\( \newcommand{\bm}[1]{\boldsymbol{#1}} \newcommand{\textm}[1]{\textsf{#1}} \newcommand{\textnormal}[1]{\textsf{#1}} \def\T{{\mkern-2mu\raise-1mu\mathsf{T}}} \newcommand{\R}{\mathbb{R}} % real numbers \newcommand{\E}{{\rm I\kern-.2em E}} \newcommand{\w}{\bm{w}} % bold w \newcommand{\bmu}{\bm{\mu}} % bold mu \newcommand{\bSigma}{\bm{\Sigma}} % bold mu \newcommand{\bigO}{O} %\mathcal{O} \renewcommand{\d}[1]{\operatorname{d}\!{#1}} \)

Chapter 7 Modern Portfolio Theory

“You must read, you must persevere, you must sit up nights, you must inquire, and exert the utmost power of your mind. If one way does not lead to the desired meaning, take another; if obstacles arise, then still another; until, if your strength holds out, you will find that clear which at first looked dark.”

— Giovanni Boccaccio

Modern portfolio theory (MPT) started with Harry Markowitz’s 1952 seminal paper “Portfolio Selection” (Markowitz, 1952), for which he would receive the Nobel prize in 1990. He put forth the idea that risk-adverse investors should optimize their portfolio based on a combination of two objectives: expected return and risk. That idea has remained central to portfolio optimization. In practice, however, the vanilla Markowitz portfolio formulation has some issues and drawbacks; as a consequence most practitioners tend to combine it with several heuristics or avoid it altogether. In this chapter, we explore the mean–variance Markowitz portfolio in its many facets.

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.