IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v250y2016i3p827-841.html
   My bibliography  Save this article

Better than pre-commitment mean-variance portfolio allocation strategies: A semi-self-financing Hamilton–Jacobi–Bellman equation approach

Author

Listed:
  • Dang, D.M.
  • Forsyth, P.A.

Abstract

We generalize the idea of semi-self-financing strategies, originally discussed in Ehrbar (1990), and later formalized in Cui et al (2012), for the pre-commitment mean-variance (MV) optimal portfolio allocation problem. The proposed semi-self-financing strategies are built upon a numerical solution framework for Hamilton–Jacobi–Bellman equations, and can be readily employed in a very general setting, namely continuous or discrete re-balancing, jump-diffusions with finite activity, and realistic portfolio constraints. We show that if the portfolio wealth exceeds a threshold, an MV optimal strategy is to withdraw cash. These semi-self-financing strategies are generally non-unique. Numerical results confirming the superiority of the efficient frontiers produced by the strategies with positive cash withdrawals are presented. Tests based on estimation of parameters from historical time series show that the semi-self-financing strategy is robust to estimation ambiguities.

Suggested Citation

  • Dang, D.M. & Forsyth, P.A., 2016. "Better than pre-commitment mean-variance portfolio allocation strategies: A semi-self-financing Hamilton–Jacobi–Bellman equation approach," European Journal of Operational Research, Elsevier, vol. 250(3), pages 827-841.
    • Handle: RePEc:eee:ejores:v:250:y:2016:i:3:p:827-841
    DOI: 10.1016/j.ejor.2015.10.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715009224
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.10.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Elena Vigna, 2014. "On efficiency of mean--variance based portfolio selection in defined contribution pension schemes," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 237-258, February.
    2. Ehrbar, Hans, 1990. "Mean-variance efficiency when investors are not required to invest all their money," Journal of Economic Theory, Elsevier, vol. 50(1), pages 214-218, February.
    3. Yacine Aït-Sahalia & Jean Jacod, 2012. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," Journal of Economic Literature, American Economic Association, vol. 50(4), pages 1007-1050, December.
    4. Leippold, Markus & Trojani, Fabio & Vanini, Paolo, 2004. "A geometric approach to multiperiod mean variance optimization of assets and liabilities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1079-1113, March.
    5. Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
    6. 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.
    7. Nicole Bäuerle & Stefanie Grether, 2015. "Complete markets do not allow free cash flow streams," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 137-146, April.
    8. Wang, J. & Forsyth, P.A., 2010. "Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 207-230, February.
    9. Łukasz Delong & Russell Gerrard, 2007. "Mean-variance portfolio selection for a non-life insurance company," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 339-367, October.
    10. Cecilia Mancini, 2009. "Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296, June.
    11. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    12. Nicole Bäuerle, 2005. "Benchmark and mean-variance problems for insurers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(1), pages 159-165, September.
    13. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2008. "Mean-variance portfolio and contribution selection in stochastic pension funding," European Journal of Operational Research, Elsevier, vol. 187(1), pages 120-137, May.
    14. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    15. Delong, Lukasz & Gerrard, Russell & Haberman, Steven, 2008. "Mean-variance optimization problems for an accumulation phase in a defined benefit plan," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 107-118, February.
    16. Tomasz R. Bielecki & Hanqing Jin & Stanley R. Pliska & Xun Yu Zhou, 2005. "Continuous‐Time Mean‐Variance Portfolio Selection With Bankruptcy Prohibition," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 213-244, April.
    17. J. Wang & P. A. Forsyth, 2012. "Comparison Of Mean Variance Like Strategies For Optimal Asset Allocation Problems," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-32.
    18. Tauchen, George & Zhou, Hao, 2011. "Realized jumps on financial markets and predicting credit spreads," Journal of Econometrics, Elsevier, vol. 160(1), pages 102-118, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cong, F. & Oosterlee, C.W., 2016. "On pre-commitment aspects of a time-consistent strategy for a mean-variance investor," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 178-193.
    2. Van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2018. "Time-consistent mean–variance portfolio optimization: A numerical impulse control approach," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 9-28.
    3. F. Cong & C. W. Oosterlee, 2017. "On Robust Multi-Period Pre-Commitment And Time-Consistent Mean-Variance Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-26, November.
    4. Cong, F. & Oosterlee, C.W., 2016. "Multi-period mean–variance portfolio optimization based on Monte-Carlo simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 23-38.
    5. De Gennaro Aquino, Luca & Sornette, Didier & Strub, Moris S., 2023. "Portfolio selection with exploration of new investment assets," European Journal of Operational Research, Elsevier, vol. 310(2), pages 773-792.
    6. Chi Kin Lam & Yuhong Xu & Guosheng Yin, 2016. "Dynamic portfolio selection without risk-free assets," Papers 1602.04975, arXiv.org.
    7. Chendi Ni & Yuying Li & Peter A. Forsyth, 2023. "Neural Network Approach to Portfolio Optimization with Leverage Constraints:a Case Study on High Inflation Investment," Papers 2304.05297, arXiv.org, revised May 2023.
    8. Duy-Minh Dang & P. A. Forsyth & K. R. Vetzal, 2017. "The 4% strategy revisited: a pre-commitment mean-variance optimal approach to wealth management," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 335-351, March.
    9. Peter A. Forsyth & Kenneth R. Vetzal, 2017. "Dynamic mean variance asset allocation: Tests for robustness," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-37, June.
    10. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    11. Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
    12. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.
    13. P. A. Forsyth & K. R. Vetzal, 2017. "Robust Asset Allocation For Long-Term Target-Based Investing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-32, May.
    14. Aivaliotis, Georgios & Palczewski, Jan, 2014. "Investment strategies and compensation of a mean–variance optimizing fund manager," European Journal of Operational Research, Elsevier, vol. 234(2), pages 561-570.
    15. Ben-Zhang Yang & Xin-Jiang He & Song-Ping Zhu, 2020. "Continuous time mean-variance-utility portfolio problem and its equilibrium strategy," Papers 2005.06782, arXiv.org, revised Nov 2020.
    16. Li, Yongwu & Qiao, Han & Wang, Shouyang & Zhang, Ling, 2015. "Time-consistent investment strategy under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 187-197.
    17. Ben-Zhang Yang & Xin-Jiang He & Song-Ping Zhu, 2020. "Mean-variance-utility portfolio selection with time and state dependent risk aversion," Papers 2007.06510, arXiv.org, revised Aug 2020.
    18. Peter A. Forsyth & Kenneth R. Vetzal, 2019. "Defined Contribution Pension Plans: Who Has Seen the Risk?," JRFM, MDPI, vol. 12(2), pages 1-27, April.
    19. Xiangyu Cui & Duan Li & Xun Li, 2014. "Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure," Papers 1403.0718, arXiv.org.
    20. Zeng, Yan & Li, Zhongfei & Lai, Yongzeng, 2013. "Time-consistent investment and reinsurance strategies for mean–variance insurers with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 498-507.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:250:y:2016:i:3:p:827-841. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.