Portfolio theory is a cornerstone of modern finance, and it is based on the idea that an investor can reduce risk by diversifying their investments across various assets. In practice, Harry Markowitz mean-variance optimization theory is expanded upon by taking into account variable and fixed transaction cost, making the model slightly more reliable. Estimation of parameters is done using historical data and the portfolios considered are those that would be of interest to Generation Z. Using transaction costs from some of Sweden's biggest and most popular banks, the impact of the transaction costs can be seen in the presented graphs. Though many more aspects could be considered to make the model even more realistic, the presented results give insight into how one might want to invest in the stock market to increase their chances of a good expected return given a minimal variance (risk).