Open Access
June 2011 Mean–variance portfolio optimization when means and covariances are unknown
Tze Leung Lai, Haipeng Xing, Zehao Chen
Ann. Appl. Stat. 5(2A): 798-823 (June 2011). DOI: 10.1214/10-AOAS422


Markowitz’s celebrated mean–variance portfolio optimization theory assumes that the means and covariances of the underlying asset returns are known. In practice, they are unknown and have to be estimated from historical data. Plugging the estimates into the efficient frontier that assumes known parameters has led to portfolios that may perform poorly and have counter-intuitive asset allocation weights; this has been referred to as the “Markowitz optimization enigma.” After reviewing different approaches in the literature to address these difficulties, we explain the root cause of the enigma and propose a new approach to resolve it. Not only is the new approach shown to provide substantial improvements over previous methods, but it also allows flexible modeling to incorporate dynamic features and fundamental analysis of the training sample of historical data, as illustrated in simulation and empirical studies.


Download Citation

Tze Leung Lai. Haipeng Xing. Zehao Chen. "Mean–variance portfolio optimization when means and covariances are unknown." Ann. Appl. Stat. 5 (2A) 798 - 823, June 2011.


Published: June 2011
First available in Project Euclid: 13 July 2011

zbMATH: 05961692
MathSciNet: MR2840176
Digital Object Identifier: 10.1214/10-AOAS422

Keywords: efficient frontier , Empirical Bayes , Markowitz’s portfolio theory , stochastic optimization

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.5 • No. 2A • June 2011
Back to Top