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Showing 3 results for Portfolio Optimization
Markowitz Revisited: Addressing Ambiguity as an Important Parameter in Portfolio Optimization
Seyed Erfan Mohammadi, Emran Mohammadi, Ahmad Makui, Kamran Shahanaghi,
Volume 34, Issue 4 (12-2023)
Abstract
Since 1952, when the mean-variance model of Markowitz introduced as a basic framework for modern portfolio theory, some researchers have been trying to add new dimensions to this model. However, most of them have neglected the nature of decision making in such situations and have focused only on adding non-fundamental and thematic dimensions such as considering social responsibilities and green industries. Due to the nature of stock market, the decisions made in this sector are influenced by two different parameters: (1) analyzing past trends and (2) predicting future developments. The former is derived objectively based on historical data that is available to everyone while the latter is achieved subjectively based on inside-information that is only available to the investor. Naturally, due to differences in the origin of their creation the bridge between these two types of analysis in order to optimize the portfolio will be a phenomenon called "ambiguity". Hence, in this paper, we revisited Markowitz's model and proposed a modification that allow incorporating not only return and risk but also incorporate ambiguity into the investment decision making process. Finally, in order to demonstrate how the proposed model can be applied in practice, it is implemented in Tehran Stock Exchange (TSE) and the experimental results are examined. From the experimental results, we can extract that the proposed model is more comprehensive than Markowitz's model and has greater ability to cover the conditions of the stock market.

A Fuzzy Approach to Portfolio Optimization in the Light of Credibility Theory and Z-numbers: An Empirical Study of Tehran Stock Exchange
Hossein Ghanbari, Mostafa Shabani, Emran Mohammadi,
Volume 36, Issue 3 (9-2025)
Abstract
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.

A hybrid AHP–SMART–ILP Framework for pProject Portfolio Selection: Evidence From a Developing Economy
Fiseha Mekonnen Guangul, Girma Tadesse Chala, Subhash Chandra,
Volume 37, Issue 2 (6-2026)
Abstract
Strategic investment decisions across multiple projects require a systematic assessment of extensive quantitative and qualitative data, especially under conditions of resource constraints and uncertainty. Traditional single-project appraisal methods often fail to identify optimal portfolios aligned with organizational goals. This study presents a hybrid project portfolio selection framework integrating the Analytic Hierarchy Process (AHP), Simple Multi-Attribute Rating Technique (SMART), and 0–1 Integer Linear Programming (ILP) to enhance decision-making clarity and robustness. The framework employs a hierarchical structure, utilizing a comprehensive set of technical, commercial, socio-economic, financial, investment, and institutional criteria. AHP establishes consistent relative weights from expert judgments, while SMART scores candidate projects, generating aggregated scores that inform an ILP optimization model aimed at maximizing portfolio utility while adhering to budget constraints, mandatory project conditions, and interdependencies. Validation is performed using real data from an Endowment Corporate Office in Ethiopia, accounting for ongoing and prospective projects under varying demand scenarios. Scenario and sensitivity analyses reveal how variations in demand and criterion weights affect project rankings and portfolio composition, alongside an assessment of portfolio risk via variance and standard deviation. The hybrid AHP–SMART–ILP approach effectively considers both tangible and intangible objectives, achieving stable portfolios that address investment complexities and interdependencies.

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