We study optimal harvesting of a renewable resource with stochastic dynamics. To focus on the effect of risk aversion, we consider a resource user who is indifferent with respect to intertemporal variability. We find that a constant escapement strategy is optimal, i.e. the stock after harvesting is constant. Under common specifications of risk aversion, increasing risk and risk aversion increase current resource use, the reason being a substitution effect, i.e. the resource user substitutes assets away from the risky resource stock. We apply the model to the case of the Eastern Baltic cod fishery and, in contrast to the previous literature, find a strong effect of risk and risk aversion on optimal harvesting.