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Large-Scale Portfolio Optimization

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  • Andre F. Perold

    (Graduate School of Business Administration, Harvard University, Boston, Massachusetts 02163)

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    Abstract

    This paper describes a practical algorithm for large-scale mean-variance portfolio optimization. The emphasis is on developing an efficient computational approach applicable to the broad range of portfolio models employed by the investment community. What distinguishes these from the "usual" quadratic program is (i) the form of the covariance matrix arising from the use of factor and scenario models of return, and (ii) the inclusion of transactions limits and costs. A third aspect is the question of whether the problem should be solved parametrically in the risk-reward trade off parameter, \lambda , or separately for several discrete values of \lambda . We show how the parametric algorithm can be made extremely efficient by "sparsifying" the covariance matrix with the introduction of a few additional variables and constraints, and by treating the transaction cost schedule as an essentially nonlinear nondifferentiable function. Then we show how these two seemingly unrelated approaches can be combined to yield good approximate solutions when minimum trading size restrictions ("buy or sell at least a certain amount, or not at all") are added. In combination, these approaches make possible the parametric solution of problems on a scale not heretofore possible on computers where CPU time and storage are the constraining factors.

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    File URL: http://dx.doi.org/10.1287/mnsc.30.10.1143
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 30 (1984)
    Issue (Month): 10 (October)
    Pages: 1143-1160

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    Handle: RePEc:inm:ormnsc:v:30:y:1984:i:10:p:1143-1160

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    Keywords: finance; portfolio;

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    Cited by:
    1. Massol, Olivier & Banal-Estañol, Albert, 2014. "Export diversification through resource-based industrialization: The case of natural gas," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1067-1082.
    2. Dokuchaev, Nikolai & Yu Zhou, Xun, 2001. "Optimal investment strategies with bounded risks, general utilities, and goal achieving," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 289-309, April.
    3. Zhang, Wei-Guo & Xiao, Wei-Lin & Xu, Wei-Jun, 2010. "A possibilistic portfolio adjusting model with new added assets," Economic Modelling, Elsevier, vol. 27(1), pages 208-213, January.
    4. Kerstens, Kristiaan & Mounir, Amine & Van de Woestyne, Ignace, 2011. "Geometric representation of the mean-variance-skewness portfolio frontier based upon the shortage function," European Journal of Operational Research, Elsevier, vol. 210(1), pages 81-94, April.
    5. Walter Murray & Howard Shek, 2012. "A local relaxation method for the cardinality constrained portfolio optimization problem," Computational Optimization and Applications, Springer, vol. 53(3), pages 681-709, December.
    6. Tsaur, Ruey-Chyn, 2013. "Fuzzy portfolio model with different investor risk attitudes," European Journal of Operational Research, Elsevier, vol. 227(2), pages 385-390.
    7. Crama, Y. & Schyns, M., 2003. "Simulated annealing for complex portfolio selection problems," European Journal of Operational Research, Elsevier, vol. 150(3), pages 546-571, November.
    8. Arenas Parra, M. & Bilbao Terol, A. & Rodriguez Uria, M. V., 2001. "A fuzzy goal programming approach to portfolio selection," European Journal of Operational Research, Elsevier, vol. 133(2), pages 287-297, January.
    9. Massol, O. & Banal-Estanol, A., 2012. "Export diversification and resource-based industrialization: the case of natural gas," Working Papers 12/01, Department of Economics, City University London.
    10. Duarte Jr, A. M., 2000. "Fast Computation of Efficient Portfolios," Finance Lab Working Papers flwp_32, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    11. Li, Ting & Zhang, Weiguo & Xu, Weijun, 2013. "Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment," Economic Modelling, Elsevier, vol. 31(C), pages 12-17.
    12. Chen, Wei & Zhang, Wei-Guo, 2010. "The admissible portfolio selection problem with transaction costs and an improved PSO algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2070-2076.
    13. Leung, Pui-Lam & Ng, Hon-Yip & Wong, Wing-Keung, 2012. "An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment," European Journal of Operational Research, Elsevier, vol. 222(1), pages 85-95.
    14. Michael Best & Xili Zhang, 2012. "The Efficient Frontier for Weakly Correlated Assets," Computational Economics, Society for Computational Economics, vol. 40(4), pages 355-375, December.
    15. Bai, Zhidong & Li, Hua & Wong, Wing-Keung, 2013. "The best estimation for high-dimensional Markowitz mean-variance optimization," MPRA Paper 43862, University Library of Munich, Germany.
    16. Zhang, Xili & Zhang, Weiguo & Xiao, Weilin, 2013. "Multi-period portfolio optimization under possibility measures," Economic Modelling, Elsevier, vol. 35(C), pages 401-408.
    17. White, D.J., 1998. "Epsilon-dominating solutions in mean-variance portfolio analysis," European Journal of Operational Research, Elsevier, vol. 105(3), pages 457-466, March.

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