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Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?

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  • Jules Binsbergen
  • Michael Brandt

Abstract

Most dynamic programming methods deployed in the portfolio choice literature involve recursions on an approximated value function. The simulation-based method proposed recently by Brandt, Goyal, Santa-Clara, and Stroud (Review of Financial Studies, 18, 831–873, 2005), relies instead on recursive uses of approximated optimal portfolio weights. We examine the relative numerical performance of these two approaches. We show that when portfolio weights are constrained by short sale restrictions for example, iterating on optimized portfolio weights leads to superior results. Value function iterations result in a lower variance but disproportionately higher bias of the solution, especially when risk aversion is high and the investment horizon is long. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Jules Binsbergen & Michael Brandt, 2007. "Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 355-367, May.
    • Handle: RePEc:kap:compec:v:29:y:2007:i:3:p:355-367
    DOI: 10.1007/s10614-006-9073-z
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    References listed on IDEAS

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    1. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
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    1. Mark Broadie & Weiwei Shen, 2016. "High-Dimensional Portfolio Optimization With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-49, June.
    2. Legendre, François & Togola, Djibril, 2016. "Explicit solutions to dynamic portfolio choice problems: A continuous-time detour," Economic Modelling, Elsevier, vol. 58(C), pages 627-641.
    3. Yichen Zhu & Marcos Escobar-Anel & Matt Davison, 2023. "A Polynomial-Affine Approximation for Dynamic Portfolio Choice," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 1177-1213, October.
    4. Rongju Zhang & Nicolas Langren'e & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2017. "Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method," Papers 1704.00416, arXiv.org, revised Jun 2019.
    5. Björn Bick & Holger Kraft & Claus Munk, 2013. "Solving Constrained Consumption-Investment Problems by Simulation of Artificial Market Strategies," Management Science, INFORMS, vol. 59(2), pages 485-503, June.
    6. T. R. B. den Haan & K. W. Chau & M. van der Schans & C. W. Oosterlee, 2020. "Rule-based Strategies for Dynamic Life Cycle Investment," Papers 2011.02596, arXiv.org.
    7. Rongju Zhang & Nicolas Langrené & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2019. "Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach," Post-Print hal-02909207, HAL.
    8. Xavier Warin, 2016. "The Asset Liability Management problem of a nuclear operator : a numerical stochastic optimization approach," Papers 1611.04877, arXiv.org.
    9. Rongju Zhang & Nicolas Langren'e & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2018. "Local Control Regression: Improving the Least Squares Monte Carlo Method for Portfolio Optimization," Papers 1803.11467, arXiv.org, revised Sep 2018.
    10. Farid Mkaouar & Jean-Luc Prigent & Ilyes Abid, 2019. "A Diffusion Model for Long-Term Optimization in the Presence of Stochastic Interest and Inflation Rates," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 367-417, June.
    11. Changhui Choi & Bong-Gyu Jang & Changki Kim & Sang-youn Roh, 2016. "Net Contribution, Liquidity, and Optimal Pension Management," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 913-948, December.
    12. Rongju Zhang & Nicolas Langren'e & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2016. "Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach," Papers 1610.07694, arXiv.org, revised Jun 2019.
    13. Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2015. "A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function," Annals of Operations Research, Springer, vol. 229(1), pages 121-158, June.
    14. Arkadiy V. Sakhartov, 2017. "Economies of Scope, Resource Relatedness, and the Dynamics of Corporate Diversification," Strategic Management Journal, Wiley Blackwell, vol. 38(11), pages 2168-2188, November.
    15. Rongju Zhang & Nicolas Langrené & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2019. "Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method," Post-Print hal-02909342, HAL.
    16. Stanislav Anatolyev & Vladimir Pyrlik, 2021. "Shrinkage for Gaussian and t Copulas in Ultra-High Dimensions," CERGE-EI Working Papers wp699, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    17. Mark Broadie & Weiwei Shen, 2017. "Numerical solutions to dynamic portfolio problems with upper bounds," Computational Management Science, Springer, vol. 14(2), pages 215-227, April.
    18. Bart Diris & Franz Palm & Peter Schotman, 2015. "Long-Term Strategic Asset Allocation: An Out-of-Sample Evaluation," Management Science, INFORMS, vol. 61(9), pages 2185-2202, September.
    19. Fei Cong & Cornelis W. Oosterlee, 2017. "Accurate and Robust Numerical Methods for the Dynamic Portfolio Management Problem," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 433-458, March.

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