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Real Estate Portfolio Management : Optimization under Risk Aversion

Author

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  • Fabrice Barthelemy
  • Jean-Luc Prigent

    () (THEMA, Universite de Cergy-Pontoise
    THEMA, Universite de Cergy-Pontoise)

Abstract

This paper deals with real estate portfolio optimization when investors are risk averse. In this framework, we determine several types of optimal times to sell a diversified real estate and analyze their properties. The optimization problem corresponds to the maximization of a concave utility function defined on the terminal value of the portfolio. We extend previous results (Baroni et al., 2007, and Barthélémy and Prigent, 2009), established for the quasi linear utility case, where investors are risk neutral. We consider four cases. In the first one, the investor knows the probability distribution of the real estate index. In the second one, the investor is perfectly informed about the real estate market dynamics. In the third case, the investor uses an intertemporal optimization approach which looks like an American option problem. Finally, the buy-and-hold strategy is considered. For these four cases we analyze numerically the solutions that we compare with those of the quasi linear case. We show that the introduction of risk aversion allows to better take account of the real estate market volatility. We also introduce the notion of compensating variation to better compare all these solutions.

Suggested Citation

  • Fabrice Barthelemy & Jean-Luc Prigent, 2011. "Real Estate Portfolio Management : Optimization under Risk Aversion," THEMA Working Papers 2011-12, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  • Handle: RePEc:ema:worpap:2011-12
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    File URL: http://thema.u-cergy.fr/IMG/documents/2011-12.pdf
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    References listed on IDEAS

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    1. Patric H. Hendershott & David C. Ling, 1984. "Prospective Changes in Tax Law and the Value of Depreciable Real Estate," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 12(3), pages 297-317.
    2. J. G. Kallberg & W. T. Ziemba, 1983. "Comparison of Alternative Utility Functions in Portfolio Selection Problems," Management Science, INFORMS, vol. 29(11), pages 1257-1276, November.
    3. Gau, George W & Wang, Ko, 1994. "The Tax-Induced Holding Periods of Real Estate Investors: Theory and Empirical Evidence," The Journal of Real Estate Finance and Economics, Springer, vol. 8(1), pages 71-85, January.
    4. Daniel McFadden, 2001. "Economic Choices," American Economic Review, American Economic Association, vol. 91(3), pages 351-378, June.
    5. Fabrice Barthélémy & Jean-Luc Prigent, 2009. "Optimal Time to Sell in Real Estate Portfolio Management," The Journal of Real Estate Finance and Economics, Springer, vol. 38(1), pages 59-87, January.
    6. André Palma & Jean-Luc Prigent, 2009. "Standardized versus customized portfolio: a compensating variation approach," Annals of Operations Research, Springer, vol. 165(1), pages 161-185, January.
    7. Baroni, Michel & Barthélémy, Fabrice & Mokrane, Mahdi, 2006. "Monte Carlo Simulations versus DCF in Real Estate Portfolio Valuation," ESSEC Working Papers DR 06002, ESSEC Research Center, ESSEC Business School.
    8. Shaun Bond & Soosung Hwang & Zhenguo Lin & Kerry Vandell, 2007. "Marketing Period Risk in a Portfolio Context: Theory and Empirical Estimates from the UK Commercial Real Estate Market," The Journal of Real Estate Finance and Economics, Springer, vol. 34(4), pages 447-461, May.
    9. de Palma, André & Prigent, Jean-Luc, 2008. "Utilitarianism and fairness in portfolio positioning," Journal of Banking & Finance, Elsevier, vol. 32(8), pages 1648-1660, August.
    10. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    11. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279-279.
    12. David Collett & Colin Lizieri & Charles Ward, 2003. "Timing and the Holding Periods of Institutional Real Estate," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 31(2), pages 205-222, June.
    13. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    14. Baroni, Michel & Barthélémy, Fabrice & Mokrane, Mahdi, 2007. "Optimal Holding Period for a Real Estate Portfolio," ESSEC Working Papers DR 07008, ESSEC Research Center, ESSEC Business School.
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    Cited by:

    1. Charles-Olivier Amédée-Manesme & Michel Baroni & Fabrice Barthélémy & Mahdi Mokrane, 2015. "The impact of lease structures on the optimal holding period for a commercial real estate portfolio," Journal of Property Investment & Finance, Emerald Group Publishing, vol. 33(2), pages 121-139, March.
    2. repec:hal:journl:hal-01070033 is not listed on IDEAS

    More about this item

    Keywords

    Real estate portfolio; Optimal holding period; Risk aversion; Real estate market volatility;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • R21 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Housing Demand

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