12. Risk-Optimal Portfolios

  1. Bernhard Pfaff

Published Online: 30 OCT 2012

DOI: 10.1002/9781118477144.ch12

Financial Risk Modelling and Portfolio Optimization with R

Financial Risk Modelling and Portfolio Optimization with R

How to Cite

Pfaff, B. (2012) Risk-Optimal Portfolios, in Financial Risk Modelling and Portfolio Optimization with R, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781118477144.ch12

Author Information

  1. Invesco Global Strategies, Germany

Publication History

  1. Published Online: 30 OCT 2012
  2. Published Print: 28 DEC 2012

ISBN Information

Print ISBN: 9780470978702

Online ISBN: 9781118477144



  • financial instruments;
  • Markowitz portfolios;
  • mean-VaR portfolio approach;
  • optimal CVaR portfolios;
  • optimal draw-down portfolios;
  • portfolio optimization methods


This chapter presents the portfolio optimization methods in which some sort of risk measure and its level are directly factored into the weightings of the financial instruments. It presents and contrasts the mean-VaR and mean-ES portfolio approaches to classical mean-variance Markowitz portfolios. The chapter elucidates the approach taken by the authors in optimizing portfolios with respect to CVaR and how portfolios of this kind relate to mean-variance and mean-VaR portfolios. It highlights the relation between mean-variance, mean-VaR and mean-CVaR portfolios in the model framework. The chapter also presents the portfolios for which some sort of draw-down measure is minimized or targeted. It presents the relevant R packages, and provides empirical applications at the end of the chapter.

Controlled Vocabulary Terms

currency instruments