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The following report constitutes a detailed description of the steps required for the investigation of the potential nexus between two basic variables , which are crude oil prices and stock returns , interpreted through the S&P500 Index, in the market of the USA. This unidirectional causal relationship will be further analyzed imposing two intermediate causes, which are investors’ sentiment and p rice earnings ratio. This means that the initial bivariate approach will be further expanded to a multivariate analysis of four different variables. The first part includes some tests for the verification of the order of integration, a basic precondition, as causality analysis is only valid under the assumption of stationarity. Secondly, the selected methods of causality checking will be analyzed based on both a tetravariate and a trivariate framework connecting all the associated variables. Consequently , the evaluation of the findings resulting from these methods as well as the main conclusions will be analytically presented. The substance of these findings is that strong causality linkages exist among the variables both directly and indirectly through the intermediate interaction of the auxiliary variables. However, there is not a clear result generally accepted among the available tests, as they all lead to different causality associations, some of which are significant and some not. In such a way, a completed investigation of the channels of causality among the selected variables using a causality chain technique is finally conducted.