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Risk aversion and block exercise of executive stock options

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  • Grasselli, Matheus
  • Henderson, Vicky
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    Abstract

    It is well documented that executives granted stock options tend to exercise early and in a few large transactions or 'blocks'. Standard risk-neutral valuation models cannot explain these patterns, and attempts to capture the exercise behavior of risk averse executives have been limited to the special case of one option. This paper solves for the optimal exercise behavior for a risk averse executive who is granted multiple stock options. We show that utility-based models do not predict block exercise behavior. Rather, the risk averse executive exercises stock options individually at a sequence of increasing price thresholds. When, in addition, the executive faces frictions such as costly exercise, he faces a trade-off between exercising little and often to maximize return, and exercising larger quantities on fewer occasions to minimize effort. This generates realistic block exercise behavior and yields new predictions. In particular, executives should begin by exercising large blocks of options, but the block sizes should become smaller over time. Our framework also allows us to study the impact of multiple exercise dates on estimates of the cost of options to the company. We find that assuming the executive can only exercise on a single occasion underestimates the cost of the options compared with allowing for optimal exercise behavior.

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    File URL: http://www.sciencedirect.com/science/article/B6V85-4SMNXP4-1/2/b46527c2d30c30f4667b328f9af31fed
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 33 (2009)
    Issue (Month): 1 (January)
    Pages: 109-127

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    Handle: RePEc:eee:dyncon:v:33:y:2009:i:1:p:109-127

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    Web page: http://www.elsevier.com/locate/jedc

    Related research

    Keywords: Stock options Compensation Risk aversion Incomplete markets Exercise Utility maximization;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. Core, John E. & Guay, Wayne R., 2001. "Stock option plans for non-executive employees," Journal of Financial Economics, Elsevier, vol. 61(2), pages 253-287, August.
    3. Henderson, Vicky & Hobson, David, 2007. "Horizon-unbiased utility functions," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1621-1641, November.
    4. Bettis, J. Carr & Bizjak, John M. & Lemmon, Michael L., 2005. "Exercise behavior, valuation, and the incentive effects of employee stock options," Journal of Financial Economics, Elsevier, vol. 76(2), pages 445-470, May.
    5. Hemmer, Thomas & Matsunaga, Steve & Shevlin, Terry, 1996. "The influence of risk diversification on the early exercise of employee stock options by executive officers," Journal of Accounting and Economics, Elsevier, vol. 21(1), pages 45-68, February.
    6. Eli Ofek & David Yermack, 2000. "Taking Stock: Equity-Based Compensation and the Evolution of Managerial Ownership," Journal of Finance, American Finance Association, vol. 55(3), pages 1367-1384, 06.
    7. Acharya, Viral V. & John, Kose & Sundaram, Rangarajan K., 2000. "On the optimality of resetting executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 65-101, July.
    8. 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.
    9. Aboody, David, 1996. "Market valuation of employee stock options," Journal of Accounting and Economics, Elsevier, vol. 22(1-3), pages 357-391, October.
    10. Bettis, J. Carr & Bizjak, John M. & Lemmon, Michael L., 2001. "Managerial Ownership, Incentive Contracting, and the Use of Zero-Cost Collars and Equity Swaps by Corporate Insiders," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 36(03), pages 345-370, September.
    11. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 835-72.
    12. Chip Heath & Steven Huddart & Mark Lang, 1999. "Psychological Factors And Stock Option Exercise," The Quarterly Journal of Economics, MIT Press, vol. 114(2), pages 601-627, May.
    13. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    14. Philip H. Dybvig & Mark Loewenstein, 2003. "Employee Reload Options: Pricing, Hedging, and Optimal Exercise," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 145-171.
    15. Huddart, Steven & Lang, Mark, 1996. "Employee stock option exercises an empirical analysis," Journal of Accounting and Economics, Elsevier, vol. 21(1), pages 5-43, February.
    16. Sircar, Ronnie & Xiong, Wei, 2007. "A general framework for evaluating executive stock options," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2317-2349, July.
    17. Murphy, Kevin J., 1999. "Executive compensation," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 38, pages 2485-2563 Elsevier.
    18. Huddart, Steven, 1994. "Employee stock options," Journal of Accounting and Economics, Elsevier, vol. 18(2), pages 207-231, September.
    19. M. R. Grasselli, 2005. "Nonlinearity, correlation and the valuation of employee stock options," Papers math/0511234, arXiv.org.
    20. Vicky Henderson, 2005. "The impact of the market portfolio on the valuation, incentives and optimality of executive stock options," Quantitative Finance, Taylor & Francis Journals, vol. 5(1), pages 35-47.
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Optimal 10b5-1 Monetization
      by quantivity in Quantivity on 2011-09-27 07:02:52
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    Cited by:
    1. Eikseth, Hans Marius & Lindset, Snorre, 2011. "Backdating executive stock options--An ex ante valuation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1731-1743, October.
    2. Bahaji, Hamza, 2012. "Cumulative Prospect Theory, employee exercise behaviour and stock options cost assessment," Economics Papers from University Paris Dauphine 123456789/9550, Paris Dauphine University.
    3. 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.
    4. Bahaji, Hamza, 2014. "Are Employee Stock Option Exercise Decisions Better Explained through the Prospect Theory?," Economics Papers from University Paris Dauphine 123456789/13098, Paris Dauphine University.
    5. Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856, arXiv.org, revised May 2014.

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