Quantitative portfolio management has evolved dramatically over the past seven decades - from Markowitz's elegant 1952 mean-variance framework to today's deep learning algorithms that rebalance portfolios in real time. Yet the underlying mathematics remains essential: no machine learning model for finance can be understood, deployed, or trusted without a firm grasp of the statistical and optimisation foundations on which it rests.

This book develops the full spectrum of quantitative portfolio management in a single, unified treatment. Part I establishes the foundations: expected returns, covariance matrices, the efficient frontier, the Capital Allocation Line, and the two-fund separation theorem. Part II covers the empirical asset pricing literature - the Capital Asset Pricing Model, the Fama-French three- and five-factor models, Jensen's alpha, and the Fama-MacBeth cross-sectional regression procedure. Part III addresses the practical challenges of real-world portfolio construction: estimation error in expected returns, Ledoit-Wolf shrinkage for covariance matrices, the Black-Litterman Bayesian model that combines market equilibrium with investor views, Hierarchical Risk Parity that avoids the instability of matrix inversion entirely, and the Equal Risk Contribution framework that allocates risk rather than capital across assets. Part IV concludes with a walk-forward backtesting framework and a complete Reinforcement Learning portfolio agent - using a REINFORCE policy gradient with EMA trend signals as the state representation - tested on a multi-asset universe of equity, gold, and commodity ETFs over 2020-2025.

Throughout, mathematical exposition is accompanied by fully reproducible Python implementations using NumPy, pandas, scikit-learn, statsmodels, and PyTorch. All data is downloaded live from Yahoo Finance and the Ken French data library, so every result in the book can be replicated with a single script. Exercises at the end of each chapter reinforce the theory and guide the reader toward further research.