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Toehold Purchase Problem: A comparative analysis of two strategies

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Listed:
  • 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

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    1. 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.
    2. Bris, Arturo, 2002. "Toeholds, takeover premium, and the probability of being acquired," Journal of Corporate Finance, Elsevier, vol. 8(3), pages 227-253, July.
    3. David Ettinger, 2009. "Takeover Contests, Toeholds and Deterrence," Scandinavian Journal of Economics, Wiley Blackwell, vol. 111(1), pages 103-124, March.
    4. Singh, Rajdeep, 1998. "Takeover Bidding with Toeholds: The Case of the Owner's Curse," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 679-704.
    5. Goldman, Eitan & Qian, Jun, 2005. "Optimal toeholds in takeover contests," Journal of Financial Economics, Elsevier, vol. 77(2), pages 321-346, August.
    6. Sris Chatterjee & Kose John & An Yan, 2012. "Takeovers and Divergence of Investor Opinion," 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. Mark Bagnoli, Barton L. Lipman, 1988. "Successful Takeovers without Exclusion," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 89-110.
    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.
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