Recent analyses propose that the key regulatory processes in fisheries are stochastic, characterized by increased recruitment variance at low stock sizes (heteroscedasticity). Here, we investigate the consequences of this idea, with the aim of testing its practical relevance to fisheries management. We argue that stock-recruitment time series are at least one order of magnitude too short to reliably fit heteroscedastic models; indeed, they are typically insufficient even to establish in which direction recruitment variance changes with stock size. Unreliable estimates of heteroscedasticity can have important management implications, depending on the sign of the coefficient of heteroscedasticity. Maximum sustainable yield (MSY) estimates from simple models, which include heteroscedasticity can be volatile, unrealistically high and sometimes non-existent, as illustrated by an analysis of North Sea cod (Gadus morhua) data. In contrast, for North Sea herring (clupea harengus) data, heteroscedasticity has a negligible effect on MSY estimates. Statistical models are useful to elucidate broad-scale regulatory processes, but will need to combined with the mechanistic understanding offered by models of population dynamics before being applied in a management setting.