Is there a risk that this will underemphasise some values when the source of error is not independent? For example, the ROI on financial instruments may be inve

Is there a risk that this will underemphasise some values when the source of error is not independent? For example, the ROI on financial instruments may be inversely correlated to the risk of losing your job. If you associate errors with each, then combine them in a way which loses this relationship, there will be problems.