Understanding the Impact of Weights Constraints in Portfolio Theory

13 Pages Posted: 20 Feb 2011  

Thierry Roncalli

Amundi Asset Management; University of Evry

Date Written: January 31, 2011

Abstract

In this article, we analyze the impact of weights constraints in portfolio theory using the seminal work of Jagannathan and Ma (2003). They show that solving the global minimum variance portfolio problem with some constraints on weights is equivalent to use a shrinkage estimate of the covariance matrix. These results may be easily extended to mean variance and tangency portfolios. From a financial point of view, the shrinkage estimate of the covariance matrix may be interpreted as an implied covariance matrix of the portfolio manager. Using the universe of the DJ Eurostoxx 50, we study the impact of weights constraints on the global minimum variance portfolio and the tangency portfolio. We illustrate how imposing lower and upper bounds on weights modify some properties of the empirical covariance matrix. Finally, we draw some conclusions in the light of recent developments in the asset management industry.

Keywords: Global minimum variance portfolio, Markowitz optimization, tangency portfolio, Lagrange coefficients, shrinkage methods, covariance matrix

JEL Classification: G11, C60

Suggested Citation

Roncalli, Thierry, Understanding the Impact of Weights Constraints in Portfolio Theory (January 31, 2011). Available at SSRN: https://ssrn.com/abstract=1761625 or http://dx.doi.org/10.2139/ssrn.1761625

Thierry Roncalli (Contact Author)

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

University of Evry ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex
France

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