Portfolio Selection via Fuzzy Mean-Variance Model

Portfolio selection is still an interesting topic, as thousands of people around the world face this decision-making. Such a decision-making process may be nontrivial due to its potential complexity. There can be a number of effecting factors. The most important are undoubtedly return and risk. These characteristics can be reflected by a well-known mean-variance model using for a portfolio selection. However, return is usually instable over time. Even risk can also vary. This instability and associated uncertainty can be effectively quantified through the fuzzy set. Then return and risk are proposed as triangular fuzzy numbers. Model with fuzzy elements can also respect the investor's vague preferences. The fuzzified mean-variance model can be solvable by fuzzy mathematical programming techniques. Model respecting a typical uncertainty is then much closer to reality. Thus, a portfolio composition can be more representative and satisfactory. The application contribution of a developed fuzzy approach is demonstrated on selecting a portfolio from stocks traded on the Czech capital market. The results are analyzed and confronted with the output of a crisp mean-variance model.