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Chapter 1 Introduction

En un lugar de La Mancha, de cuyo nombre no quiero acordarme …

— Miguel de Cervantes Saavedra, Don Quixote

Modern portfolio theory started with Harry Markowitz’s 1952 seminal paper “Portfolio Selection” (Markowitz, 1952), for which he would later receive the Nobel Prize in Economic Sciences1 in 1990. He put forth the idea that risk-averse investors should optimize their portfolio based on a combination of two objectives: expected return and risk. Until today, that idea has remained central to portfolio optimization. In practice, however, the vanilla Markowitz portfolio formulation does not perform as anticipated. Consequently, most practitioners either combine it with various heuristics or refrain from using it altogether.

Over the past 70 years, researchers and practitioners have reconsidered the Markowitz portfolio formulation, leading to numerous variations, enhancements, and alternatives. These include robust optimization methods, alternative risk measures, regularization through sparsity, improved covariance matrix estimators via random matrix theory, robust estimators for heavy tails, factor models, mean models, volatility clustering models, risk parity formulations, and more.

This book explores practical financial data modeling and portfolio optimization, covering a wide range of variations and extensions. It systematically starts with mathematical formulations and proceeds to develop practical numerical algorithms, supplemented with code examples to enhance understanding.

  • The financial data modeling considered herein moves away from the unrealistic Gaussian assumption and delves into more realistic models based on heavy-tailed distributions. It encompasses an array of topics, ranging from basic time series models, making extensive use of Kalman filtering methods, to state-of-the-art techniques for estimating financial graphs.

  • The portfolio formulations covered in this book span a wide range, from the original 1952 Markowitz’s mean–variance portfolio and 1966 maximum Sharpe ratio portfolio, to more sophisticated formulations such as Kelly-based portfolios, utility-based portfolios, high-order portfolios, downside risk portfolios, semi-variance portfolios, CVaR portfolios, drawdown portfolios, risk parity portfolios, graph-based portfolios, index tracking portfolios, robust portfolios, bootstrapped portfolios, bagged portfolios, pairs trading portfolios, statistical arbitrage portfolios, and deep learning portfolios, among others.

The primary focus and central theme of this book is on practical algorithms for portfolio formulations that can be effortlessly executed on a standard computer.

This material will be published by Cambridge University Press as Portfolio Optimization: Theory and Application by Daniel P. Palomar. This pre-publication version is free to view and download for personal use only; not for re-distribution, re-sale, or use in derivative works. © Daniel P. Palomar 2025.

References

Markowitz, H. M. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.

  1. To be exact, what is usually referred to as the Nobel Prize in Economic Sciences is actually the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.↩︎