In the last decades, CAPM model has been of great interest in the scientific scene. Despite all the criticism, the improvement of the static CAPM, which has generated new dynamic models, provided investors with stronger guarantee through financial transactions. The CAPM and its static version were and are still very important in the financial scene. Nowadays, more sophisticated adaptations of the CAPM are found, which allow us to explain some matters in finance that had remained unqualified for a couple of time. Considering such discussion about the CAPM validity, this study aims to create a basis for reflection upon the conditional model, comparing it with the static one. In order to verify such facts, tests of conditional models are examined (with beta varying throughout the exercise), something uncommonly studied in the literature. Such tests are suitable to incorporate variances and covariance that change at long run. Methodological wise, the study tested the conditional CAPM model borrowing a leaf from Jagannathan and Wang using macroeconomics and financial variables from the Brazilian sustainability Companies. Based on our findings, there is evidence that the conditional CAPM of Jagannathan and Wang for the North American market is perfectly applicable to the Brazilian sustainability Companies.