Analytical Models for Investment Portfolio Optimization

Abstract

Investment portfolio optimization has become essential for managing risk and maximizing returns in increasingly complex and volatile financial markets. Traditional portfolio selection methods often relied on intuition, whereas modern analytical models use quantitative techniques such as mean-variance optimization, Capital Asset Pricing Model (CAPM), multi-factor models, and stochastic optimization to support informed investment decisions. This study presents a comprehensive analytical framework that integrates financial data preprocessing, risk estimation, portfolio optimization, and performance evaluation using metrics such as expected return, portfolio variance, Sharpe ratio, Value at Risk (VaR), and diversification efficiency. The framework enables dynamic portfolio rebalancing by continuously analyzing market conditions and adjusting investment strategies. Experimental results demonstrate that analytical optimization methods outperform traditional allocation approaches by improving returns, reducing risk, enhancing diversification, and increasing investment stability. The study concludes that combining mathematical optimization with statistical financial analysis provides a reliable foundation for intelligent portfolio management, while future integration with Artificial Intelligence (AI), Big Data, Reinforcement Learning, and sustainable investment strategies will further enhance investment decision-making.