A New Possibilistic Mean–Variance Model Based on the Principal Components Analysis: An Application on the Turkish Holding Stocks
Furkan Goktas and Ahmet Duran
Possibility Theory is a great tool to deal with the imprecise probability. However, the possibilistic counterpart of the mean-variance (MV) model has serious shortcomings. Thus, we propose a new possibilistic MV model, which depends on the Principal Components Analysis. The proposed model enables to incorporate subjective judgments into the portfolio selection. In addition, it captures the asymmetry in the return data unlike the MV model. The proposed model is also tractable as the MV model since it can be expressed as a concave quadratic maximization problem. After laying down the theoretical points, we illustrate it 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 proposed model and the MV model.
Keywords: Portfolio selection, imprecise probability, possibility theory, fuzzy logic, triangular fuzzy numbers, subjective judgments, principal components analysis, mean-variance model.