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Tax Basis And Nonlinearity In Cash Stream Valuation
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Tax Basis And Nonlinearity In Cash Stream Valuation

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  • Jaime Cuevas Dermody
  • R. Tyrrell Rockafellar

Abstract

The value of a future cash stream is often taken to be its net present value with respect to some term structure. This means that a linear formula is used in which each future payment is discounted by a factor deemed appropriate for the date on which the payment will be made. In a money market with taxes and shorting costs, however, there is no theoretical support for the existence of a universal term structure for this purpose. What is worse, reliance on linear formulas can be seriously inaccurate relative to true worth and can lead to paradoxes of disequilibrium. A consistent no‐arbitrage theory of valuation in such a market requires instead that taxed and untaxed investors be grouped in separate classes with different valuation operators. Such operators are linear to scale but nonlinear with respect to addition. Here it is established that although these valuation operators provide general bounds applicable across an entire class, individual investors within a tax class can have more special operators because of the influence of existing holdings. These customized valuation operators have the feature of not even being linear to scale. In consequence of this nonlinearity, investors from the same or different tax classes can undertake advantageous trades even when the market is in a no‐arbitrage state, but such trade opportunities are limited. Some degree of activity in financial markets can thereby be understood without appeal to differences in utility functions or temporary disequilibrium due to random disturbances.

Suggested Citation

  • Jaime Cuevas Dermody & R. Tyrrell Rockafellar, 1995. "Tax Basis And Nonlinearity In Cash Stream Valuation," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 97-119, April.
    • Handle: RePEc:bla:mathfi:v:5:y:1995:i:2:p:97-119
    DOI: 10.1111/j.1467-9965.1995.tb00104.x
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    Cited by:

    1. Teemu Pennanen, 2014. "Optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 18(4), pages 733-754, October.
    2. Jouini, Elyes & Koehl, Pierre-F. & Touzi, Nizar, 2000. "Optimal investment with taxes: an existence result," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 373-388, May.
    3. Stefan Jaschke & Richard Stehle & Stephan Wernicke, 2000. "Arbitrage und die Gültigkeit des Barwertprinzips im Markt für Bundeswertpapiere," Schmalenbach Journal of Business Research, Springer, vol. 52(5), pages 440-468, August.
    4. Elyès Jouini, 2003. "Market imperfections , equilibrium and arbitrage," Post-Print halshs-00167131, HAL.
    5. Stehle, Richard & Jaschke, Stefan R. & Wernicke, S., 1998. "Tax clientele effects in the German bond market," SFB 373 Discussion Papers 1998,11, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Teemu Pennanen, 2008. "Arbitrage and deflators in illiquid markets," Papers 0807.2526, arXiv.org, revised Apr 2009.
    7. Paolo Guasoni & Mikl'os R'asonyi, 2015. "Hedging, arbitrage and optimality with superlinear frictions," Papers 1506.05895, arXiv.org.
    8. repec:dau:papers:123456789/5600 is not listed on IDEAS
    9. Frank Milne & Edwin H. Neave, 2003. "A General Equilibrium Financial Asset Economy With Transaction Costs And Trading Constraints," Working Paper 1082, Economics Department, Queen's University.
    10. Napp, Clotilde, 2001. "Pricing issues with investment flows Applications to market models with frictions," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 383-408, June.
    11. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 57-83, January.
    12. Bjarne Jensen, 2009. "Valuation before and after tax in the discrete time, finite state no arbitrage model," Annals of Finance, Springer, vol. 5(1), pages 91-123, January.

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