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Article

Constrained Optimization for Portfolio Construction

Laurence Wormald and van der Merwe Elmarie
The Journal of Investing Spring 2012, 21 (1) 44-59; DOI: https://doi.org/10.3905/joi.2012.21.1.044
Laurence Wormald
is the head of research at SunGard APT in London, UK.
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  • For correspondence: laurence.wormald@sungard.com
van der Merwe Elmarie
is a research analyst at SunGard APT in London, UK.
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  • For correspondence: elmarie.vandermerwe@sungard.com
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Abstract

This article deals with the relationship between conventional shrinkage approaches to the construction of the covariance matrix for portfolio optimization and the various types of constraints available in modern numerical algorithms for solving optimization problems. In particular, we consider the use of quadratic constraints on each part of the total risk (variance) measure, such as the systematic or specific risk associated with a factor risk model. By placing constraints on each part of the risk (perhaps in conjunction with constraints on the total risk), solutions are obtained that differ from the conventional constrained mean–variance solutions. We consider the use of this approach in the light of recent work focusing on portfolio optimization with alpha (expected return) terms that are cross-sectionally correlated with the risk factors of the model used to estimate the covariance matrix. To illustrate the practical value of this approach, using a well-documented set of alphas, we set out the results of a 13-year simulation exercise over the Russell 3000 Growth U.S. equity universe. The results, which can be of intuitive interest to investors, demonstrate how constraints that have the effect of shrinkage on the covariance matrix associated with the spanned part of the alpha will result in different portfolio allocations.

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The Journal of Investing: 21 (1)
The Journal of Investing
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Spring 2012
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Constrained Optimization for Portfolio Construction
Laurence Wormald, van der Merwe Elmarie
The Journal of Investing Feb 2012, 21 (1) 44-59; DOI: 10.3905/joi.2012.21.1.044

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Constrained Optimization for Portfolio Construction
Laurence Wormald, van der Merwe Elmarie
The Journal of Investing Feb 2012, 21 (1) 44-59; DOI: 10.3905/joi.2012.21.1.044
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  • Article
    • Abstract
    • SHRINKAGE, FACTOR MODELS, AND OPTIMIZATION ISSUES
    • EVIDENCE FROM QUANTITATIVE EQUITY STRATEGIES
    • EMPIRICAL RESULTS
    • SIMULATOR SETUP AND ASSUMPTIONS
    • RESULTS
    • MEAN–VARIANCE SPACE
    • STYLE SCORES
    • CONCLUSIONS
    • ENDNOTE
    • REFERENCES
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