Systems are exposed to a variety of risks, including those known as background or systematic risks. Therefore, advanced economic, financial, and engineering models incorporate such risks, thus inevitably making the models more challenging to explore. A number of natural questions arise. First and foremost, is the given system affected by any of such risks? If so, then is the system affected by the risks at the input or output stage, or at both stages? In the present paper we construct an algorithm that answers such questions. Even though the algorithm is based on intricate probabilistic considerations, its practical implementation is easy.