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Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions

Author

Listed:
  • Bruce I. Jacobs

    (Jacobs Levy Equity Management, 100 Campus Drive, P.O. Box 650, Florham Park, New Jersey 07932-0650)

  • Kenneth N. Levy

    (Jacobs Levy Equity Management, 100 Campus Drive, P.O. Box 650, Florham Park, New Jersey 07932-0650)

  • Harry M. Markowitz

    (Harry Markowitz Company, 1010 Turquoise Street, Suite 245, San Diego, California 92109)

Abstract

This paper presents fast algorithms for calculating mean-variance efficient frontiers when the investor can sell securities short as well as buy long, and when a factor and/or scenario model of covariance is assumed. Currently, fast algorithms for factor, scenario, or mixed (factor and scenario) models exist, but (except for a special case of the results reported here) apply only to portfolios of long positions. Factor and scenario models are used widely in applied portfolio analysis, and short sales have been used increasingly as part of large institutional portfolios. Generally, the critical line algorithm (CLA) traces out mean-variance efficient sets when the investor’s choice is subject to any system of linear equality or inequality constraints. Versions of CLA that take advantage of factor and/or scenario models of covariance gain speed by greatly simplifying the equations for segments of the efficient set. These same algorithms can be used, unchanged, for the long-short portfolio selection problem provided a certain condition on the constraint set holds. This condition usually holds in practice.

Suggested Citation

  • Bruce I. Jacobs & Kenneth N. Levy & Harry M. Markowitz, 2005. "Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions," Operations Research, INFORMS, vol. 53(4), pages 586-599, August.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:4:p:586-599
    DOI: 10.1287/opre.1050.0212
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    References listed on IDEAS

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    Cited by:

    1. Guerard, John, 2023. "Harry Markowitz: An appreciation," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1496-1501.
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    3. Khodamoradi, T. & Salahi, M. & Najafi, A.R., 2020. "Robust CCMV model with short selling and risk-neutral interest rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    4. J. Davis & P. Hagelstein & I. Lackner & R. Piziak, 2020. "The Efficient Frontier and International Portfolio Diversification in Taxable and Tax-Privileged Accounts," Journal of Finance and Investment Analysis, SCIENPRESS Ltd, vol. 9(2), pages 1-3.
    5. Andras Niedermayer & Daniel Niedermayer, 2006. "Applying Markowitz's Critical Line Algorithm," Diskussionsschriften dp0602, Universitaet Bern, Departement Volkswirtschaft.
    6. Cristiano Arbex Valle, 2024. "Portfolio optimisation: bridging the gap between theory and practice," Papers 2407.00887, arXiv.org, revised Sep 2024.
    7. Jarrod Wilcox & Frank Fabozzi, 2009. "A Discretionary Wealth Approach to Investment Policy," Yale School of Management Working Papers amz2434, Yale School of Management.
    8. Yu, Jing-Rung & Lee, Wen-Yi, 2011. "Portfolio rebalancing model using multiple criteria," European Journal of Operational Research, Elsevier, vol. 209(2), pages 166-175, March.
    9. Al Janabi, Mazin A.M. & Arreola Hernandez, Jose & Berger, Theo & Nguyen, Duc Khuong, 2017. "Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1121-1131.
    10. Tiago P. Filomena & Miguel A. Lejeune, 2014. "Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 308-329, April.
    11. 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.
    12. Atskanov, Isuf, 2015. "Dynamic optimization of an investment portfolio on European stock markets using pair copulas," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 40(4), pages 84-105.
    13. Mazin A.M. Al Janabi, 2021. "Is optimum always optimal? A revisit of the mean‐variance method under nonlinear measures of dependence and non‐normal liquidity constraints," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(3), pages 387-415, April.
    14. Bermin, Hans-Peter & Holm, Magnus, 2021. "Leverage and risk relativity: how to beat an index," Knut Wicksell Working Paper Series 2021/1, Lund University, Knut Wicksell Centre for Financial Studies.
    15. Tahereh Khodamoradi & Maziar Salahi & Ali Reza Najafi, 2021. "Cardinality-constrained portfolio optimization with short selling and risk-neutral interest rate," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 197-214, June.
    16. Li, Hua & Bai, Zhidong & Wong, Wing-Keung & McAleer, Michael, 2022. "Spectrally-Corrected Estimation for High-Dimensional Markowitz Mean-Variance Optimization," Econometrics and Statistics, Elsevier, vol. 24(C), pages 133-150.
    17. Marie Briere & Ariane Szafarz, 2017. "Factor Investing: The Rocky Road from Long-Only to Long-Short," Working Papers CEB 17-013, ULB -- Universite Libre de Bruxelles.
    18. Barbara Alemanni & Mario Maggi & Pierpaolo Uberti, 2021. "Unleveraged Portfolios and Pure Allocation Return," JRFM, MDPI, vol. 14(11), pages 1-11, November.
    19. Jarrod Wilcox & Frank Fabozzi, 2009. "A Discretionary Wealth Approach to Investment Policy," Yale School of Management Working Papers amz2434, Yale School of Management.
    20. Avkiran, Necmi K. & Morita, Hiroshi, 2010. "Predicting Japanese bank stock performance with a composite relative efficiency metric: A new investment tool," Pacific-Basin Finance Journal, Elsevier, vol. 18(3), pages 254-271, June.
    21. Miguel A. Lejeune & Gülay Samatlı-Paç, 2013. "Construction of Risk-Averse Enhanced Index Funds," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 701-719, November.
    22. Vrinda Dhingra & Shiv Kumar Gupta & Amita Sharma, 2023. "Norm constrained minimum variance portfolios with short selling," Computational Management Science, Springer, vol. 20(1), pages 1-35, December.
    23. Manfred Gilli & Enrico Schumann & Giacomo di Tollo & Gerda Cabej, 2011. "Constructing 130/30-portfolios with the Omega ratio," Journal of Asset Management, Palgrave Macmillan, vol. 12(2), pages 94-108, June.
    24. J J Glen, 2011. "Mean-variance portfolio rebalancing with transaction costs and funding changes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 667-676, April.
    25. 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.

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