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Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs

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  • Tiago P. Filomena

    (Federal University of Rio Grande do Sul)

  • Miguel A. Lejeune

    (The George Washington University)

Abstract

We consider a probabilistic portfolio optimization model including fixed and proportional transaction costs. We derive a deterministic equivalent of the probabilistic model for fat-tailed portfolio returns. We develop a method which finds provably near-optimal solutions in minimal amount of time for industry-sized (up to 2000 assets) problems. To solve the mixed-integer nonlinear programming (MINLP) deterministic formulation equivalent to the stochastic problem, we design a mathematical programming-based warm-start heuristic. The tests show the computational efficiency of the heuristic which is more than an order of magnitude faster than Cplex in finding high-quality solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:1:d:10.1007_s10957-013-0348-y
    DOI: 10.1007/s10957-013-0348-y
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    1. Rustem, Berc, 1994. "Stochastic and robust control of nonlinear economic systems," European Journal of Operational Research, Elsevier, vol. 73(2), pages 304-318, March.
    2. Michael J. Best & Jaroslava Hlouskova, 2005. "An Algorithm for Portfolio Optimization with Transaction Costs," Management Science, INFORMS, vol. 51(11), pages 1676-1688, November.
    3. Mao, James C T, 1970. "Essentials of Portfolio Diversification Strategy," Journal of Finance, American Finance Association, vol. 25(5), pages 1109-1121, December.
    4. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2010. "No-arbitrage conditions, scenario trees, and multi-asset financial optimization," European Journal of Operational Research, Elsevier, vol. 206(3), pages 609-613, November.
    5. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    6. Miguel Lobo & Maryam Fazel & Stephen Boyd, 2007. "Portfolio optimization with linear and fixed transaction costs," Annals of Operations Research, Springer, vol. 152(1), pages 341-365, July.
    7. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    8. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    9. Osorio, Maria A. & Gulpinar, Nalan & Rustem, Berc, 2008. "A mixed integer programming model for multistage mean-variance post-tax optimization," European Journal of Operational Research, Elsevier, vol. 185(2), pages 451-480, March.
    10. Kumar Muthuraman & Sunil Kumar, 2006. "Multidimensional Portfolio Optimization With Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 301-335, April.
    11. Owen, Joel & Rabinovitch, Ramon, 1983. "On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
    12. M. J. Best & J. Hlouskova, 2007. "An Algorithm for Portfolio Optimization with Variable Transaction Costs, Part 1: Theory," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 563-581, December.
    13. M. J. Best & J. Hlouskova, 2007. "An Algorithm for Portfolio Optimization with Variable Transaction Costs, Part 2: Computational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 531-547, December.
    14. Campbell Harvey & John Liechty & Merrill Liechty & Peter Muller, 2010. "Portfolio selection with higher moments," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 469-485.
    15. Leonard MacLean & William Ziemba, 1999. "Growth versus security tradeoffs indynamic investment analysis," Annals of Operations Research, Springer, vol. 85(0), pages 193-225, January.
    16. M. C. Chiu & D. Li, 2009. "Asset-Liability Management Under the Safety-First Principle," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 455-478, December.
    17. Frank Fabozzi & Dashan Huang & Guofu Zhou, 2010. "Robust portfolios: contributions from operations research and finance," Annals of Operations Research, Springer, vol. 176(1), pages 191-220, April.
    18. Pierre Bonami & Miguel A. Lejeune, 2009. "An Exact Solution Approach for Integer Constrained Portfolio Optimization Problems Under Stochastic Constraints," Post-Print hal-00421756, HAL.
    19. 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.
    20. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 1: Principles of Inference," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 207-219, November.
    21. Thapa, Chandra & Poshakwale, Sunil S., 2010. "International equity portfolio allocations and transaction costs," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2627-2638, November.
    22. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    23. Miguel Lejeune, 2011. "A VaR Black–Litterman model for the construction of absolute return fund-of-funds," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1489-1501.
    24. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, October.
    25. Dumas, Bernard & Luciano, Elisa, 1991. "An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-595, June.
    26. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 2: Empirical Results," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 221-247, November.
    27. Wenbo Hu & Alec Kercheval, 2010. "Portfolio optimization for student t and skewed t returns," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 91-105.
    28. Hans Kellerer & Renata Mansini & M. Speranza, 2000. "Selecting Portfolios with Fixed Costs and Minimum Transaction Lots," Annals of Operations Research, Springer, vol. 99(1), pages 287-304, December.
    29. N. J. Jobst & M. D. Horniman & C. A. Lucas & G. Mitra, 2001. "Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 489-501.
    30. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.
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    Cited by:

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    3. Leonardo Riegel Sant’Anna & Tiago Pascoal Filomena & Pablo Cristini Guedes & Denis Borenstein, 2017. "Index tracking with controlled number of assets using a hybrid heuristic combining genetic algorithm and non-linear programming," Annals of Operations Research, Springer, vol. 258(2), pages 849-867, November.
    4. Ran Ji & Miguel A. Lejeune, 2018. "Risk-budgeting multi-portfolio optimization with portfolio and marginal risk constraints," Annals of Operations Research, Springer, vol. 262(2), pages 547-578, March.
    5. Moarefdoost, M. Mohsen & Lamadrid, Alberto J. & Zuluaga, Luis F., 2016. "A robust model for the ramp-constrained economic dispatch problem with uncertain renewable energy," Energy Economics, Elsevier, vol. 56(C), pages 310-325.
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    7. Alberto J. Lamadrid & Hao Lu & Timothy D. Mount, 2024. "A simple way to integrate distributed storage into a wholesale electricity market," Journal of Regulatory Economics, Springer, vol. 65(1), pages 27-63, June.

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