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Illiquid Assets and Optimal Portfolio Choice

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  • Eduardo S. Schwartz
  • Claudio Tebaldi

Abstract

The presence of illiquid assets, such as human wealth or a family owned business, complicates the problem of portfolio choice. This paper is concerned with the problem of optimal asset allocation and consumption in a continuous time model when one asset cannot be traded. This illiquid asset, which depends on an uninsurable source of risk, provides a liquid dividend. In the case of human capital we can think about this dividend as labor income. The agent is endowed with a given amount of the illiquid asset and with some liquid wealth which can be allocated in a market where there is a risky and a riskless asset. The main point of the paper is that the optimal allocations to the two liquid assets and consumption will critically depend on the endowment and characteristics of the illiquid asset, in addition to the preferences and to the liquid holdings held by the agent. We provide what we believe to be the first analytical solution to this problem when the agent has power utility of consumption and terminal wealth. We also derive the value that the agent assigns to the illiquid asset. The risk adjusted valuation procedure we develop can be used to value both liquid and illiquid assets, as well as contingent claims on those assets.

Suggested Citation

  • Eduardo S. Schwartz & Claudio Tebaldi, 2006. "Illiquid Assets and Optimal Portfolio Choice," NBER Working Papers 12633, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:12633
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    Cited by:

    1. Salvatore Federico & Paul Gassiat & Fausto Gozzi, 2017. "Impact Of Time Illiquidity In A Mixed Market Without Full Observation," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 401-437, April.
    2. 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.
    3. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
    4. Ljudmila A. Bordag & Ivan P. Yamshchikov, 2015. "Optimization problem for a portfolio with an illiquid asset: Lie group analysis," Papers 1512.06295, arXiv.org.
    5. Xing, Ran, 2016. "The liquidity management of institutional investors and the pricing of liquidity risk," Other publications TiSEM 1df96fc1-de24-4e94-a747-3, Tilburg University, School of Economics and Management.
    6. L. A. Bordag & I. P. Yamshchikov & D. Zhelezov, 2015. "Portfolio optimization in the case of an asset with a given liquidation time distribution," Post-Print hal-01186961, HAL.
    7. Martin Hoesli & Eva Liljeblom & Anders Loflund, 2014. "The Effect of Lock-Ups on the Suggested Real Estate Portfolio Weight," International Real Estate Review, Global Social Science Institute, vol. 17(1), pages 1-22.
    8. Michael Ludkovski & Hyekyung Min, 2010. "Illiquidity Effects in Optimal Consumption-Investment Problems," Papers 1004.1489, arXiv.org, revised Sep 2010.
    9. Michael Ludkovski & Qunying Shen, 2012. "European Option Pricing with Liquidity Shocks," Papers 1205.1007, arXiv.org.
    10. Ljudmila A. Bordag & Ivan P. Yamshchikov & Dmitry Zhelezov, 2014. "Portfolio optimization in the case of an asset with a given liquidation time distribution," Papers 1407.3154, arXiv.org.
    11. Sergio Mayordomo & Maria Rodriguez-Moreno & Juan Ignacio Pe�a, 2014. "Portfolio choice with indivisible and illiquid housing assets: the case of Spain," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 2045-2064, November.
    12. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 32, July-Dece.
    13. Yuji Yamada, 2012. "Properties of Optimal Smooth Functions in Additive Models for Hedging Multivariate Derivatives," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 19(2), pages 149-179, May.
    14. Salvatore Federico & Paul Gassiat, 2014. "Viscosity Characterization of the Value Function of an Investment-Consumption Problem in Presence of an Illiquid Asset," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 966-991, March.
    15. Salvatore Federico & Paul Gassiat & Fausto Gozzi, 2015. "Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation," Finance and Stochastics, Springer, vol. 19(2), pages 415-448, April.
    16. Michael Ludkovski & Qunying Shen, 2013. "European Option Pricing With Liquidity Shocks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-30.
    17. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    18. Ebele Sabina Nsofor, 2016. "Market Liquidity as a Determinant of Stock Market Development in Nigeria," International Journal of Empirical Finance, Research Academy of Social Sciences, vol. 5(1), pages 11-21.
    19. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2016.

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    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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