Multi-criteria fuzzy portfolio optimization with considering different levels of investor expectations

Objective

The objective of the present research is the optimization of investment portfolios, considering all significant criteria for investors in a fuzzy environment, taking into account various levels of investor expectations for each criterion based on their risk preferences. On one hand, the utilization of fuzzy logic in modeling this problem can enhance its alignment with real-world conditions by accommodating uncertainty in input data. On the other hand, the proposed model for portfolio selection incorporates not only risk and return as key factors for investors but also considers other important factors. These factors include risk, short-term and long-term returns, liquidity, maximum and minimum investment ratios in each asset, dividend distribution, and cardinality constraint (the number of assets within the portfolio). Another objective of this research is to present an innovative model compared to existing ones by incorporating a logistic fuzzy membership function to model various levels of investor expectations. This enables the formation of investment portfolios based on the priority of investors with different risk appetites regarding different criteria.

Methods

The method of conducting this research is that initially, the optimization modeling of a nonlinear multi-objective problem in a fuzzy environment is addressed, considering all crucial factors for investors. Subsequently, employing quantitative methods and the foundations of fuzzy logic, we transform the problem into a single-objective linear problem, making it amenable to solution using conventional optimization methods and software. Ultimately, utilizing data from the 50 most active companies on the Tehran Stock Exchange (TSE) market, we implement the model and conduct an analysis of the results.

Results

The research results indicate that the proposed model yields a return of more than twice the performance compared to the index of the 50 most active companies on the Tehran Stock Exchange (TSE) market for both aggressive and conservative investors. Additionally, the presented model, by incorporating a logistic-shaped membership function for various problem objectives, can be customized for investors with aggressive (risk-tolerant) or conservative (risk-averse) strategies. This customization is attributed to the presence of a parameter determining the shape of the membership function in logistic functions, allowing the prioritization of different factors such as risk, short-term and long-term returns, liquidity, or dividend distribution for investors with varying levels of risk tolerance

Conclusion

The utilization of logistic-shaped membership functions in a fuzzy environment, along with diverse criteria, can personalize the investment portfolio selection model for investors with different characteristics. This customization enables investors with various risk tolerances to construct a portfolio according to their priorities. This adaptability significantly contributes to the practical applicability of the portfolio selection problem in the real world. Furthermore, employing computational methods and fuzzy principles allows the transformation of a nonlinear multi-objective problem into a single-objective linear model, facilitating its implementation and resolution.