IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v233y2015i1p135-15610.1007-s10479-014-1574-x.html
   My bibliography  Save this article

Portfolio optimization with transaction costs: a two-period mean-variance model

Author

Listed:
  • Ying Fu
  • Kien Ng
  • Boray Huang
  • Huei Huang

Abstract

In this paper, we study a multiperiod mean-variance portfolio optimization problem in the presence of proportional transaction costs. Many existing studies have shown that transaction costs can significantly affect investors’ behavior. However, even under simple assumptions, closed-form solutions are not easy to obtain when transaction costs are considered. As a result, they are often ignored in multiperiod portfolio analysis, which leads to suboptimal solutions. To provide better insight for this complex problem, this paper studies a two-period problem that considers one risk-free and one risky asset. Whenever there is a trade after the initial asset allocation, the investor incurs a linear transaction cost. Through a mean-variance model, we derive the closed-form expressions of the optimal thresholds for investors to re-allocate their resources. These thresholds divide the action space into three regions. Some important properties of the analytical solution are identified, which shed light on solving multiperiod problems. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Ying Fu & Kien Ng & Boray Huang & Huei Huang, 2015. "Portfolio optimization with transaction costs: a two-period mean-variance model," Annals of Operations Research, Springer, vol. 233(1), pages 135-156, October.
    • Handle: RePEc:spr:annopr:v:233:y:2015:i:1:p:135-156:10.1007/s10479-014-1574-x
    DOI: 10.1007/s10479-014-1574-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-014-1574-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-014-1574-x?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. Wagner, Wolf, 2010. "Diversification at financial institutions and systemic crises," Journal of Financial Intermediation, Elsevier, vol. 19(3), pages 373-386, July.
    2. Kuan, Chung-Ming & Yeh, Jin-Huei & Hsu, Yu-Chin, 2009. "Assessing value at risk with CARE, the Conditional Autoregressive Expectile models," Journal of Econometrics, Elsevier, vol. 150(2), pages 261-270, June.
    3. Zhang, Wei-Guo & Zhang, Xi-Li & Xu, Wei-Jun, 2010. "A risk tolerance model for portfolio adjusting problem with transaction costs based on possibilistic moments," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 493-499, June.
    4. Michael J. Best & Jaroslava Hlouskova, 2005. "An Algorithm for Portfolio Optimization with Transaction Costs," Management Science, INFORMS, vol. 51(11), pages 1676-1688, 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. 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.
    7. 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.
    8. Gulpinar, Nalan & Rustem, Berc, 2007. "Worst-case robust decisions for multi-period mean-variance portfolio optimization," European Journal of Operational Research, Elsevier, vol. 183(3), pages 981-1000, December.
    9. Junna Bi & Qingbin Meng & Yongji Zhang, 2014. "Dynamic mean-variance and optimal reinsurance problems under the no-bankruptcy constraint for an insurer," Annals of Operations Research, Springer, vol. 212(1), pages 43-59, January.
    10. 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.
    11. George M. Constantinides, 1979. "Multiperiod Consumption and Investment Behavior with Convex Transactions Costs," Management Science, INFORMS, vol. 25(11), pages 1127-1137, November.
    12. 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.
    13. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    14. Andre F. Perold, 1984. "Large-Scale Portfolio Optimization," Management Science, INFORMS, vol. 30(10), pages 1143-1160, October.
    15. Hong Liu, 2004. "Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets," Journal of Finance, American Finance Association, vol. 59(1), pages 289-338, February.
    16. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    17. Maria Osorio & Nalan Gülpınar & Berç Rustem, 2008. "A general framework for multistage mean-variance post-tax optimization," Annals of Operations Research, Springer, vol. 157(1), pages 3-23, January.
    18. Pelsser, Antoon & Vorst, Ton, 1996. "Transaction costs and efficiency of portfolio strategies," European Journal of Operational Research, Elsevier, vol. 91(2), pages 250-263, June.
    19. Hakansson, Nils H, 1971. "Multi-Period Mean-Variance Analysis: Toward A General Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 26(4), pages 857-884, September.
    20. Chen, Andrew H Y & Jen, Frank C & Zionts, Stanley, 1971. "The Optimal Portfolio Revision Policy," The Journal of Business, University of Chicago Press, vol. 44(1), pages 51-61, January.
    21. Kozhan, Roman & Schmid, Wolfgang, 2009. "Asset allocation with distorted beliefs and transaction costs," European Journal of Operational Research, Elsevier, vol. 194(1), pages 236-249, April.
    22. Gerard Gennotte & Alan Jung, 1994. "Investment Strategies under Transaction Costs: The Finite Horizon Case," Management Science, INFORMS, vol. 40(3), pages 385-404, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Cheng & Gong, Xiaomin & Zhang, Jingshu & Chen, Zhiwei, 2023. "Dynamic portfolio allocation for financial markets: A perspective of competitive-cum-compensatory strategy," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 84(C).
    2. Carroll, Rachael & Conlon, Thomas & Cotter, John & Salvador, Enrique, 2017. "Asset allocation with correlation: A composite trade-off," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1164-1180.
    3. Marco Bonomelli & Rosella Giacometti & Sergio Ortobelli Lozza, 2020. "Joint tails impact in stochastic volatility portfolio selection models," Annals of Operations Research, Springer, vol. 292(2), pages 833-848, September.
    4. Moawia Alghalith & Xu Guo & Cuizhen Niu & Wing-Keung Wong, 2017. "Input Demand Under Joint Energy and Output Prices Uncertainties," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-12, August.

    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. 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.
    2. Zhang, Xili & Zhang, Weiguo & Xiao, Weilin, 2013. "Multi-period portfolio optimization under possibility measures," Economic Modelling, Elsevier, vol. 35(C), pages 401-408.
    3. Areski Cousin & J'er^ome Lelong & Tom Picard, 2023. "Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approach," Papers 2305.16152, arXiv.org, revised Jun 2023.
    4. 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.
    5. Dai, Min & Wang, Hefei & Yang, Zhou, 2012. "Leverage management in a bull–bear switching market," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1585-1599.
    6. 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.
    7. Areski Cousin & Jérôme Lelong & Tom Picard, 2023. "Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approach," Working Papers hal-04086378, HAL.
    8. Buckley, Winston S. & Brown, Garfield O. & Marshall, Mario, 2012. "A mispricing model of stocks under asymmetric information," European Journal of Operational Research, Elsevier, vol. 221(3), pages 584-592.
    9. Vasyl Golosnoy, 2010. "No-transaction bounds and estimation risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 487-493.
    10. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    11. Dokuchaev, Nikolai, 2010. "Optimality of myopic strategies for multi-stock discrete time market with management costs," European Journal of Operational Research, Elsevier, vol. 200(2), pages 551-556, January.
    12. 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.
    13. Yongyang Cai & Kenneth L. Judd & Rong Xu, 2013. "Numerical Solution of Dynamic Portfolio Optimization with Transaction Costs," NBER Working Papers 18709, National Bureau of Economic Research, Inc.
    14. Krastyu Georgiev & Young Kim & Stoyan Stoyanov, 2015. "Periodic portfolio revision with transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 337-359, June.
    15. Michal Czerwonko & Stylianos Perrakis, 2016. "Portfolio Selection with Transaction Costs and Jump-Diffusion Asset Dynamics I: A Numerical Solution," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 1-23, December.
    16. Miguel, Víctor de & Mei, Xiaoling & Nogales, Francisco J., 2013. "Multiperiod portfolio selection with transaction and market-impact costs," DES - Working Papers. Statistics and Econometrics. WS ws131615, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. Loewenstein, Mark, 2000. "On optimal portfolio trading strategies for an investor facing transactions costs in a continuous trading market," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 209-228, March.
    18. Fu, Chenpeng & Lari-Lavassani, Ali & Li, Xun, 2010. "Dynamic mean-variance portfolio selection with borrowing constraint," European Journal of Operational Research, Elsevier, vol. 200(1), pages 312-319, January.
    19. Davi Valladão & Thuener Silva & Marcus Poggi, 2019. "Time-consistent risk-constrained dynamic portfolio optimization with transactional costs and time-dependent returns," Annals of Operations Research, Springer, vol. 282(1), pages 379-405, November.
    20. Mei, Xiaoling & Nogales Martín, Francisco Javier, 2015. "Portfolio selection with proportional transaction costs and predictability," DES - Working Papers. Statistics and Econometrics. WS ws1521, Universidad Carlos III de Madrid. Departamento de Estadística.

    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:spr:annopr:v:233:y:2015:i:1:p:135-156:10.1007/s10479-014-1574-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.