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This study tests and compares two versions of the general equilibrium relationship for the prediction of expected returns: the static version of the CAPM and the conditional CAPM version that considers non-stationary estimates of the coefficients over a given period. The first concern was about the explanatory power of each model and compared the effects of economic variables, and the second was to examine the occurrence of structural changes, and which periods impacted the behavior of the coefficients. The analysis was conducted on daily data of indexes representing stocks traded on the Bovespa during the period from 1st December 2005 to October 31, 2008 (721 observations). To have a minimum number of observations and estimate consistently the parameters of the regression models and so that the Newey-West correction could correct the problem of inefficiency of the coefficients violated when the classical assumptions of absence of autocorrelation and heteroscedasticity waste in some cases, had to consider breaks that were statistically more significant through the control of the monitoring period. Thus, after applying the tests to verify hypotheses classical OLS, it was found that the model chosen was the conditional CAPM, showing small Akaike information criteria (AIC) and Schwarz (BIC) without the presence of structural break. When considering the presence of structural breaks in time series, there were changes in systemic risk and total over the period observed. From these results, it is recommended to investigate the possible events that led to disruption in the series, noting the factors that contributed to such interference. [ABSTRACT FROM AUTHOR]