The model known as capital asset pricing model - CAPM defines the beta parameter as the constant that measures the expected return variation of an asset in relation to the equity premium. Parameter beta stability is crucial to apply the use of historical data in the pricing of assets and assessing the cost of capital of companies. This dissertation assessed parameter beta stability in the period from July 1994 to June 2008, a total of 168 months for a sample of 41 traded stocks on the São Paulo Stock Exchange - BOVESPA. The index of that stock exchange - Ibovespa was used as a market index proxy. The statistical test known as the Chow Test was applied, and regressions were carried out in cross sections not overlapping periods. From the Chow Test results, a significant percentage of betas of the sample are shown to be statistically stable. However, the analysis of crosssection regressions in different subperiods showed that the betas calculated based on historical data have very little participation in explanation of the parameter value calculated for subsequent period. The study also tested the adjustment proposed by Vasicek but concludes that the latter contributes very little to forecast power of historical betas.