1. ¹is President and CEO of Axioma, Inc., a New York-based company that produces portfolio construction analytics. Before founding Axioma, he was an associate professor of decision, risk and operations at Columbia Business School from 1993 to 1998. He completed his PhD in Operations Research at Carnegie Mellon University's Graduate School of Industrial Administation.
2. ²is Director of Research and Development, for Axioma, Inc., where he develops specialised optimisation solution techniques for financial problems and improved portfolio management methodologies and software. He earned a PhD in Industrial Engineering and Management Science and a Master of Science degree in Industrial Engineering and Management Science from Northwestern University, and a Bachelor of Science degree in Applied Mathmetics from Auburn University.

Correspondence: Sebastián Ceria, Axioma. Inc., 100 5th Avenue, Suite 901, New York, NY, 10011, USA, Tel: +1 (212) 901 1000, Fax: +1 (212) 901 1911; e-mail: sceria@axiomainc.com

Received 17 May 2006.

Abstract

The authors explore the negative effect that estimation error has on mean-variance optimal portfolios. It is shown that asset weights in mean-variance optimal portfolios are very sensitive to slight changes in input parameters. This instability is magnified by the presence of constrains that asset managers typically impose on their portfolios. The authors propose to use robust mean variance, a new technique which is based on robust optimisation, a deterministic framework designed to explicitly consider parameter uncertainty in optimisation problems. Alternative uncertainty regions that create a less conservative robust problem are introduced. In fact, the authors' proposed approach does not assume that all estimation errors will negatively affect the portfolios, as is the case in traditional robust optimisation, but rather that there are as many errors with negative consequences as there are errors with positive consequences. The authors demonstrate through extensive computational experiments that portfolios generated with their proposed robust mean variance methodolgy typically outperform traditional mean variance portfolios in a variety of investment scenarios. Additionally, robust mean variance portfolios are usually less sensitive to input parameters.