The level of natural hedge, i.e. the (negative) correlation between price and yield levels, is an important determinant for farmers’ income risks and their demand for risk management instruments. The natural hedge is often approximated with correlations observed at more aggregated levels, e.g. the county level. This induces biases because the natural hedge at the farm-level is smaller than on more aggregated levels. In this paper, we put this idea one step forward and investigate the empirical relationship between price-yield correlations and the underlying crop acreage, using farm-level data for 5 crops in Switzerland. We find that, for instance, a 1% increase in area under maize and intensive barley leads to a change in the correlation by -0.02 and -0.08, respectively. Thus, larger farms have a stronger natural hedge. Using a revenue insurance example, we show that this information can be used to adjust insurance premiums for each farm.