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Illiquid Assets and Optimal Portfolio Choice

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  • Eduardo S. Schwartz
  • Claudio Tebaldi
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    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.

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    Bibliographic Info

    Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12633.

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    Date of creation: Oct 2006
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    Handle: RePEc:nbr:nberwo:12633

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    Cited by:
    1. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, Springer, vol. 15(2), pages 297-342, June.
    2. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi & Elena Vigna, 2012. "Income drawdown option with minimum guarantee," Carlo Alberto Notebooks, Collegio Carlo Alberto 272, Collegio Carlo Alberto.
    3. Salvatore Federico & Paul Gassiat, 2012. "Viscosity characterization of the value function of an investment-consumption problem in presence of illiquid assets," Papers 1211.1286, arXiv.org.
    4. Sergio Mayordomo & María Rodríguez-Moreno & Juan Ignacio Peña, 2012. "Portfolio Choice with Indivisible and Illiquid Housing Assets: The Case of Spain," Faculty Working Papers, School of Economics and Business Administration, University of Navarra 24/12, School of Economics and Business Administration, University of Navarra.
    5. Yuji Yamada, 2012. "Properties of Optimal Smooth Functions in Additive Models for Hedging Multivariate Derivatives," Asia-Pacific Financial Markets, Springer, Springer, vol. 19(2), pages 149-179, May.
    6. Salvatore Federico & Paul Gassiat & Fausto Gozzi, 2013. "Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation," Papers 1301.0280, arXiv.org.
    7. Martin Hoesli & Eva Liljeblom & Anders Loflund, 2014. "The Effect of Lock-Ups on the Suggested Real Estate Portfolio Weight," International Real Estate Review, Asian Real Estate Society, Asian Real Estate Society, vol. 17(1), pages 1-22.
    8. Michael Ludkovski & Qunying Shen, 2012. "European Option Pricing with Liquidity Shocks," Papers 1205.1007, arXiv.org.

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