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Understanding the Impact of Weights Constraints in Portfolio Theory

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  • Roncalli, Thierry

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.

Suggested Citation

  • Roncalli, Thierry, 2010. "Understanding the Impact of Weights Constraints in Portfolio Theory," MPRA Paper 36753, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:36753
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    File URL: https://mpra.ub.uni-muenchen.de/36753/1/MPRA_paper_36753.pdf
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    References listed on IDEAS

    as
    1. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    2. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    3. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    4. repec:dau:papers:123456789/4688 is not listed on IDEAS
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    Cited by:

    1. Bruder, Benjamin & Hereil, Pierre & Roncalli, Thierry, 2011. "Managing sovereign credit risk in bond portfolios," MPRA Paper 36673, University Library of Munich, Germany.
    2. Bruder, Benjamin & Roncalli, Thierry, 2012. "Managing risk exposures using the risk budgeting approach," MPRA Paper 37246, University Library of Munich, Germany.
    3. Giovanni Bonaccolto & Sandra Paterlini, 2020. "Developing new portfolio strategies by aggregation," Annals of Operations Research, Springer, vol. 292(2), pages 933-971, September.

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    More about this item

    Keywords

    global minimum variance portfolio; Markowitz optimization; tangency portfolio; Lagrange coefficients; shrinkage methods; covariance matrix;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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