Roncalli, Thierry (2010): Understanding the Impact of Weights Constraints in Portfolio Theory.

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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.
Item Type:  MPRA Paper 

Original Title:  Understanding the Impact of Weights Constraints in Portfolio Theory 
Language:  English 
Keywords:  global minimum variance portfolio, Markowitz optimization, tangency portfolio, Lagrange coefficients, shrinkage methods, covariance matrix 
Subjects:  G  Financial Economics > G1  General Financial Markets > G11  Portfolio Choice; Investment Decisions C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C60  General 
Item ID:  36753 
Depositing User:  Thierry Roncalli 
Date Deposited:  18. Feb 2012 14:06 
Last Modified:  12. Feb 2013 20:49 
References:  Choueifaty Y. and Coignard Y. (2008), Towards Maximum Diversification, Journal of Portfolio Management, 35(1), pp. 4051. Demey P., Maillard S. and Roncalli T. (2010), RiskBased Indexation, Lyxor White Paper, 1, www.lyxor.com. Jagannathan J. and Ma T. (2003), Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps, Journal of Finance, 58(4), pp. 16511683. Ledoit, O. and Wolf, M. (2003), Improved Estimation of the Covariance Matrix of Stock Returns With an Application to Portfolio Selection, Journal of Empirical Finance, 10(5), pp. 603621. Maillard S., Roncalli T. and Teïletche J. (2008), The Properties of Equally Weighted Risk Contribution Portfolios, Journal of Portfolio Management, 36(4), pp. 6070. Martellini L. (2008), Toward the Design of Better Equity Benchmarks, Journal of Portfolio Management, 34(4), pp. 18. Roncalli T. (2010), La Gestion d’Actifs Quantitative, Economica. Yanou G. (2010), The BlackLitterman Model: Wrong Views v.s. Opportunity Cost, Working Paper, ssrn.com/abstract=1722237. Yanou G. (2010), MeanVariance Framework and Diversification Objective: Theoretical and Empirical Implications, Working Paper, ssrn.com/abstract=1722285 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/36753 