A New Portfolio Optimization Model Under Tracking-Error Constraint with Linear Uncertainty Distributions.

Area of Science:

• Quantitative Finance
• Financial Engineering
• Operations Research

Background:

• The enhanced index tracking problem aims to construct a portfolio that surpasses benchmark returns with minimal tracking error.
• Traditional approaches often model stock returns as random variables, which may not fully capture real-world market uncertainties.
• Uncertainty theory offers an alternative framework for modeling imprecise financial data.

Purpose of the Study:

• To address the enhanced index tracking problem by employing uncertainty theory.
• To propose a novel nonlinear uncertain optimization model for enhanced index tracking.
• To analyze the properties of the tracking portfolio frontier and the relationship between portfolio risk, return, and benchmark parameters.

Main Methods:

• Development of a nonlinear uncertain optimization model: the uncertain mean-absolute downside deviation enhanced index tracking model.
• Derivation of an analytical solution for the proposed model under linear uncertainty distributions of stock returns.
• Experimental validation to demonstrate the model's effectiveness in managing tracking error.

Main Results:

• The tracking portfolio frontier is characterized as a continuous curve, potentially consisting of multiple line segments.
• Conditions are established where both the tracking portfolio's return and risk increase in relation to the benchmark's return and risk.
• Experimental results confirm the proposed model's efficacy in controlling tracking error.

Conclusions:

• The proposed nonlinear uncertain optimization model provides a robust framework for enhanced index tracking under uncertainty.
• The analytical solution offers insights into the structure of the efficient frontier in an uncertain environment.
• The model demonstrates practical effectiveness in minimizing tracking error, outperforming benchmarks with greater precision.