We investigate the impact of a non-financial background risk ˜" on the preference rankings between two independent financial risks ˜z1 and ˜z2 for an expected-utility maximizer. More precisely, we provide necessary and sufficient conditions for the alternative (x0 + ˜z1, y0 + ˜") to be preferred to (x0 + ˜z2, y0 + ˜") whenever (x0 + ˜z1, y0) is preferred to (x0 + ˜z2, y0). Utility functions that preserve the preference rankings are fully characterized. Their practical relevance is discussed in light of recent results on the constraints for the modeling of the preference for the disaggregation of harms.