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Toehold Purchase Problem: A comparative analysis of two strategies

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  • Iryna Banakh
  • Taras Banakh
  • Pavel Trisch
  • Myroslava Vovk

Abstract

Toehold purchase, defined here as purchase of one share in a firm by an investor preparing a tender offer to acquire majority of shares in it, reduces by one the number of shares this investor needs for majority. In the paper we construct mathematical models for the toehold and no-toehold strategies and compare the expected profits of the investor and the probabilities of takeover the firm in both strategies. It turns out that the expected profits of the investor in both strategies coincide. On the other hand, the probability of takeover the firm using the toehold strategy is considerably higher comparing to the no-toehold strategy. In the analysis of the models we apply the apparatus of incomplete Beta functions and some refined bounds for central binomial coefficients.

Suggested Citation

  • Iryna Banakh & Taras Banakh & Pavel Trisch & Myroslava Vovk, 2012. "Toehold Purchase Problem: A comparative analysis of two strategies," Papers 1204.2065, arXiv.org, revised Sep 2014.
    • Handle: RePEc:arx:papers:1204.2065
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    References listed on IDEAS

    as
    1. Singh, Rajdeep, 1998. "Takeover Bidding with Toeholds: The Case of the Owner's Curse," The Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 679-704.
    2. David Ettinger, 2009. "Takeover Contests, Toeholds and Deterrence," Scandinavian Journal of Economics, Wiley Blackwell, vol. 111(1), pages 103-124, March.
    3. Ravid, S. Abraham & Spiegel, Matthew, 1999. "Toehold strategies, takeover laws and rival bidders," Journal of Banking & Finance, Elsevier, vol. 23(8), pages 1219-1242, August.
    4. Bris, Arturo, 2002. "Toeholds, takeover premium, and the probability of being acquired," Journal of Corporate Finance, Elsevier, vol. 8(3), pages 227-253, July.
    5. Mark Bagnoli & Barton L. Lipman, 1996. "Stock Price Manipulation Through Takeover Bids," RAND Journal of Economics, The RAND Corporation, vol. 27(1), pages 124-147, Spring.
    6. Sris Chatterjee & Kose John & An Yan, 2012. "Takeovers and Divergence of Investor Opinion," The Review of Financial Studies, Society for Financial Studies, vol. 25(1), pages 227-277.
    7. repec:dau:papers:123456789/5449 is not listed on IDEAS
    8. Goldman, Eitan & Qian, Jun, 2005. "Optimal toeholds in takeover contests," Journal of Financial Economics, Elsevier, vol. 77(2), pages 321-346, August.
    9. Betton, Sandra & Eckbo, B. Espen & Thorburn, Karin S., 2009. "Merger negotiations and the toehold puzzle," Journal of Financial Economics, Elsevier, vol. 91(2), pages 158-178, February.
    10. Sanford J. Grossman & Oliver D. Hart, 1980. "Takeover Bids, the Free-Rider Problem, and the Theory of the Corporation," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 42-64, Spring.
    11. Mark Bagnoli, Barton L. Lipman, 1988. "Successful Takeovers without Exclusion," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 89-110.
    Full references (including those not matched with items on IDEAS)

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