A new approach to the bi-criteria multi-period fuzzy portfolio selection

The proposed approach to the bi-criteria multi-period fuzzy portfolio selection is based on the observation that the treating the variance as a measure of portfolio risk provides sometimes questionable results. Therefore, the simple criteria of portfolio risk and return are proposed. Based on them and three popular methods for local criteria aggregation, a new fuzzy portfolio selection one-period model has been developed. It is shown that this model provides reasonable results coinciding with common sense. Based on this model, a new two-stage bi-criteria optimization approach to portfolio selection has been developed, tested and used as a main component of proposed multi-period portfolio selection model. A method for obtaining fuzzy distributions of stocks returns based on real market data is developed and used for the optimal portfolio selection. In some cases, to make the presentation of developed methods features more transparent, the problem simplification, when all market decisions (Buy, Sell and Hold) were considered as right ones was used. But finally, the real-world market decisions which are generated using the stock trading expert system based on the real market data were used for the portfolio selection. To do this, the known stock trading expert system has been applied, which was adapted for the conditions of the considered stock markets (NYSE and NASDAQ) providing best results after optimization. Using the real-world examples, it is shown that incorporating the stock signals (decisions) Buy, Sell and Hold in the multi-period portfolio selection models improves strongly the models results making them closer to reality.