyzed models thus offers some universal concepts that hold across their range. Our results also indicate that complex dynamics are observed not only for the benchmark parameter settings but also for other combinations of parameter values for most models. This opens new avenues for future research and specifically motivates examining the models in more detail by focusing on other dynamic properties in addition to the herein presented multifractality.