An Application for Portfolio Optimization, Risk Sensitivity and Efficient Frontier Visualization in Mathematica

The present study develops a flexible and interactive decision‑support application for portfolio optimization, grounded in Modern Portfolio Theory and implemented within the Mathematica computational environment. The tool enables users to construct, analyze, and evaluate investment portfolios dynamically, incorporating real-time sensitivity analysis. In accordance with contemporary portfolio theory, it integrates two principal optimization strategies: (a) the Minimum Variance Portfolio and (b) the Maximum Sharpe Ratio Portfolio. The computational framework ingests real stock market data (Yahoo Finance), from which returns and covariance matrices are calculated. The resulting data serves as inputs for solving the corresponding optimization problems under user‑defined constraints. A key feature of the tool is the ability to perform real‑time sensitivity analysis with respect to expected returns, as well as to interactively adjust the risk‑aversion coefficient, providing users with immediate visual and numerical feedback. Interpretability is enhanced through graphical representations of the Efficient Frontier, overlaid with the optimal portfolios and the Capital Market Line on a unified plot. These visualizations support both educational and practical financial decision‑making. Overall, the tool offers a novel contribution by offering a hands‑on, visually rich, and analytically rigorous environment for understanding and applying portfolio optimization methods using real‑world data.