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

Chapter 11 Risk Parity Portfolios

“To dare the impossible is no mark of a wise man.”

— Euripides

Markowitz’s mean–variance portfolio optimizes a trade-off between expected return and risk measured by the variance. Alternative measures of risk to the variance or volatility can be certainly entertained.

However, measuring the risk of the portfolio with a single number provides a limited view. Instead, a more refined characterization comes from employing a risk profile that quantifies the amount of risk contributed by each constituent asset. This refined risk characterization allows a proper control of the portfolio risk diversification and will be explored in this chapter.

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 2024.