The problem of finding an optimal strategy to execute a trade is well-known to portfolio managers. The market impact of the execution is associated with transaction costs to the manager. Following the model proposed by Almgren and Chriss in 2000 , we find an optimal strategy associated with the trade execution in a mean-variance sense. Moreover, we find an efficient frontier of strategies. We also fit the model to Ibovespa Future's real trade data, and find statistical evidence that the model works.