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We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. By assuming idealized conditions of perfect forecast ability for the future return and volatility of stocks and short selling, we show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio between predicted and realized risk. Bootstrap analysis indicates that this improvement is obtained in a wide range of the parameters N (number of assets) and T (investment horizon). The predicted and realized risk level and the relative portfolio composition of the selected portfolio for a given value of the portfolio return are also investigated for each considered filtering method. We also show that several of the results obtained by assuming idealized conditions are still observed under the more realistic assumptions of no short selling and mean return and volatility forecasting …