Robust optimization is a significant tool to deal with the uncertainty of parameters. However, the robust versions of the mean - variance (MV) model have serious shortcomings. Thus, we propose new robust versions of the MV model and its possibilistic counterpart, based on the Principal Component Analysis. We also derive their analytical solutions when the risk-free asset and short positioning are allowed. In addition, we suggest an eigenvalue approach to manage their conservativeness. After laying down the theoretical points, we illustrate them by using a real data set of six holding stocks trading on the Borsa Istanbul (BIST). We also compare the profitability and performance results of the existing models and the proposed robust models.