Investment Portfolio Optimization with Fuzzy Parameters Considering Value at Risk and Suitability with Risk Tolerance and Risk-taking Indices for Retail Investors

Subject Areas : Financial engineering

Ali Namaki ¹ , Saeid Shirkound ² , Amirsina Jirofti ³

1 - Department of Financial Management, Faculty of Management, University of Tehran, Tehran, Iran
2 - Department of Financial Management, Faculty of Management, University of Tehran, Tehran, Iran
3 - Department of Financial Engineering, Kish International Campus, University of Tehran, Tehran, Iran

Received: 2024-08-19 Accepted : 2025-04-03 Published : 2025-06-21

Keywords: Investment Portfolio Optimization, Value at Risk, Suitability Consideration in Investment, Fuzzy Logic in Investment Management,

Abstract :

The present study addresses the issue of portfolio optimization, aiming to develop a model that simultaneously considers optimality and suitability with the risk tolerance and risk-taking indices for retail investors in an uncertain environment. To this end, Z-numbers, which are a recent advancement in fuzzy logic and consist of a pair of fuzzy numbers, are utilized to model the uncertainty in input data. Additionally, the Value at Risk (VaR) is employed to measure portfolio risk, and a formula for calculating this metric is developed through the fuzzy credibility theory. To align with risk tolerance and risk-taking indices, demographic indicators of individual investors are considered, along with the clustering of assets using the K-means method. For the implementation and testing of the model, data from the 50 most active companies listed on the Tehran Stock Exchange between the beginning of 1399 and the end of 1402 were used. The model testing results indicate that incorporating the suitability consideration can personalize the investment portfolio for investors with different risk characteristics. Future research could explore the use of other asset clustering methods and consider the model in a multi-period framework.

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