Classical method of portfolio selection is based on minimizing the variabi- lity of the portfolio. The Law of Large Numbers tells us that in case of longer investment horizon it should be enough to invest in the asset with the highest expected return which will eventually outperform any other portfolio. In our thesis we will suggest some portfolio creation methods which will create Maxi- mum Return Portfolios. These methods will be based on finding the asset with maximal expected return. That way we will avoid the problem of estimation errors of expected returns. Two of those methods will be selected based on the results of simulation analysis. Those two methods will be tested with the real stock data and compared with the S&P 500 index. Results of the testing suggest that our portfolios could have an application in the real world. Mainly because our portfolios showed to be significantly better than the index in the case of 10 year investment horizon. 1