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Optimal Selling Time of a Stock under Capital Gains Taxes

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  • Christoph Kuhn
  • Budhi Arta Surya
  • Bjorn Ulbricht

Abstract

We investigate the impact of capital gains taxes on optimal investment decisions in a quite simple model. Namely, we consider a risk neutral investor who owns one risky stock from which she assumes that it has a lower expected return than the riskless bank account and determine the optimal stopping time at which she sells the stock to invest the proceeds in the bank account up to the maturity date. In the case of linear taxes and a positive riskless interest rate, the problem is nontrivial because at the selling time the investor has to realize book profits which triggers tax payments. We derive a boundary that is continuous and increasing in time and decreasing in the volatility of the stock such that the investor sells the stock at the first time its price is smaller or equal to this boundary.

Suggested Citation

  • Christoph Kuhn & Budhi Arta Surya & Bjorn Ulbricht, 2014. "Optimal Selling Time of a Stock under Capital Gains Taxes," Papers 1501.00026, arXiv.org.
    • Handle: RePEc:arx:papers:1501.00026
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    References listed on IDEAS

    as
    1. Christoph Kuhn & Bjorn Ulbricht, 2013. "Modeling capital gains taxes for trading strategies of infinite variation," Papers 1309.7368, arXiv.org, revised Jun 2015.
    2. Abel Cadenillas & Stanley R. Pliska, 1999. "Optimal trading of a security when there are taxes and transaction costs," Finance and Stochastics, Springer, vol. 3(2), pages 137-165.
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    4. Victor DeMiguel & Raman Uppal, 2005. "Portfolio Investment with the Exact Tax Basis via Nonlinear Programming," Management Science, INFORMS, vol. 51(2), pages 277-290, February.
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    7. Erik J. Baurdoux & Nan Chen & Budhi A. Surya & Kazutoshi Yamazaki, 2014. "Optimal double stopping of a Brownian bridge," Papers 1409.2226, arXiv.org, revised Dec 2014.
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