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Risk Aversion, Indivisible Timing Options, and Gambling

Author

Listed:
  • Vicky Henderson

    (Oxford-Man Institute, University of Oxford, Oxford OX2 6ED, United Kingdom)

  • David Hobson

    (Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom)

Abstract

In this paper we model the behavior of a risk-averse agent who seeks to maximize expected utility and who has an indivisible asset and a timing option over when to sell this asset. Our main contribution is to show that, contrary to intuition, optimal behavior for such a risk-averse agent can include risk-increasing gambles. For example, a manager with a choice over when to disinvest from a project, a private homeowner with a property to sell, or an employee with a grant of American-style stock options may be better off taking positions in other assets with zero Sharpe ratio that are uncorrelated with the underlying project, house, or stock price risk. The results have wider implications for the modeling and interpretation of portfolio optimization problems involving American-style timing decisions.

Suggested Citation

  • Vicky Henderson & David Hobson, 2013. "Risk Aversion, Indivisible Timing Options, and Gambling," Operations Research, INFORMS, vol. 61(1), pages 126-137, February.
  • Handle: RePEc:inm:oropre:v:61:y:2013:i:1:p:126-137
    DOI: 10.1287/opre.1120.1131
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    References listed on IDEAS

    as
    1. Decamps, Jean-Paul & Mariotti, Thomas, 2004. "Investment timing and learning externalities," Journal of Economic Theory, Elsevier, vol. 118(1), pages 80-102, September.
    2. Jennifer N. Carpenter, 2000. "Does Option Compensation Increase Managerial Risk Appetite?," Journal of Finance, American Finance Association, vol. 55(5), pages 2311-2331, October.
    3. Pindyck, Robert S, 1982. "Adjustment Costs, Uncertainty, and the Behavior of the Firm," American Economic Review, American Economic Association, vol. 72(3), pages 415-427, June.
    4. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 835-872.
    5. Andrew Postlewaite & Larry Samuelson & Dan Silverman, 2008. "Consumption Commitments and Employment Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(2), pages 559-578.
    6. Jensen, Michael C. & Meckling, William H., 1976. "Theory of the firm: Managerial behavior, agency costs and ownership structure," Journal of Financial Economics, Elsevier, vol. 3(4), pages 305-360, October.
    7. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    8. James E. Smith & Robert F. Nau, 1995. "Valuing Risky Projects: Option Pricing Theory and Decision Analysis," Management Science, INFORMS, vol. 41(5), pages 795-816, May.
    9. Jonathan E. Ingersoll, Jr., 2006. "The Subjective and Objective Evaluation of Incentive Stock Options," The Journal of Business, University of Chicago Press, vol. 79(2), pages 453-488, March.
    10. Kahl, Matthias & Liu, Jun & Longstaff, Francis A., 2003. "Paper millionaires: how valuable is stock to a stockholder who is restricted from selling it?," Journal of Financial Economics, Elsevier, vol. 67(3), pages 385-410, March.
    11. Suleyman Basak & Anna Pavlova & Alexander Shapiro, 2007. "Optimal Asset Allocation and Risk Shifting in Money Management," The Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1583-1621, 2007 21.
    12. Hugonnier, Julien & Morellec, Erwan, 2007. "Corporate control and real investment in incomplete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1781-1800, May.
    13. Dybvig, Philip H & Lippman, Steven A, 1983. "An Alternative Characterization of Decreasing Absolute Risk Aversion," Econometrica, Econometric Society, vol. 51(1), pages 223-224, January.
    14. Carpenter, Jennifer N. & Stanton, Richard & Wallace, Nancy, 2010. "Optimal exercise of executive stock options and implications for firm cost," Journal of Financial Economics, Elsevier, vol. 98(2), pages 315-337, November.
    15. Guo, Xin & Miao, Jianjun & Morellec, Erwan, 2005. "Irreversible investment with regime shifts," Journal of Economic Theory, Elsevier, vol. 122(1), pages 37-59, May.
    16. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    17. Jonathan Evans & Vicky Henderson & David Hobson, 2008. "Optimal Timing For An Indivisible Asset Sale," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 545-567, October.
    18. repec:bla:jfinan:v:53:y:1998:i:4:p:1213-1243 is not listed on IDEAS
    19. James E. Smith & Kevin F. McCardle, 1998. "Valuing Oil Properties: Integrating Option Pricing and Decision Analysis Approaches," Operations Research, INFORMS, vol. 46(2), pages 198-217, April.
    20. Kevin J. Murphy & Brian J. Hall, 2000. "Optimal Exercise Prices for Executive Stock Options," American Economic Review, American Economic Association, vol. 90(2), pages 209-214, May.
    21. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    22. Ng Yew Kwang, 1965. "Why do People Buy Lottery Tickets? Choices Involving Risk and the Indivisibility of Expenditure," Journal of Political Economy, University of Chicago Press, vol. 73(5), pages 530-530.
    23. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    24. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    25. Grasselli, Matheus & Henderson, Vicky, 2009. "Risk aversion and block exercise of executive stock options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 109-127, January.
    26. repec:bla:jfinan:v:59:y:2004:i:1:p:207-225 is not listed on IDEAS
    27. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    28. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    29. Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128, January.
    30. Hayne E. Leland., 1998. "Agency Costs, Risk Management, and Capital Structure," Research Program in Finance Working Papers RPF-278, University of California at Berkeley.
    31. Hartman, Richard, 1972. "The effects of price and cost uncertainty on investment," Journal of Economic Theory, Elsevier, vol. 5(2), pages 258-266, October.
    32. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2005. "Investment Timing Under Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 472-500, May.
    33. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    34. Abel, Andrew B, 1983. "Optimal Investment under Uncertainty," American Economic Review, American Economic Association, vol. 73(1), pages 228-233, March.
    35. H. Dharma Kwon, 2010. "Invest or Exit? Optimal Decisions in the Face of a Declining Profit Stream," Operations Research, INFORMS, vol. 58(3), pages 638-649, June.
    36. Jianjun Miao & Neng Wang, 2004. "Investment, Hedging, and Consumption Smoothing," Finance 0407014, University Library of Munich, Germany.
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    2. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.
    3. David Hobson & Yeqi Zhu, 2014. "Optimal consumption and sale strategies for a risk averse agent," Papers 1409.3394, arXiv.org.
    4. Vasquez, Markus, 2017. "Utility of wealth with many indivisibilities," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 20-27.
    5. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    6. Choi, Kyoung Jin & Kwak, Minsuk & Shim, Gyoocheol, 2017. "Time preference and real investment," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 18-33.
    7. Jakub Trybu{l}a, 2014. "Merton problem with one additional indivisible asset," Papers 1403.3223, arXiv.org.
    8. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    9. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    10. Tsionas, Mike G. & Mamatzakis, Emmanuel & Ongena, Steven, 2020. "Does risk aversion affect bank output loss? The case of the Eurozone," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1127-1145.

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