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

Chapter 12 Graph-Based Portfolios

“Too much and too little wine. Give him none, he cannot find truth; give him too much, the same.”

— Blaise Pascal

Amid an overload of information in the modern era, graphs provide a convenient and compact way to represent big data, analyze the structure of large networks, and extract patterns that may otherwise go unnoticed. In the context of financial data, graphs of assets provide key information for modern portfolio design that may be incorporated, for example, into the basic mean–variance portfolio formulation (which obtains the portfolio as a trade-off between the expected return and the risk measured by the variance). Nevertheless, exactly how to use this graph information in the portfolio optimization process is still an open question. This chapter explores some attempts in the literature.

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.