PORTFOLIO OPTIMIZATION USING MODERN PORTFOLIO THEORY (MPT) AND MARKOWITZ EFFICIENT FRONTIER MODELING TECHNIQUES

Abstract

This review paper provides a comprehensive taxonomic synthesis of portfolio optimization frameworks, tracking the evolution of asset allocation from classical quantitative foundations to advanced data-driven models. It begins with Harry Markowitz’s 1952 Modern Portfolio Theory (MPT), outlining its pioneering use of variance as a symmetrical risk metric and its vulnerability to estimation errors, which often turn optimizers into "estimation-error maximizers". To address these challenges, the paper analyzes Post-Modern Portfolio Theory (PMPT), which incorporates asymmetrical risk metrics like downside deviation and integrates high-frequency intraday data to capture downside realized semivariance and price jumps.  The evaluation then shifts to parameter stabilization techniques, highlighting the Bayesian framework of the Black-Litterman model, which combines market equilibrium priors with subjective views to mitigate input sensitivity. Moving beyond classical boundaries, the paper reviews Robust Portfolio Optimization (RPO) and Mixed Conditional Value-at-Risk (MCVaR) frameworks designed to counter tail risk under non-parametric uncertainty sets. It also examines the computational challenges introduced by real-world market frictions and mixed-integer constraints, assessing how metaheuristic algorithms navigate these non-convex spaces. Finally, the paper highlights contemporary breakthroughs in artificial intelligence, comparing the traditional "predict-then-optimize" paradigm with decision-focused, end-to-end Smart Predict-then-Optimize (SPO) loss functions, alongside deep neural and graph networks. By structuring these methodologies into a comparative matrix, this review highlights the transition from rigid historical estimation toward adaptive, decision-focused, and robust risk management frameworks capable of navigating modern financial markets.