The risk concept is defined as the distribution of the unexpected results from variations in the values of the variables that describe the market. However, the variable risk is not observable and its measurement depends on which model is used in its evaluation. Thus, the application of different models could result in significant different risk forecasts.The goal of this study is to carry out a comparison within the largest used models (sample variance in the last k observations, exponentially smoothing models and the Bollerslev s model GARCH(1,1)). The study compares the models mentioned above regarding its forecast capability of the volatility for portfolios of selected brazilian stocks. The volatility forecasts will be compared to the actual out of sample volatility. As long as the actual volatility is not an observable variable, the same procedure adopted by RiskMetrics in the calculation of the optimum decay factor will be used: it assumes the premise that the average return of which one of the stock portfolios is equal zero and, as the consequence of this fact, the one step variance forecast of the portfolio return carried out on date t is equal to expected value of the squared return of date t.The final objective is to conclude, using backtesting techniques, which of the forecasting volatility models show the best performance regarding the comparison criterions vis-a-vis the demanding computer efforts. By this way, it was aimed to evaluate which of them offer the best cost-benefit relation for the brazilian equity market.