IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v18y2014i1p1-37.html
   My bibliography  Save this article

Transaction costs, trading volume, and the liquidity premium

Author

Listed:
  • Stefan Gerhold
  • Paolo Guasoni
  • Johannes Muhle-Karbe
  • Walter Schachermayer

Abstract

In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volume. At the first order, the liquidity premium equals the spread, times share turnover, times a universal constant. The results are robust to consumption and finite horizons. We exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also found explicitly. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2014. "Transaction costs, trading volume, and the liquidity premium," Finance and Stochastics, Springer, vol. 18(1), pages 1-37, January.
    • Handle: RePEc:spr:finsto:v:18:y:2014:i:1:p:1-37
    DOI: 10.1007/s00780-013-0210-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00780-013-0210-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00780-013-0210-y?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. Dybvig, Philip H & Rogers, L C G & Back, Kerry, 1999. "Portfolio Turnpikes," The Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 165-195.
    2. Marianne Akian & Agnès Sulem & Michael I. Taksar, 2001. "Dynamic Optimization of Long‐Term Growth Rate for a Portfolio with Transaction Costs and Logarithmic Utility," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 153-188, April.
    3. 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.
    4. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 7, pages 207-227, World Scientific Publishing Co. Pte. Ltd..
    5. Dumas, Bernard, 1991. "Super contact and related optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 675-685, October.
    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. Luttmer, Erzo G J, 1996. "Asset Pricing in Economies with Frictions," Econometrica, Econometric Society, vol. 64(6), pages 1439-1467, November.
    8. Lo, Andrew W & Wang, Jiang, 2000. "Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 257-300.
    9. S. Gerhold & J. Muhle-Karbe & W. Schachermayer, 2013. "The dual optimizer for the growth-optimal portfolio under transaction costs," Finance and Stochastics, Springer, vol. 17(2), pages 325-354, April.
    10. 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.
    11. Anthony W. Lynch & Sinan Tan, 2011. "Explaining the Magnitude of Liquidity Premia: The Roles of Return Predictability, Wealth Shocks, and State‐Dependent Transaction Costs," Journal of Finance, American Finance Association, vol. 66(4), pages 1329-1368, August.
    12. Jin Hyuk Choi & Mihai Sirbu & Gordan Zitkovic, 2012. "Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs," Papers 1204.0305, arXiv.org, revised Jun 2012.
    13. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    14. Michael Taksar & Michael J. Klass & David Assaf, 1988. "A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 277-294, May.
    15. J. Kallsen & J. Muhle-Karbe, 2010. "On using shadow prices in portfolio optimization with transaction costs," Papers 1010.4989, arXiv.org.
    16. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    17. Grossman, Sanford J. & Vila, Jean-Luc, 1992. "Optimal Dynamic Trading with Leverage Constraints," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(2), pages 151-168, June.
    18. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    19. Maxim Bichuch, 2011. "Asymptotic Analysis for Optimal Investment in Finite Time with Transaction Costs," Papers 1112.2749, arXiv.org.
    20. Paolo Guasoni & Scott Robertson, 2012. "Portfolios and risk premia for the long run," Papers 1203.1399, arXiv.org.
    21. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, May.
    22. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
    23. Hong Liu & Mark Loewenstein, 2002. "Optimal Portfolio Selection with Transaction Costs and Finite Horizons," The Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 805-835.
    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. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2011. "Transaction Costs, Trading Volume, and the Liquidity Premium," Papers 1108.1167, arXiv.org, revised Jan 2013.
    2. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    3. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302, arXiv.org, revised May 2017.
    4. Paolo Guasoni & Johannes Muhle-Karbe, 2012. "Portfolio Choice with Transaction Costs: a User's Guide," Papers 1207.7330, arXiv.org.
    5. Yingting Miao & Qiang Zhang, 2023. "Optimal Investment and Consumption Strategies with General and Linear Transaction Costs under CRRA Utility," Papers 2304.07672, arXiv.org.
    6. 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.
    7. 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.
    8. Xinfu Chen & Min Dai & Wei Jiang & Cong Qin, 2022. "Asymptotic analysis of long‐term investment with two illiquid and correlated assets," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1133-1169, October.
    9. Albert Altarovici & Max Reppen & H. Mete Soner, 2016. "Optimal Consumption and Investment with Fixed and Proportional Transaction Costs," Papers 1610.03958, arXiv.org.
    10. Ren Liu & Johannes Muhle-Karbe & Marko H. Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org, revised Sep 2017.
    11. Arjmandi, Nabi, 2023. "Optimal Portfolio Rebalancing with Sweep Under Transaction Cost," MPRA Paper 117162, University Library of Munich, Germany.
    12. Johannes Muhle-Karbe & Ren Liu, 2012. "Portfolio Selection with Small Transaction Costs and Binding Portfolio Constraints," Papers 1205.4588, arXiv.org, revised Jan 2013.
    13. Yaroslav Melnyk & Frank Thomas Seifried, 2018. "Small†cost asymptotics for long†term growth rates in incomplete markets," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 668-711, April.
    14. Florent Gallien & Serge Kassibrakis & Semyon Malamud, 2018. "Hedge or Rebalance: Optimal Risk Management with Transaction Costs," Risks, MDPI, vol. 6(4), pages 1-14, October.
    15. S. Gerhold & J. Muhle-Karbe & W. Schachermayer, 2013. "The dual optimizer for the growth-optimal portfolio under transaction costs," Finance and Stochastics, Springer, vol. 17(2), pages 325-354, April.
    16. Baojun Bian & Xinfu Chen & Min Dai & Shuaijie Qian, 2021. "Penalty method for portfolio selection with capital gains tax," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 1013-1055, July.
    17. Stefan Gerhold & Johannes Muhle-Karbe & Walter Schachermayer, 2010. "The dual optimizer for the growth-optimal portfolio under transaction costs," Papers 1005.5105, arXiv.org, revised Oct 2010.
    18. Vayanos, Dimitri & Wang, Jiang, 2013. "Market Liquidity—Theory and Empirical Evidence ," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1289-1361, Elsevier.
    19. Martin Herdegen & Johannes Muhle-Karbe, 2018. "Stability of Radner equilibria with respect to small frictions," Finance and Stochastics, Springer, vol. 22(2), pages 443-502, April.
    20. Isaenko, Sergei, 2010. "Portfolio choice under transitory price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2375-2389, November.

    More about this item

    Keywords

    Transaction costs; Long-run; Portfolio choice; Liquidity premium; Trading volume; 91G10; 91G80; G11; G12;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    Statistics

    Access and download statistics

    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:finsto:v:18:y:2014:i:1:p:1-37. 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.