A Fuzzy Approach to Portfolio Optimization in the Light of Credibility Theory and Z-numbers: An Empirical Study of Tehran Stock Exchange

Portfolio optimization has emerged as a cornerstone of modern financial theory, maintaining its position as one of the field’s most dynamic and extensively studied areas. While numerous optimization models have been developed and implemented, they fundamentally grapple with the persistent challenge of market uncertainty - an inherent and inescapable characteristic of financial markets. This uncertainty necessitates practical quantification methods to improve the reliability of financial projections, among which fuzzy theory has proven particularly valuable. However, despite its advantages over conventional approaches, traditional fuzzy theory contains a fundamental flaw in its underlying assumption: the presumed absolute reliability of fuzzy number estimations. This critical limitation undermines its effectiveness in real-world applications where information quality varies significantly. To address this gap, this paper proposes a novel portfolio optimization framework that integrates Z-number theory with credibilistic Conditional Value-at-Risk (CVaR) to address both the uncertainty and reliability of asset return estimates. Traditional fuzzy portfolio models often overlook the critical dimension of information quality, potentially leading to suboptimal allocations. Our approach overcomes this limitation by incorporating expert reliability assessments as an integral component of the optimization process through Z-numbers, where the first component represents fuzzy return estimates and the second quantifies their reliability. The model incorporates practical constraints, including cardinality limits and position sizing rules, to ensure real-world applicability. Using data from the Tehran Stock Exchange, we demonstrate that the Z-number-enhanced model produces more stable and economically rational portfolios compared to conventional fuzzy approaches. The results show that considering reliability leads to different asset allocations, with improved risk-adjusted performance. A key contribution is the demonstration that information quality measurably impacts portfolio outcomes, establishing reliability assessment as a necessary element in fuzzy portfolio optimization. This framework provides individual investors and portfolio managers with a more applicated tool for decision-making under uncertainty, especially valuable in markets with varying information quality across assets.

کلیدواژه ها:

Portfolio optimization ، Conditional Value at Risk (CVaR) ، Fuzzy approach ، Credibility theory ، Z-numbers ، Practical Constraints