IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1610.00395.html
   My bibliography  Save this paper

Optimal Portfolios of Illiquid Assets

Author

Listed:
  • T. R. Hurd
  • Quentin H. Shao
  • Tuan Tran

Abstract

This paper investigates the investment behaviour of a large unregulated financial institution (FI) with CARA risk preferences. It shows how the FI optimizes its trading to account for market illiquidity using an extension of the Almgren-Chriss market impact model of multiple risky assets. This expected utility optimization problem over the set of adapted strategies turns out to have the same solutions as a mean-variance optimization over deterministic trading strategies. That means the optimal adapted trading strategy is both deterministic and time-consistent. It is also found to have an explicit closed form that clearly displays interesting properties. For example, the classic constant Merton portfolio strategy, a particular solution of the frictionless limit of the problem, behaves like an attractor in the space of more general solutions. The main effect of temporary market impact is to slow down the speed of convergence to this constant Merton portfolio. The effect of permanent market impact is to incentivize the FI to buy additional risky assets near the end of the period. This property, that we name the Ponzi property, is related to the creation and bursting of bubbles in the market. The proposed model can be used as a stylized dynamic model of a typical FI in the study of the asset fire sale channel relevant to understanding systemic risk and financial stability.

Suggested Citation

  • T. R. Hurd & Quentin H. Shao & Tuan Tran, 2016. "Optimal Portfolios of Illiquid Assets," Papers 1610.00395, arXiv.org.
  • Handle: RePEc:arx:papers:1610.00395
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1610.00395
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Huyên Pham & Peter Tankov, 2008. "A Model Of Optimal Consumption Under Liquidity Risk With Random Trading Times," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 613-627, October.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
    4. Rodrigo Cifuentes & Hyun Song Shin & Gianluigi Ferrucci, 2005. "Liquidity Risk and Contagion," Journal of the European Economic Association, MIT Press, vol. 3(2-3), pages 556-566, 04/05.
    5. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    6. Alexander Schied & Torsten Schoneborn & Michael Tehranchi, 2010. "Optimal Basket Liquidation for CARA Investors is Deterministic," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 471-489.
    7. David B. Brown & Bruce Ian Carlin & Miguel Sousa Lobo, 2010. "Optimal Portfolio Liquidation with Distress Risk," Management Science, INFORMS, vol. 56(11), pages 1997-2014, November.
    8. 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.
    9. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    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. Phillip Monin, 2014. "Hedging Market Risk in Optimal Liquidation," Working Papers 14-08, Office of Financial Research, US Department of the Treasury.
    2. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    3. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    4. Forsyth, P.A. & Kennedy, J.S. & Tse, S.T. & Windcliff, H., 2012. "Optimal trade execution: A mean quadratic variation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1971-1991.
    5. Kashyap, Ravi, 2020. "David vs Goliath (You against the Markets), A dynamic programming approach to separate the impact and timing of trading costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    6. Olivier Gu'eant & Jean-Michel Lasry & Jiang Pu, 2014. "A convex duality method for optimal liquidation with participation constraints," Papers 1407.4614, arXiv.org, revised Dec 2014.
    7. Olivier Gu'eant, 2012. "Optimal execution and block trade pricing: a general framework," Papers 1210.6372, arXiv.org, revised Dec 2014.
    8. Roman Gayduk & Sergey Nadtochiy, 2015. "Liquidity Effects of Trading Frequency," Papers 1508.07914, arXiv.org, revised May 2017.
    9. Lokka, A. & Xu, Junwei, 2020. "Optimal liquidation trajectories for the Almgren-Chriss model," LSE Research Online Documents on Economics 106977, London School of Economics and Political Science, LSE Library.
    10. Roman Gayduk & Sergey Nadtochiy, 2016. "Endogenous Formation of Limit Order Books: Dynamics Between Trades," Papers 1605.09720, arXiv.org, revised Jun 2017.
    11. Daniel Hern'andez-Hern'andez & Harold A. Moreno-Franco & Jos'e Luis P'erez, 2017. "Periodic strategies in optimal execution with multiplicative price impact," Papers 1705.00284, arXiv.org, revised May 2018.
    12. 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.
    13. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    14. Jin Hyuk Choi & Tae Ung Gang, 2021. "Optimal investment in illiquid market with search frictions and transaction costs," Papers 2101.09936, arXiv.org, revised Aug 2021.
    15. Olivier Gu'eant, 2013. "Permanent market impact can be nonlinear," Papers 1305.0413, arXiv.org, revised Mar 2014.
    16. Mourad Lazgham, 2018. "Regularity properties in a state-constrained expected utility maximization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 185-240, October.
    17. Edirisinghe, Chanaka & Jeong, Jaehwan & Chen, Jingnan, 2021. "Optimal portfolio deleveraging under market impact and margin restrictions," European Journal of Operational Research, Elsevier, vol. 294(2), pages 746-759.
    18. Arne Lokka & Junwei Xu, 2020. "Optimal liquidation for a risk averse investor in a one-sided limit order book driven by a Levy process," Papers 2002.03379, arXiv.org, revised Oct 2020.
    19. Masashi Ieda, 2015. "A dynamic optimal execution strategy under stochastic price recovery," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-24, December.
    20. Mauricio Junca, 2011. "Stochastic impulse control on optimal execution with price impact and transaction cost," Papers 1103.3482, arXiv.org, revised Jan 2013.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1610.00395. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.